Dark Matter The Case of Sterile Neutrino

合集下载

暗物质成品

暗物质成品

What is dark matter?
About 65 years ago, the first time that evidence of the existence of dark matter. At that time, Fulizizha Popovich found a large cluster of galaxies in the galaxy has a very high velocity, unless the quality of galaxy clusters is based on the number of calculations in which stars are more than 100 times the value, or cluster of galaxies can not bound lives of these galaxies. After decades of observation and analysis confirmed this. Although the nature of dark matter is still unknown, but by 80 years, accounting for about 20% of the energy density of dark matter to be widely accepted.
What is dark matter?
now we know that dark matter has become an important part of the universe. The total mass of dark matter is ordinary matter, 6.3 times the energy density in the universe, accounting for 1 / 4, but also important is that dark matter dominated the formation of cosmic structures. Now the nature of dark matter remains a mystery, but assuming it is a weak interaction of subatomic particles, then the resulting large-scale structure of the universe is consistent with the observations. Recently, however, the structure of galaxies and galaxy subanalysis shows that this assumption and the difference between observations, which at the same time provide a variety of possible dark matter theory was useless. Small-scale structure through the density, distribution, evolution and its environment studies can distinguish between these potential dark matter model for the nature of dark matter to bring a new dawn.

犯罪心理1-5季名言

犯罪心理1-5季名言

Season 5◎Episode 1: Nameless, Faceless(2009.09.23)●a weak man has doubts before a decision.A strong man has them afterwards.——Karl krauss 【卡尔·克劳斯(上世纪上半叶最杰出德语作家和语言大师之一,1874 - 1936):弱者在决策前迟疑,强者则反之。

】(Rossi)(本集片尾没有出现名言)◎Episode 2: Haunted(2009.09.30)●one need not be a chamber to be haunted.one need not be a house.The brain has corridors surpassing material place.——Emily dickinson【艾米莉·狄金森(美国诗人,1830 - 1886 ):无需亲临幽室便能体味精神折磨,无需亲临暗宅,思想能带你穿越置身其中。

】(Hotch)●there is no witness so dreadful, no accuser so terri ble,as the conscience that dwells in the heart of every man.——Polybius【波里比阿(古希腊历史学家,约公元前204 - 122年):没有可怕至极的证人,没有恐怖之至的原告,因为良心存在于每个人心中。

】(Hotch)◎Episode 3: Reckoner(2009.10.07)●Justice without force is powerless.Force without justice is tyrannical.——Blaise Pascal【帕斯卡(法国哲学家,1623 - 1662):正义缺少武力是无能,武力缺少正义是暴政。

Investigating the Nature of Dark Matter

Investigating the Nature of Dark Matter

Investigating the Nature of DarkMatterThe phrase “dark matter” has become a buzzword in modern astrophysics as well as popular culture, and yet we still know very little about what dark matter really is. It is a mysterious substance that makes up 27% of the universe and that cannot be observed directly, but can only be inferred from the gravitational effects it has on visible matter. Therefore, dark matter is a topic of intense research and debate in the scientific community. In this article, we will explore the key aspects of dark matter and the different ways scientists are working to uncover its nature.What is Dark Matter?As mentioned, dark matter is a substance that does not emit, absorb or reflect light, hence its name. It does not interact strongly with electromagnetic forces, but it does with gravity, which is why its presence can be inferred from the gravitational effects it has on visible matter. One of the most well-known examples of this is the rotation curve of spiral galaxies. According to the laws of classical mechanics, the velocity of stars and gas in a galaxy should decrease as one moves away from the center, as the gravitational attraction of the visible matter decreases. However, observations have shown that the velocity remains constant or even increases, suggesting that there is an invisible mass that is causing this anomaly. This invisible mass is the dark matter.Another piece of evidence for the existence of dark matter is the distribution of matter in the universe as revealed by the cosmic microwave background radiation, which is the afterglow of the Big Bang. The pattern of temperature fluctuations in this radiation shows that the matter in the universe is not distributed evenly, but is rather clumped up in large structures such as galaxies and clusters of galaxies. However, this clumping up cannot be explained solely by the gravitational influence of visible matter; there must be an additional source of gravity, i.e. dark matter, to explain the observed distribution.Moreover, measurements of the large-scale structure of the universe, such as the distribution of galaxies and galaxy clusters, also point to the existence of dark matter.What is Dark Matter Made of?Despite its importance in shaping the structure of the universe, the identity of dark matter remains unknown. There are several hypotheses about what dark matter might be made of, but none of them has been conclusively proven yet. One popular hypothesis is that dark matter is composed of weakly interacting massive particles (WIMPs), which are hypothetical particles that would interact with normal matter only through the weak nuclear force and gravity. The idea is that WIMPs were produced in the early universe when it was hot and dense, and have been moving around freely ever since. If they collide with normal matter, they would transfer some of their energy and momentum, producing detectable signals. In fact, several experiments have been designed to detect WIMP interactions, such as the Large Underground Xenon (LUX) experiment and the Super Cryogenic Dark Matter Search (SuperCDMS).Another hypothesis is that dark matter is made of axions, which are theoretical particles that were originally proposed to explain a different problem in physics, the strong CP problem. The idea is that axions would be very light and weakly interacting, making them difficult to detect, but would still affect the motion of galaxies and other cosmic structures. The Axion Dark Matter eXperiment (ADMX) is currently searching for evidence of axions in a laboratory at the University of Washington.A third hypothesis is that dark matter is composed of primordial black holes, which are black holes that were formed by the collapse of a density fluctuation in the early universe. The idea is that these black holes could have a mass range that would make them more likely to be dark matter, and that their interactions with normal matter could produce observable effects. However, this hypothesis is less favored by most researchers, as the formation and stability of such black holes would require very specific conditions.ConclusionDespite decades of research, the nature of dark matter remains one of the most intriguing and elusive topics in astrophysics. It remains a theoretical construct that cannot be directly observed, but its effects on the motion and structure of the cosmos are undeniable. Researchers are continuing to study dark matter using a variety of tools and techniques, from telescopes that measure gravitational lensing to underground experiments that look for WIMP interactions. The hope is that someday we will finally be able to unravel the mystery of what dark matter is made of, and in doing so, gain a better understanding of the universe and our place in it.。

Evolution of the Fine Structure Constant Driven by Dark Matter and the Cosmological Constan

Evolution of the Fine Structure Constant Driven by Dark Matter and the Cosmological Constan
2
Physics Department, McGill University, 3600 University St, Montreal,Quebec H3A 2T8, Canada
D´ epartement de Physique, Universit´ e du Qu´ ebec ` a Montr´ eal C.P. 8888, Succ. Centre-Ville, Montr´ eal, Qu´ ebec, Canada, H3C 3P8
1
Introduction
Speculations that fundamental constants may vary in time and/or space go back to the original idea of Dirac [1]. Despite the reputable origin, this idea has not received much attention during the last fifty years for the two following reasons. First, there exist various sensitive experimental checks that coupling constants do not change (See, e.g. [2]). Second, for a long time there has not been any credible theoretical framework which would predict such changes. Our theoretical mindset, however, has changed since the advent of the string theory. One of the most interesting low-energy features of string theory is the possible presence of a massless scalar particle, the dilaton, whose vacuum expectation value defines the size of the effective gauge coupling constants. A change in the dilaton v.e.v. induces a change in the fine structure constant as well as the other gauge and Yukawa couplings. The stabilization of the dilaton v.e.v., which usually renders the dilaton massive, represents one of the fundamental challenges to be addressed before string theory can aspire to describe the observable world. Besides the dilaton, string theory often predicts the presence of other massless or nearly massless moduli fields, whose existence may influence particle physics and cosmology and may also change the effective values of the coupling constants as well. Independent of the framework of string theory, Bekenstein [3] formulated a dynamical model of “changing α”. The model consists of a massless scalar field which has a linear −1 φFµν F µν , where M∗ is an associated coupling to the F 2 term of the U (1) gauge field, M∗ mass scale and thought to be of order the Planck scale. A change in the background value of φ, can be interpreted as a change of the effective coupling constant. Bekenstein noticed that F 2 has a non-vanishing matrix element over protons and neutrons, of order (10−3 − 10−2 )mN . This matrix element acts as a source in the φ equation of motion and naturally leads to the cosmological evolution of the φ field driven by the baryon energy density. Thus, the change in φ translates into a change in α on a characteristic time scale comparable to the lifetime of the Universe or larger. However, the presence of a massless scalar field φ in the theory leads to the existence of an additional attractive force which does not respect Einstein’s weak universality principle. The extremely accurate checks of the latter [4] lead to a firm lower limit on M∗ , M∗ /MPl > 103 that confines possible changes of α to the range ∆α < 10−10 − 10−9 for 0 < z < 5 [3, 5]. This range is five orders of magnitude tighter than the change ∆α/α ≃ 10−5 indicated in the observations of quasar absorption spectra at z = 0.5 − 3.5 and recently reported by Webb et al. [6]. Given the potential fundamental importance of such a result, one should remain cautious until this result is independently verified. Nevertheless, leaving aside the issue regarding the reliability of the conclusions reached by Webb et al. [6], it is interesting to explore the possibility of constructing a dynamical model, including 1

Accomodating Solar and Atmospheric Neutrino Deficits, Hot Dark Matter, and a Double Beta De

Accomodating Solar and Atmospheric Neutrino Deficits, Hot Dark Matter, and a Double Beta De
UCSB–HEP–94-03 UMD-PP-94-90 February,1994 Accommodating solar and atmospheric neutrino deficits, hot dark matter, and a double beta decay signal
arXiv:hep-ph/9402231v2 9 Feb 1994
−6 2 2 −3 a)Small − angle MSW, ∆m2 ei ∼ 6 × 10 eV , sin 2θei ∼ 7 × 10 ,
2
−6 2 2 b)Large − angle MSW, ∆m2 ei ∼ 9 × 10 eV , sin 2θei ∼ 0.6, −10 eV2 , sin2 2θ ∼ 0.9. c)Vacuum oscillation, ∆m2 ei ei ∼ 10
(1)
Of these, (a) is favored over (b) by the fits to the solar neutrino data [9], and both (b) and (c) are disfavored by information from the neutrino burst from supernova 1987A [11]. B. Atmospheric Neutrino Deficit The second set of experiments indicating non-zero neutrino masses and mixings has to do with atmospheric νµ ’s and νe ’s arising from the decays of π ’s and K ’s and the subsequent decays of secondary muons produced in the final states of the π and K decays. In the underground experiments the νµ and ν ¯µ produce muons and the νe and ν ¯e lead to e± . Observations of µ± and e± indicate a far lower value for νµ and ν ¯µ than suggested by na¨ ıve counting arguments which imply that N (νµ + ν ¯µ ) = 2N (νe + ν ¯e ). More precisely, the ratio of µ events to e-events can be normalized to the ratio of calculated fluxes to reduce flux uncertainties, giving [3] R(µ/e) = 0.60 ± 0.07 ± 0.05 (Kamiokande), = 0.54 ± 0.05 ± 0.12 (IMB), = 0.69 ± 0.19 ± 0.09 (Soudan II). Combining these results with observations of upward going muons by Kamiokande [3], IMB [3], and Baksan [12] and the negative Fr´ ejus [13] and NUSEX [14] results leads to the conclusion [15] that neutrino oscillations can give an explanation of these results, provided

The mysteries of the universe Dark matter

The mysteries of the universe Dark matter

The mysteries of the universe DarkmatterDark matter is one of the most enigmatic and perplexing concepts in the field of astrophysics and cosmology. It is a substance that makes up a significantportion of the universe, yet it remains largely elusive and mysterious to scientists. The existence of dark matter was first proposed in the 1930s by Swiss astronomer Fritz Zwicky, who observed that the visible matter in the Coma galaxy cluster could not account for the gravitational forces that were holding thecluster together. This led him to hypothesize the presence of unseen "dark" matter that was responsible for the gravitational effects. Since then, numerous observations and experiments have provided compelling evidence for the existenceof dark matter, but its true nature continues to elude researchers. One of the most compelling lines of evidence for dark matter comes from the study of the rotation curves of galaxies. When astronomers measure the velocities of stars and gas in a galaxy as a function of their distance from the galactic center, theyfind that the velocities do not decrease as expected with increasing distance. Instead, the velocities remain constant or even increase, indicating the presence of additional unseen mass that is providing the gravitational pull to keep thestars and gas in their orbits. This discrepancy between the observed motion of galactic objects and the visible matter in galaxies has led scientists to conclude that there must be a significant amount of dark matter present in galaxies, outweighing the visible matter by a factor of about six to one. Another piece of evidence for dark matter comes from the study of the large-scale structure of the universe. Observations of the cosmic microwave background radiation, the afterglow of the Big Bang, have revealed subtle patterns in the distribution of matter onthe largest scales. These patterns can be explained by the presence of dark matter, which exerts gravitational forces to shape the distribution of galaxies and galaxy clusters in the universe. Additionally, the gravitational lensing of distant galaxies by intervening mass concentrations, such as galaxy clusters, provides further evidence for the presence of dark matter. The bending of light from these distant galaxies can only be explained by the gravitational influence of unseenmass, which is consistent with the properties of dark matter. Despite the overwhelming evidence for the existence of dark matter, its true nature remains a profound mystery. Dark matter does not emit, absorb, or reflect light, making it invisible to telescopes and other instruments that rely on electromagnetic radiation for detection. This has made it incredibly challenging for scientists to directly observe and study dark matter, leading to a wide range of theoretical and experimental efforts to uncover its properties. One of the leading candidates for the identity of dark matter is a type of particle that interacts only weakly with ordinary matter and electromagnetic forces, known as a weakly interacting massive particle (WIMP). WIMPs are a theoretical class of particles that arise in extensions of the standard model of particle physics, and they are thought to have been produced in the early universe in sufficient quantities to account for the observed abundance of dark matter today. Numerous experiments around the world are dedicated to detecting WIMPs through their rare interactions with ordinary matter, such as through the recoil of atomic nuclei in underground detectors or the production of secondary particles in particle accelerators. Another potential explanation for dark matter is the existence of primordial black holes, which are hypothesized to have formed in the early universe from the gravitational collapse of overdense regions. These black holes would not emit significant amounts oflight or other radiation, making them difficult to detect directly. However, their gravitational influence on surrounding matter could betray their presence, and ongoing observational campaigns are searching for the signatures of primordial black holes in the universe. In addition to these particle-based and astrophysical explanations, some scientists have proposed modifications to the laws of gravity as an alternative to dark matter. These modified gravity theories seek to explain the observed gravitational effects in galaxies and galaxy clusters without invoking the presence of additional unseen mass. While these theories have had some success in reproducing certain observational data, they have yet to provide a comprehensive and consistent explanation for the full range of evidence for dark matter. The search for dark matter continues to be a vibrant and active area of research in astrophysics and particle physics. New generations of experiments are pushing the boundaries of sensitivity and precision in the huntfor dark matter particles, while astronomers are mapping the distribution ofmatter in the universe with ever-increasing detail. The discovery of dark matter would represent a profound breakthrough in our understanding of the fundamental constituents of the universe and the forces that govern its evolution. It would also have far-reaching implications for our understanding of the cosmos, from the formation of galaxies and galaxy clusters to the ultimate fate of the universe itself. The quest to unravel the mysteries of dark matter is not just ascientific endeavor, but also a deeply human one. It speaks to our innatecuriosity about the nature of the universe and our place within it. Therealization that the majority of the matter in the universe is invisible and fundamentally different from the matter we interact with on a daily basis is both humbling and awe-inspiring. It challenges our preconceived notions of the cosmos and forces us to confront the limits of our current understanding. The search for dark matter is a testament to the human spirit of exploration and discovery, as we strive to push the boundaries of knowledge and unlock the secrets of the universe. In conclusion, dark matter remains one of the most captivating and tantalizing mysteries in modern science. Its existence is supported by a wealth of observational evidence, yet its true nature continues to elude us. Whether it is composed of exotic particles, primordial black holes, or a modification of thelaws of gravity, the discovery of dark matter would revolutionize our understanding of the cosmos and our place within it. The ongoing quest to uncover the secrets of dark matter is a testament to the enduring human spirit ofcuriosity and exploration, as we continue to push the boundaries of knowledge and strive to unlock the mysteries of the universe.。

The Science of Dark Matter and Its Discovery

The Science of Dark Matter and Its Discovery

The Science of Dark Matter and ItsDiscoveryIntroductionDark matter is an elusive substance that makes up about 27% of the universe. It neither emits nor absorbs light, making it invisible to telescopes. Scientists have been studying dark matter for decades, and its discovery is considered one of the greatest mysteries of modern physics. In this article, we will delve into the science of dark matter, its properties, and the research that has led to its discovery.What is Dark Matter?Dark matter is a hypothetical substance that does not interact with light or any other form of electromagnetic radiation. It is invisible to telescopes, but its presence is inferred from its gravitational effects on objects that emit light. Dark matter is thought to be five times more abundant than visible matter, which is what stars, planets, and galaxies are made of.The Properties of Dark MatterAlthough scientists have yet to observe dark matter directly, they have been able to infer its properties from its gravitational effects. Dark matter is thought to be cold, meaning that its particles move relatively slowly. It is also believed to be non-interacting, meaning that it does not interact with other particles except through the force of gravity.Dark matter is widely thought to be made up of weakly interacting massive particles (WIMPs), which are particles that interact with each other only through the weak force and gravity. Other proposed candidates for dark matter particles include axions and sterile neutrinos, but these have not been observed directly.The Search for Dark MatterThe search for dark matter has been ongoing for several decades. One of the most promising methods for detecting dark matter involves looking for the energetic particles that result from the annihilation of dark matter particles. This method is called indirect detection and involves searching for gamma rays, neutrinos, or cosmic rays that are produced by the decay or annihilation of dark matter particles.Another way to detect dark matter is through the direct detection method, which involves looking for the recoil of atomic nuclei in a detector after they have been struck by dark matter particles. This method requires a sophisticated detector that can detect even the slightest signal. Several experiments are currently underway to detect dark matter particles using these methods.Discovery of Dark MatterThe discovery of dark matter can be traced back to the 1930s when Swiss astronomer Fritz Zwicky observed that the visible matter in the Coma cluster of galaxies was not enough to hold the cluster together. He hypothesized the presence of invisible matter that was holding the cluster together, which he called dark matter.Over the years, other scientists have provided evidence for the existence of dark matter. In the 1970s, Vera Rubin and Kent Ford studied the rotation curves of galaxies and found that the observed mass could not account for the observed rotation speeds. They concluded that there must be more mass in the form of dark matter that was holding the galaxies together.More recently, the European Space Agency’s Planck satellite produced a detailed map of the cosmic microwave background radiation, which is thought to be leftover radiation from the Big Bang. The map provided strong evidence for the existence of dark matter and its abundance in the universe.ConclusionThe discovery of dark matter is one of the most exciting and challenging areas of modern physics. Scientists continue to search for dark matter using a variety of methods, including indirect and direct detection. Although dark matter has yet to be observeddirectly, its presence and properties can be inferred from its gravitational effects on visible matter. As we continue to unravel the mysteries of dark matter, we are sure to gain new insights and a deeper understanding of the universe we inhabit.。

The-Dark-Triad-of-personality-and-unethical-behavior-at-different-times-of-day

The-Dark-Triad-of-personality-and-unethical-behavior-at-different-times-of-day

The Dark Triad of personality and unethical behavior at different times of dayKarolin Roeser a ,Victoria E.McGregor a ,Sophia Stegmaier a ,Johanna Mathew a ,Andrea Kübler a ,Adrian Meule b ,⁎a Institute of Psychology,University of Würzburg,Marcusstr.9-11,D-97070Würzburg,GermanybDepartment of Psychology and Center for Cognitive Neuroscience,University of Salzburg,Hellbrunner Str.34,A-5020Salzburg,Austriaa b s t r a c ta r t i c l e i n f o Article history:Received 10August 2015Accepted 1September 2015Available online 10September 2015Keywords:Dark Triad Narcissism PsychopathyMachiavellianism MoralityMorning Morality EffectThe Dark Triad of personality –narcissism,Machiavellianism,and psychopathy –is characterized by callous ma-nipulation and social exploitation.Thus,dark personalities should be more prone to unethical behavior.Unethical behavior has been shown to vary during the course of the day with individuals displaying lower morality in the evening (Morning Morality Effect,MME).Hence,the present study investigated the association between the Dark Triad and unethical behavior as a function of time of day in an experimental design.Participants (N =195)com-pleted the study either in the morning or in the evening.In one task,participants had the choice to cheat on a fictitious partner for monetary bene fit at the partner's expense.In a second task,they had the opportunity to lie about their performance for personal gain.Machiavellianism scores positively predicted unethical behavior in the first task.In the second task,psychopathy scores positively predicted lying.Neither could the MME be rep-licated,nor did time of day moderate the in fluence of the Dark Triad on unethical behavior.Thus,the present study indicates that the dark traits are differentially related to aspects of unethical behavior,such that Machiavel-lians display a preference for complex deception,while psychopaths engage in impulsive cheating.©2015Elsevier Ltd.All rights reserved.1.1.IntroductionThe Dark Triad of personality (Paulhus &Williams,2002)comprises three socially aversive and malevolent personality traits,namely narcis-sism,Machiavellianism,and psychopathy.Narcissism is characterized by grandiosity,entitlement,dominance,and superiority (Raskin &Hall,1979),Machiavellianism can be described as a manipulative per-sonality (Paulhus &Williams,2002),and individuals with psychopathic traits have high sensation seeking and impulsivity along with callous af-fect and low empathy (Hare,1985).Although offensive,the Dark Triad traits do not represent pathological concepts per se.Instead,individuals with dark personalities may very well be within the normal range of functioning (Furnham,Richards,&Paulhus,2013).The three traits have distinct theoretical origins.Narcissism and psy-chopathy were originally proposed to represent mental disorders,which found their way into mainstream personality research by the development of the Narcissistic Personality Inventory (NPI,Raskin &Hall,1979)and the Self-Report Psychopathy (SRP)scale (Hare,1985),respectively.The concept of Machiavellianism has a philosophical background as it is named for Niccolo Machiavelli,a politician and phi-losopher in the Florentine Republic around 1500.Machiavellianism emerged as a personality trait through the work of Christie and Geis(1970),who delineated the Mach-IV as a measure of Machiavellianism.Despite their different etiologies,these personalities share common features,for example disagreeableness (Paulhus &Williams,2002),ma-nipulation and callousness (Jones &Figueredo,2013),and social exploi-tation (Jonason,Li,&Teicher,2010).However,they are not equivalent,but rather “overlapping but distinct constructs ”(Paulhus &Williams,2002,p.556).Since the original publication of the concept in 2002,the Dark Triad has gained much scienti fic attention.Among various outcome mea-sures,for example workplace behavior (O'Boyle,Forsyth,Banks,&McDaniel,2012)or mating strategies (Jonason,Li,Webster,&Schmitt,2009),unethical behavior has been related to the dark traits:Psychopa-thy and Machiavellianism predicted exam copying and plagiarism,respectively (Nathanson,Paulhus,&Williams,2006;Williams,Nathanson,&Paulhus,2010).Baughman,Jonason,Lyons,and Vernon (2014)found that the Dark Triad,especially Machiavellianism and psy-chopathy,was associated with lying in an academic context,but also with dishonesty toward mates.Jonason,Lyons,Baughman,and Vernon (2014)reported that dark personalities make use of various inter-and intra-sexual deception tactics,suggesting that the Dark Triad traits re flect cheating strategies.Kouchaki and Smith (2014)investigated cheating as a form of un-ethical behavior,but from a very different perspective:In four indepen-dent experiments,it was demonstrated that participants engaged in more unethical behavior in the afternoon compared to the morningPersonality and Individual Differences 88(2016)73–77⁎Corresponding author.E-mail address:adrian.meule@sbg.ac.at (A.Meule)./10.1016/j.paid.2015.09.0020191-8869/©2015Elsevier Ltd.All rightsreserved.Contents lists available at ScienceDirectPersonality and Individual Differencesj o u r n a l h o me p a g e :ww w.e l s e v i e r.c o m /l o c a t e /p a i dhours.To explain this so-called Morning Morality Effect(MME),the au-thors referred to the strength model of self-regulation.According to this model,the capacity to exert self-control relies on a limited resource that depletes when demanded(Baumeister,Bratslavsky,Muraven,&Tice, 1998;Muraven&Baumeister,2000).Self-control comprises the ability to resist temptations and the willpower to act according to moral stan-dards.Indeed,it has been shown that the depletion of self-regulatory re-sources negatively affects ethical behavior(Gino,Schweitzer,Mead,& Ariely,2011;Mead,Baumeister,Gino,Schweitzer,&Ariely,2009). Given that many situations in daily life require self-control(Hofmann, Baumeister,Forster,&Vohs,2012),self-control resources might dimin-ish gradually throughout the day,resulting in a greater likelihood of self-regulatory failures,including lying or cheating,in the afternoon or evening as compared to the morning hours.In one of their experiments,Kouchaki and Smith(2014)found that lower moral awareness in the afternoon me-diated the effect of time of day on cheating.Moreover,they report that moral disengagement moderated the MME such that the MME was espe-cially evident in those with a low propensity to morally disengage.As previous studies have demonstrated an influence of the Dark Triad and time of day on unethical behavior,the present study aimed at bringing these aspects together.Participants completed the study ei-ther in the morning or in the evening,which included a measure of Dark Triad personality traits and two tasks,in which they could cheat or lie.In contrast to previous studies,we decided to operationalize cheating and lying experimentally instead of using self-report questionnaires.It was expected that(1)individuals would be more likely to cheat or lie in the evening than in the morning,thus replicating the MME,and that (2)higher scores on Dark Triad personality traits would be associated with a higher likelihood of cheating or lying.In the original study by Kouchaki and Smith(2014),individual differences(moral disengage-ment)moderated the MME.As the Dark Triad should comprise a ten-dency to morally disengage,we also explored possible interactive effects between time of day and scores on Dark Triad personality traits. Specifically,we examined the possibility that unethical behavior in the evening would be particularly observed in individuals scoring high on Dark Triad traits or vice versa.1.2.Methods1.2.1.ParticipantsData were collected via an online survey tool(https://www. soscisurvey.de/).The link to the study was distributed via social net-works,local online platforms and student mailing lists.As an incentive, participants who completed the study had the chance to win one out of ten online shopping vouchers.A total of N=243participants started the survey,but data from n=48participants were excluded from anal-yses because they did not complete the entire study.Thefinal sample comprised n=195participants(70.8%female,n=138).Mean age was M=25.73years(SD=6.96)and mean sleep duration during the past night was M=7.26h(SD=1.43).1.2.2.Measures1.2.2.1.Short Dark Triad(SD3)The SD3(Jones&Paulhus,2014)assesses the Dark Triad personality traits with27items(nine items per subscale).Items are scored on a five-point scale ranging from strongly disagree to strongly agree.The psychopathy subscale includes items related to impulsivity,callous manipulation and antisocial behavior.The Machiavellianism subscale includes items related to cynicism and manipulation tactics.The narcis-sism subscale includes items related to selfishness and a sense of gran-diosity.Internal consistencies wereα=.76(Machiavellianism),α= .68(narcissism),andα=.69(psychopathy)in the current study and, thus,comparable to those reported in the validation studies(Jones& Paulhus,2014).1.2.2.2.Global vigor and affect(GVA)The GVA instrument(Monk,1989)was used to control for partici-pants'current vigor and affective state.It consists of eight items asking for current alertness,sadness,tension,effort,happiness,weariness, calmness,and sleepiness.Participants respond on a visual analog scale anchored very little(0)and very much(100).Global vigor is calculated with the formula[(alert)+300−(sleepy)−(effort)−(weary)]/4 and global affect with the formula[(happy)+(calm)+200−(sad)−(tense)]/4.Each formula yields a value between0and100 with higher values indicating higher vigor and more positive affect, respectively.1.2.2.3.Message-TaskTo operationalize unethical behavior we used a decision-making task(Gneezy,2005),in which participants had the opportunity to lie in order to allegedly raise the amount of the voucher(see below).The task was slightly changed as compared to the task used by Kouchaki and Smith(2014):The payment options mentioned in our task were higher and had greater differences than those used by Kouchaki and Smith(2014)to increase the probability of cheating.Participants were told that a second player would be involved.This second player wasfic-titious,which the participants did not know.Participants were given two payment options.Thefirst option was for the benefit of the second player,the second option was in favor of the participant:“Option1:You will receive5.00€,whereas Player2will receive15.00€.”and“Option2: You will receive7.00€,whereas Player2will receive5.00€.”Participants were told that the actual payment would depend on Player2's choice. To inform Player2about the payment options,participants had to choose between two messages,which allegedly would be sent toficti-tious Player2.Thefirst message was veracious,the second message var-iation was a lie:“Message A:Option1can bring you more money than Option2.”versus“Message B:Option2will bring you more money than Option1.”Deciding to lie was therefore clearly linked to afinancial incentive in this task.In the current study,22.1%(n=43)participants chose the dishonest message option.1.2.2.4.Matrix-TaskAs a second task to operationalize unethical behavior,we used a vi-sual search task as used by Mazar,Amir,and Ariely(2008)and Kouchaki and Smith(2014).In this task,participants were able to increase their profit level by making false statements about their performance.Partic-ipants were presented a total of20matrices.Each matrix contained three rows and four columns consisting of a total of12-digit numbers with one or two decimals(Fig.1)and was presented for15s.During these15s,participants had tofind two numbers which summed up to 10.Of the20presented matrices,13were solvable.Each presentation was followed by a page,on which the participant had to indicate wheth-er he or she had found the two numbers or not.Indicating that the ma-trix was solved resulted in a profit increase of2.50€.Choosing the option“Not found”did not yield any profit increase.It was notexpected Fig.1.Example of a matrix used in the Matrix-Task to operationalize unethical behavior.74K.Roeser et al./Personality and Individual Differences88(2016)73–77to name or remember the two numbers after the15s,therefore the re-sult was not checked,which enabled participants to cheat.The order of the matrices was programmed in a way that thefirst seven matrices were solvable.Afterwards,a randomly determined sequence of the re-maining13matrices followed,which was identical for all subjects. This visual search task does not require mathematical skills or above-average intelligence(Mazar et al.,2008).The mean number of lies in the current study was M=1.15(SD=1.71,range0–7).1.2.3.ProcedureData were collected between7and10a.m.and4–7p.m.without randomized assignment,that is,participants could choose freely if they participated in the morning or in the evening.As a cover story, participants were told that the study investigated cognitive abilities at different times of day.They were also informed about the opportunity to win one out of ten online shopping vouchers and that the vouchers' value could be increased during the tasks.After providing the sociodemographic information,participants completed the GVA,the Matrix-,and the Message-Task.The SD3was presented at the end of the survey.Finally,participants were debriefed.They were informed about thefictitiousness of the partner in the Message-Task and that the vouchers hadfixed values of57€each.1.2.4.Data analysesDifferences in age,sleep duration,GVA scores,and sex distribution between individuals who participated in the morning or in the evening were tested with independent t-tests andχ2-test,respectively.Differ-ences in SD3scores between men and women were compared with in-dependent t-tests.Associations between SD3scores and continuous study variables were examined with Pearson correlation coefficients.Logistic regression analyses were used to examine predictors of choice in the Message-Task(message A[honest]coded0and message B[dishonest]coded1).Three models were run for each SD3subscale separately with time of day,SD3subscale and the interaction term time of day×SD3subscale as predictor variables.In step2,variables that were associated with SD3scores(sex and GVA scores,see below) were entered as covariates.Linear regression analyses were used to examine predictors of the number of lies in the Matrix-Task.Three models were run for each SD3subscale separately with time of day,SD3subscale and the interac-tion term time of day×SD3subscale as predictor variables.In step2, variables that were associated with SD3scores(sex and GVA scores, see below)were entered as covariates.All regression analyses were conducted using PROCESS for SPSS(Hayes,2013).Continuous predictor variables were mean-centered before calculating the product terms.For all statistical tests,exact p-values are reported,except when p b.001.p-Values of≥0.05are denoted as ns.1.3.Results1.3.1.Participant characteristicsOne-hundred eleven individuals participated in the morning and84 individuals participated in the evening.Groups did not differ in age, sleep duration,global vigor,global affect(all t s b1.78,ns)or sex distri-bution(χ2(1)=1.20,ns).Men scored higher than women on all three subscales of the SD3(Machiavellianism:M men=3.10,SD=0.67vs. M women=2.69,SD=0.52;psychopathy:M men=2.31,SD=0.55vs. M women=1.78,SD=0.49;narcissism:M men=2.92,SD=0.55vs. M women=2.69,SD=0.55;all t s N2.65,p b.01).Global affect was negatively correlated with scores on the Machiavellianism(r=−.17, p=.02)and psychopathy subscales(r=−.24,p=.001).Scores on the Machiavellianism subscale were positively correlated with scores on the psychopathy(r=.49,p b.001)and narcissism subscales(r=.26,p b.001).Scores on the psychopathy subscale were positively corre-lated with scores on the narcissism subscale(r=.31,p b.001).1.3.2.Message-TaskMachiavellianism scores predicted message choice such that higher scores were associated with a higher likelihood of selecting the dishon-est message(Table1).This effect was not moderated by time of day.In-cluding potential covariates revealed that global vigor also predicted message choice such that a higher current vigor was associated with a lower likelihood of selecting the dishonest message(Table1).This, however,did not influence the association between Machiavellianism and message choice.None of the other variables significantly predicted message choice.1.3.3.Matrix-TaskPsychopathy scores predicted the number of lies such that higher scores were associated with a higher number of lies(Table2).This effect was not moderated by time of day.Including potential covariates did not influence the association between psychopathy and number of lies and none of the other variables significantly predicted number of lies.1.4.DiscussionThe present study aimed at investigating if people are more likely to cheat or lie in the evening,if personality features,namely the Dark Triad of personality,are associated with these behaviors and if time of day and personality are interactively associated with these outcomes.Ourfirst hypothesis referred to replicating the MME(Kouchaki&Smith,2014). However,time of day did not affect cheating or lying in our study,that is,the MME could not be replicated.A possible reason might be that our study did not include a randomized assignment.Instead,partic-ipants chose their preferred time of participation.This might have resulted in a self-selection bias such that the depletion of the self-regulatory resource might have been less pronounced in people who decided to participate in the evening.Therefore,the MME may have not emerged,because the self-regulatory resource in individ-uals participating in the evening was not sufficiently depleted.How-ever,in the original publication by Kouchaki and Smith(2014),the MME occurred no matter whether participants self-selected their preferred time of participation or were randomly assigned into the morning or afternoon session.Previous studies have shown that motivation and success impor-tance can compensate for self-control resource depletion(Muraven& Slessareva,2003;Stewart,Wright,Hui,&Simmons,2009).Given that the current sample was recruited from the investigators'social environ-ment,their motivation and effort might have been stronger than in par-ticipants in the original study.Further,our sample–specifically in the Matrix Task–was extremely honest and thus,we had little variance in these data.However,Kouchaki and Smith(2014)demonstrated the MME in both undergraduate students and U.S.adults.Although the MME has been replicated by Koukachi and Smith themselves,future replication studies by other research teams are necessary to determine if the MME may only occur in certain samples(e.g.,may dependent on culture)or under specific circumstances.Our second hypothesis was that Dark Triad traits would be associat-ed with a higher likelihood of unethical behavior.In contrast to previous studies,we did not rely on self-reports orfictitious scenarios,but oper-ationalized cheating and lying situations.Although it has been shown that dark personalities report using various tactics of social influence (Jonason&Webster,2012),we found that Machiavellianism and psy-chopathy were differentially related to cheating and lying in our two tasks.The Message-Task included afictitious partner and a sophisticat-ed cover story,requiring a high amount of cognitive effort.In this task, Machiavellianism positively predicted cheating.The Matrix-Task,in75K.Roeser et al./Personality and Individual Differences88(2016)73–77contrast,animated participants to lie via a quick and simple click,which was related to higher scores on psychopathy.Indeed,it has been shown that psychopathy is closely related to dysfunctional impulsivity stem-ming from poor self-regulation(Jones&Paulhus,2011).In a study by Baughman et al.(2014),who investigated self-reported lying frequency, all three Dark Triad traits were associated with lying.However,this as-sociation was entirely attributable to psychopathy and Machiavellian-ism.Consistent with ourfindings,Baughman et al.(2014)report that Machiavellianism was related to planning and constructing original and detailed deception.In line with previousfindings,narcissism did not predict unethical behavior in the current study.A possible explanation might be that nar-cissism is the“brightest”,that is,the least malicious,among the Dark Triad traits(Rauthmann&Kolar,2012,2013).Moreover,Jonason and Tost(2010)found low self-control in psychopaths and to some extent in Machiavellians,but not in narcissists.Taken together,these results suggest that among the dark personalities,narcissists might be least susceptible to moral disengagement.Our third hypothesis was that time of day and Dark Triad personality may be interactively related to unethical behavior.For example,Gunia, Barnes,and Sah(2014)argue that unethical behavior cannot simply be explained by individual characteristics or a given situation.Instead,the interplay between personal and situational features(person×situation fit)may determine whether people behave unethically or not.However, this idea was not supported in the current study.Thus,results suggest that the unethical behavior displayed by individuals scoring high onTable1Results of logistic regression analyses predicting message choice in the Message-Task.N=195Step1Step2B SE p95%CI B SE p95%CIMachiavellianismTime of day0.230.36ns−0.47,0.940.130.39ns−0.63,0.88 Machiavellianism0.680.30.020.09,1.280.980.36.010.27,1.70 Time of day×Machiavellianism−0.060.60ns−1.24,1.120.010.65ns−1.27,1.29 Sex––––−0.550.45ns−1.43,0.34 Global affect––––−0.010.01ns−0.03,0.02 Global vigor––––−0.020.01.02−0.04,−0.00PsychopathyTime of day0.160.35ns−0.53,0.850.060.37ns−0.67,0.78 Psychopathy0.100.31ns−0.51,0.720.000.37ns−0.73,0.74 Time of day×psychopathy0.480.62ns−0.73,1.690.540.64ns−0.72,1.79 Sex––––−0.120.45ns−1.00,0.77 Global affect––––−0.010.01ns−0.03,0.01 Global vigor––––−0.020.01.04−0.04,−0.00NarcissismTime of day0.230.35ns−0.46,0.920.150.37ns−0.59,0.88 Narcissism0.400.31ns−0.22,1.020.520.34ns−0.14,1.18 Time of day×narcissism0.200.64ns−1.06,1.450.120.66ns−1.18,1.42 Sex––––−0.230.41ns−1.04,0.58 Global affect––––−0.010.01ns−0.03,0.01 Global vigor––––−0.020.01.04−0.04,−0.00Notes.Significant predictors are printed in boldface.Table2Results of linear regression analyses predicting the number of lies in the Matrix-Task.N=195Step1Step2B SE p95%CI B SE p95%CIMachiavellianismTime of day−0.070.25ns−0.56,0.42−0.110.26ns−0.62,0.40 Machiavellianism0.160.21ns−0.25,0.570.100.23ns−0.35,0.56 Time of day×Machiavellianism0.110.42ns−0.71,0.930.060.43ns−0.78,0.90 Sex––––0.490.29ns−0.09,1.07 Global affect––––0.010.01ns−0.01,0.03 Global vigor––––−0.000.01ns−0.02,0.01PsychopathyTime of day−0.110.25ns−0.59,0.38−0.120.25ns−0.62,0.38 Psychopathy0.510.22.020.07,0.940.550.25.030.05,1.05 Time of day×psychopathy0.170.44ns−0.69,1.030.100.44ns−0.77,0.97 Sex––––0.240.30ns−0.36,0.84 Global affect––––0.010.01ns−0.00,0.03 Global vigor––––−0.000.01ns−0.02,0.01NarcissismTime of day−0.080.25ns−0.58,0.41−0.150.26ns−0.67,0.36 Narcissism0.060.22ns−0.38,0.50−0.090.23ns−0.55,0.36 Time of day×narcissism−0.520.46ns−1.42,0.39−0.620.46ns−1.54,0.29 Sex––––0.550.28ns−0.01,1.10 Global affect––––0.010.01ns−0.01,0.03 Global vigor––––−0.000.01ns−0.02,0.01Notes.Significant predictors are printed in boldface.76K.Roeser et al./Personality and Individual Differences88(2016)73–77Machiavellianism and psychopathy appears to be unaffected by momentary circumstances such as time of day.While the procedure used in the current study may have high ecological validity,future studies are needed on the MME or daytime-dependent behaviors of dark personalities using randomized assign-ment to experimental conditions.Another limitation may be that poten-tial confounding variables like motivation or cognitive abilities were not assessed,which may relate to personality styles or may change throughout the day.However,we did control for current vigor and af-fect,which did not influence ourfindings.This is consistent with the re-sults of Kouchaki and Smith(2014),who excluded changes in affective states as an alternative explanation for the MME.Finally,the current sample consisted predominantly of highly academically educated female university students.Thus,our sample may have had high self-regulatory skills not affected by time of day.Although sex was unrelated to task performance,it would be desirable to investigate more heteroge-neous samples(regarding age,education,etc.)in future studies.According to the present study,unethical behavior can be consid-ered a function of personality,namely Machiavellianism and psychopa-thy,and,to some extent,a matter of reduced mental vigor.We conclude that the Dark Triad traits are differentially related to aspects of unethical behavior,such that Machiavellians display a preference for complex de-ception,while psychopaths engage in impulsive cheating.This adds to a better understanding of how dark personalities interact with their social environment.AcknowledgmentsAM is supported by a grant of the European Research Council(ERC-StG-2014639445NewEat).ReferencesBaughman,H.M.,Jonason,P.K.,Lyons,M.,&Vernon,P.A.(2014).Liar liar pants onfire: Cheater strategies linked to the Dark Triad.Personality and Individual Differences,71, 35–38.Baumeister,R.F.,Bratslavsky,E.,Muraven,M.,&Tice,D.M.(1998).Ego depletion:Is the active self a limited resource?Journal of Personality and Social Psychology,74, 1252–1265.Christie,R.,&Geis,F.L.(1970).Studies on Machaivellism.New York:Academic Press. Furnham,A.,Richards,S.C.,&Paulhus,D.L.(2013).The Dark Triad of personality:A 10year review.Social and Personality Psychology Compass,7,199–216.Gino,F.,Schweitzer,M.E.,Mead,N.L.,&Ariely,D.(2011).Unable to resist temptation: How self-control depletion promotes unethical anizational Behavior and Human Decision Processes,115,191–203.Gneezy,U.(2005).Deception:The role of consequences.American Economic Review,95, 384–394.Gunia,B.C.,Barnes,C.M.,&Sah,S.(2014).The morality of larks and owls:Unethical be-havior depends on chronotype as well as time of day.Psychological Science,25, 2272–2274.Hare,R.D.(1985).Comparison of procedures for the assessment of psychopathy.Journal of Consulting and Clinical Psychology,53,7–16.Hayes,A.F.(2013).Introduction to mediation,moderation,and conditional process analysis.New York:The Guilford Press.Hofmann,W.,Baumeister,R.F.,Forster,G.,&Vohs,K.D.(2012).Everyday temptations:An experience sampling study of desire,conflict,and self-control.Journal of Personality and Social Psychology,102,1318–1335.Jonason,P.K.,&Tost,J.(2010).I just cannot control myself:The Dark Triad and self-control.Personality and Individual Differences,49,611–615.Jonason,P.K.,&Webster,G.D.(2012).A protean approach to social influence:Dark Triad personalities and social influence tactics.Personality and Individual Differences,52, 521–526.Jonason,P.K.,Li,N.P.,&Teicher,E.A.(2010).Who is James Bond?:The Dark Triad as an agentic social style.Individual Differences Research,8,111–120.Jonason,P.K.,Li,N.P.,Webster,G.D.,&Schmitt,D.P.(2009).The Dark Triad:facilitating a short-term mating strategy in men.European Journal of Personality,23,5–18. Jonason,P.K.,Lyons,M.,Baughman,H.M.,&Vernon,P.A.(2014).What a tangled web we weave:The Dark Triad traits and deception.Personality and Individual Differences,70, 117–119.Jones,D.N.,&Figueredo,A.J.(2013).The core of darkness:Uncovering the heart of the dark triad.European Journal of Personality,27,521–531.Jones,D.N.,&Paulhus,D.L.(2011).The role of impulsivity in the Dark Triad of personality.Personality and Individual Differences,51,679–682.Jones,D.N.,&Paulhus,D.L.(2014).Introducing the Short Dark Triad(SD3):A brief mea-sure of dark personality traits.Assessment,21,28–41.Kouchaki,M.,&Smith,I.H.(2014).The morning morality effect:The influence of time of day on unethical behavior.Psychological Science,25,95–102.Mazar,N.,Amir,O.,&Ariely,D.(2008).The dishonesty of honest people:A theory of self-concept maintenance.Journal of Marketing Research,45,633–644.Mead,N.L.,Baumeister,R.F.,Gino,F.,Schweitzer,M.E.,&Ariely,D.(2009).Too tired to tell the truth:Self-control resource depletion and dishonesty.Journal of Experimental Social Psychology,45,594–597.Monk,T.H.(1989).A visual analog scale technique to measure global vigor and affect.Psychiatry Research,27,89–99.Muraven,M.,&Baumeister,R.F.(2000).Self-regulation and depletion of limited re-sources:Does self-control resemble a muscle?Psychological Bulletin,126,247–259. Muraven,M.,&Slessareva,E.(2003).Mechanisms of self-control failure:Motivation and limited resources.Personality and Social Psychology Bulletin,29,894–906. Nathanson,C.,Paulhus,D.L.,&Williams,K.M.(2006).Predictors of a behavioral measure of scholastic cheating:Personality and competence but not demographics.Contemporary Educational Psychology,31,97–122.O'Boyle,E.H.,Forsyth,D.R.,Banks,G.C.,&McDaniel,M.A.(2012).A meta-analysis of the Dark Triad and work behavior:A social exchange perspective.The Journal of Applied Psychology,97,557–579.Paulhus,D.L.,&Williams,K.M.(2002).The Dark Triad of personality:Narcissism,Machi-avellianism,and psychopathy.Journal of Research in Personality,36,556–563. Raskin,R.N.,&Hall,C.S.(1979).A narcissistic personality inventory.Psychological Reports, 45,590.Rauthmann,J.F.,&Kolar,G.P.(2012).How“dark”are the Dark Triad traits?Examining the perceived darkness of narcissism,Machiavellianism,and psychopathy.Personality and Individual Differences,53,884–889.Rauthmann,J.F.,&Kolar,G.P.(2013).Positioning the Dark Triad in the interpersonal circumplex:The friendly-dominant narcissist,hostile-submissive Machiavellian,and hostile-dominant psychopath?Personality and Individual Differences,54,622–627. Stewart,C.C.,Wright,R.A.,Hui,S.K.A.,&Simmons,A.(2009).Outcome expectancy as a moderator of mental fatigue influence on cardiovascular response.Psychophysiology,46,1141–1149.Williams,K.M.,Nathanson,C.,&Paulhus,D.L.(2010).Identifying and profiling scholastic cheaters:Their personality,cognitive ability,and motivation.Journal of Experimental Psychology.Applied,16,293–307.77K.Roeser et al./Personality and Individual Differences88(2016)73–77。

Antimatter Signatures of Gravitino Dark Matter Decay

Antimatter Signatures of Gravitino Dark Matter Decay

April 2008

E-mail addresses: alejandro.ibarra@desy.de, david.tran@desy.de
1
Introduction
Models with local supersymmetry predict the existence of a particle with extremely weak interactions: the gravitino. In contrast to the supersymmetric partners of the Standard Model particles, whose masses are expected to lie in the electroweak domain, the gravitino can have a mass ranging between a few eV and several TeV without conflicting with any laboratory experiment. Therefore, the gravitino can very naturally be the lightest supersymmetric particle (LSP), and if it is sufficiently long-lived, it could constitute the dark matter of the Universe [1]. Gravitinos were produced in the early Universe by scatterings in the thermal plasma, but did not subsequently annihilate due to their extremely weak interactions. Therefore, a relic population of gravitinos is expected in the present Universe with a density given by [2] Ω3/2 h2 ≃ 0.27 TR 1010 GeV 100 GeV m3/2 mg 1 TeV

Dark Matter Introduction

Dark Matter Introduction

a rXiv:as tr o-ph/4245v12Fe b24INTRODUCTION Martin J Rees Institute of Astronomy,Madingley Road,Cambridge,CB30HA Abstract It is embarrassing that 95%of the universe is unaccounted for.Galax-ies and larger-scale cosmic structures are composed mainly of ‘dark mat-ter’whose nature is still unknown.Favoured candidates are weakly-interacting particles that have survived from the very early universe,but more exotic options cannot be excluded.(There are strong arguments that the dark matter is not composed of baryons).Intensive experimental searches are being made for the ‘dark’particles (which pervade our entire galaxy),but we have indirect clues to their nature too.Inferences from galactic dynamics and gravitational lensing allow astronomers to ‘map’the dark matter distribution;comparison with numerical simulations of galaxy formation can constrain (eg)the particle velocities and collision cross sections.And,of course,progress in understanding the extreme physics of the ultra-early universe could offer clues to what particle might have existed then,and how many would have survived.The mean cosmic density of dark matter (plus baryons)is now pinned down to be only about 30%of the so-called critical density corresponding to a ‘flat’universe.However,other recent evidence –microwave back-ground anisotropies,complemented by data on distant supernovae –re-veals that our universe actually is ‘flat’,but that its dominant ingredient (about 70%of the total mass-energy)is something quite unexpected —‘dark energy’pervading all space,with negative pressure.We now con-front two mysteries:(i)Why does the universe have three quite distinct basic ingredients –baryons,dark matter and dark energy –in the proportions (roughly)5%,25%and 70%?(ii)What are the (almost certainly profound)implications of the ‘dark energy’for fundamental physics?1SOME HISTORYAstronomers have long known that galaxies and clusters would fly apart unless they were held together by the gravitational pull of much more material than we actually see.The strength of the case built up gradually.The argument that clusters of galaxies would be unbound without dark matter dates back to Zwicky (1937)and others in the 1930s.Kahn and Woltjer (1959)pointed out that the motion of Andromeda towards us implied that there must be dark matter in our Local1Group of galaxies.But the dynamical evidence for massive halos(or‘coronae’) around individual galaxiesfirmed up rather later(e.g.Roberts and Rots1973, Rubin,Thonnard and Ford1978).Two1974papers were specially influential in the latter context.Here is a quote from each:The mass of galactic coronas exceeds the mass of populations ofknown stars by one order of magnitude,as do the effective dimen-sions.....The mass/luminosity ratio rises to f=100for spiral andf=120for elliptical galaxies.With H=50km/sec/Mpc this ratiofor the Coma cluster is170(Einasto,Kaasik and Saar1974)Currently-available observations strongly indicate that the mass ofspiral galaxies increases almost linearly with radius to nearly1Mpc....and that the ratio of this mass to the light within the Holmberg ra-dios,f,is200(M/L⊙).(Ostriker,Peebles and Yahil,1974).The amount of dark matter,and how it is distributed,is now far better estab-lished than it was when those papers were written.The immense advances in delineated dark matter in clusters and in individual galaxies are manifest in the programme for this meeting.The rapid current progress stems from the con-fluence of several new kinds of data within the same few-year interval:optical surveys of large areas and high redshifts,CMBfluctuation measurements,sharp X-ray images,and so forth.The progress has not been solely observational.Over the last20years,a com-pelling theoretical perspective for the emergence of cosmic structure has been developed.The expanding universe is unstable to the growth of structure,in the sense that regions that start offvery slightly overdense have their expansion slowed by their excess gravity,and evolve into conspicuous density contrasts. According to this‘cold dark matter’(CDM)model,the present-day structure of galaxies and clusters is moulded by the gravitational aggregation of non-baryonic matter,which is an essential ingredient of the early universe(Pagels and Primack1982,Peebles1982,Blumenthal et al.1984,Davis et al.1985). These models have beenfirmed up by vastly improved simulations,rendered possible by burgeoning computer power.And astronomers can now compare these‘virtual universes’with the real one,not just at the present era but(by observing very distant objects)can probe back towards the formative stages when thefirst galaxies emerged.The following comments are intended to provide a context for the later papers. (For that reason,I do not give detailed references to the topics covered by other speakers–just some citations of historical interest).22THE CASE FOR DARK MATTER2.1BaryonsThe inventory of cosmic baryons is readily compiled.Stars and their remnants, and gas in galaxies,contribute no more than1%of the critical density(i.e.they giveΩb<0.01).However several percent more could be contributed by diffuse material pervading intergalactic space:warm gas(with kT≃0.1keV)in groups of galaxies and loose clusters,and cooler gas pervading intergalactic space that manifests itself via the‘picket fence’absorption lines in quasar spectra.(Rich clusters are rare,so their conspicuous gas content,at several KeV,is not directly significant for the total inventory,despite its importance as a probe)These baryon estimates are concordant with those inferred by matching the He and D abundances at the birth of galaxies with the predicted outcome of nucle-osynthesis in the big bang,which is sensitive to the primordial baryon/photon ratio,and thus toΩb.The observational estimates havefirmed up,with im-proved measurements of deuterium in high-z absorbing clouds.The bestfit occurs forΩb≃0.02h−2where h is the Hubble constant in units of100km s−1 Mpc−1.Observations favour h≃0.7.Ωb is now pinned down by a variety of argument to be0.04−0.05.This corre-sponds to only∼0.3baryons per cubic metre,a value so low that it leaves little scope for dark baryons.(It is therefore unsurprising that the MACHO/OGLE searches should have found that compact objects do not make a substantial contribution to the total mass of our own galactic halo.)2.2How much dark matter?An important recent development is thatΩDM can now be constrained to a value around0.25by several independent lines of evidence:(i)One of the most ingenious and convincing arguments comes from noting that baryonic matter in clusters–in galaxies,and in intracluster gas–amounts to 0.15−0.2of the inferred virial mass(White et al.1993).If clusters were a fair sample of the universe,this would then be essentially the same as the cosmic ratio of baryonic to total mass.Such an argument could not be applied to an individual galaxy,because baryons segregate towards the centre.However, there is no such segregation on the much larger scale of clusters:only a small correction is necessary to allow for baryons expelled during the cluster formation process.3(ii)Very distant galaxies appear distorted,owing to gravitational lensing by intervening galaxies and clusters.Detailed modelling of the mass-distributions needed to cause the observed distortions yields a similar estimate.This is a straight measurement ofΩDM which(unlike(i))does not involve assumptions aboutΩb,though it does depend on having an accurate measure of the clustering amplitude.(iii)Another argument is based on the way density contrasts grow during the cosmic expansion:in a low density universe,the expansion kinetic energy over-whelms gravity,and the growth of structure saturates at recent epochs.The existence of conspicuous clusters of galaxies with redshifts as large as z=1 is hard to reconcile with the rapid recent growth of structure that would be expected ifΩDM were unity.More generally,numerical simulations based on the cold dark matter(CDM)model model are a betterfit to the present-day structure for this value ofΩDM(partly because the initialfluctuation spectrum has too little long-wavelength power ifΩDM is unity).Other methods will soon offer independent estimates.For instance,ΩDM can be estimated from the deviations from the Hubbleflow induced by large-scale irregularities in the mass distribution on supercluster scales.2.3What could the dark matter be?The dark matter is not primarily baryonic.The amount of deuterium calculated to emerge from the big bang would be far lower than observed if the average baryon density were∼2(rather than∼0.3)per cubic metre.Extra exotic par-ticles that do not participate in nuclear reactions,however,would not scupper the concordance.Beyond the negative statement that it is non-baryonic,the nature of the dark matter still eludes us.This key question may yield to a three-pronged attack: 1.Direct detection.Important recent measurements suggest that neutrinos have non-zero masses;this result has crucially important implications for physics beyond the standard model.The inferred neutrino masses seem,how-4ever,too low to be cosmologically important.If the masses and cross-sections of supersymmetric particles were known,it should be possible to predict how many survive,and their contribution toΩ,with the same confidence with which we can compute the nuclear reactions that control primordial nucleosynthesis. Associated with such progress,we might expect a better understanding of how the baryon-antibaryon asymmetry arose,and the consequence forΩb.Optimists may hope for progress on still more exotic options.3.Simulations of galaxy formation and large-scale structureus that the temperaturefluctuations should be biggest on a particular length scale that is related to the distance a sound wave can travel in the early uni-verse.The angular scale corresponding to this length depends,however,on the geometry of the universe.If dark matter and baryons were all,we wouldn’t be in aflat universe–the geometry would be hyperbolic.Distant objects would look smaller than in aflat universe.In2001-02,measurements from balloons and from Antarctica pinned down the angular scale of this‘doppler peak’:the results indicated‘flatness’–a result now confirmed with greater precision by the WMAP satellite.A value of0.3forΩDM would imply(were there no other energy in the universe) an angle smaller by almost a factor of2–definitely in conflict with observations. So what’s the other70%?It is not dark matter but something that does not cluster–some energy latent in space.The simplest form of this idea goes back to 1917when Einstein introduced the cosmological constant,or lambda.A positive lambda can be interpreted,in the context of the ordinary Friedman equations, as afixed positive energy density in all space.This leads to a repulsion because, according to Einstein’s equation,gravity depends on pressure as well as density, and vacuum energy has such a large negative pressure–tension–that the net effect is repulsive.Einstein’s cosmological constant is just one of the options.A class of more general models is being explored(under names such as‘quintessence’)where the energy is time-dependent.Any form of dark energy must have negative pressure to be compatible with observations–unclustered relativistic particles, for instance,can be ruled out as candidates.The argument is straightforward: at present,dark energy dominates the universe–it amounts to around70% of the total mass-energy.But had it been equally dominant in the past,it would have inhibited the growth of the density contrasts in cosmic structures, which occurred gravitational instability.This is because the growth timescale for gravitational instability is∼(Gρc)−12when curvature is unimportant.Ifρtotal exceedsρc,the expansion is faster,so the growth is impeded.(Meszaros,1974)In the standard model,density contrasts in the dark matter grow by nearly 1000since recombination.If this growth had been suppressed,the existence of present-day clusters would therefore require irregularities that were already of substantial amplitude at the recombination epoch,contrary to the evidence from CMBfluctuations.For the‘dark energy’to be less dominant in the past,its density must depend on the scale factor R more slowly than the R−3dependence of pressure-free matter–i.e.its PdV work must be negative.Cosmologists have introduced a parameter w such that p=wρc2.A more detailed treatment yields the requirement that w<−0.5.This comes from taking account of baryons and dark matter,and requiring that dark energy should not have inhibited the6growth of structure so much that it destroyed the concordance between the CMBfluctuations(which measure the amplitude at recombination)and the present-day inhomogeneity.Note however that unless its value is-1(the special case of a classical cosmological constant)w will generally be time-dependent. In principle w(t)can be pinned down by measuring the Hubble expansion rate at different redshiftsThis line of argument would in itself have led to a prediction of accelerating cosmic expansion.However,as it turned out,studies of the redshift versus the apparent brightness of distant SNIa–strongly suggestive if not yet completely compelling–had already conditioned us to the belief that galaxies are indeed dispersing at an accelerating rate.As often in science,a clear picture gradually builds up,but the order in which the bits of the jigsaw fall into place is a matter of accident or contingency.CMBfluctuations alone can now pin downΩDM and the curvature independent of all the other measurements.The‘modern’interest in the cosmological constant stems from its interpretation as a vacuum energy.This leads to the reverse problem:Why is lambda at least120powers of10smaller than its‘natural’value,even though the effective vacuum density must have been very high in order to drive inflation.If lambda is fully resurrected,it will be a posthumous‘coup’for de Sitter.His model,dating from the1920s,not only describes inflation,but would then also describe future aeons of our cosmos with increasing accuracy.Only for the50-odd decades of logarithmic time between the end of inflation and the present would it need modification!.But of course the dark energy could have a more complicated and time-dependent nature–though it must have negative pressure,and it must not participate in gravitational clustering.4SUMMARY AND PROSPECTSCosmologists can now proclaim with confidence(but with some surprise too) that,in round numbers,our universe consists of5%baryons,25%dark matter, and70%dark energy.It is indeed embarrassing that95%of the universe is unaccounted for:even the dark matter is of quite uncertain nature,and the dark energy is a complete mystery.The network of key arguments is summarised in Figure1.Historically,the supernova evidence camefirst.But had the order of events been different,one could have predicted an acceleration on the basis of CDM evidence alone;the supernovae would then have offered gratifying corroboration(despite the unease about possible poorly-understood evolutionary effects).Our universe isflat,but with a strange mix of ingredients.Why should these all7give comparable contributions(within a modest factor)when they could have differed by a hundred powers of ten?In the coming decade,we can expect advances on several fronts.Physicists may well develop clearer ideas on what determined the favouritism for matter over antimatter in the early universe,and on the particles that make up the dark matter.Understanding the dark energy,and indeed the big bang itself,is perhaps a remoter goal,but ten years from now theorists may well have replaced the boisterous variety of ideas on the ultra-early universe by afirmer best buy. They will do this by discovering internal inconsistencies in some contending theories,and thereby narrowing down thefield.Better still,maybe one theory will earn credibility by explaining things we can observe,so that we can apply it confidently even to things we cannot directly observe.In consequence,we may have a better insight into the origin of thefluctuations,the dark energy,and perhaps the big bang itself.Inflation models have two generic expectations;that the universe should beflat and that thefluctuations should be gaussian and adiabatic(the latter because baryogenesis would occur at a later stage than inflation).But other features of thefluctuations are in principle measurable and would be a diagnostic of the specific physics.One,the ratio of the tensor and scalar amplitudes of thefluctuations,will have to await the next generation of CMB experiments, able to probe the polarization on small angular scales.Another discriminant among different theories is the extent to which thefluctuations deviate from a Harrison-Zeldovich scale-independent format(n=1in the usual notation);they could follow a different power law(i.e.be tilted),or have a‘rollover’so that the spectral slope is itself a function of scale.Such effects are already being constrained by WMAP data,in combination with evidence on smaller scales from present-day clustering,from the statistics of the Lyman alpha absorption-line‘forest’in quasar spectra,and from indirect evidence on when thefirst minihalos collapsed,signalling the formation of thefirst Population III stars that ended the cosmic dark age.In parallel,there will be progress in‘environmental cosmology’.The new gen-eration of10-metre class ground based telescopes will give more data on the universe at earlier cosmic epochs,as well as better information on gravitational lensing by dark matter.And there will be progress by theorists too.The behaviour of the dark matter,if influenced solely by gravity,can already be simulated with sufficient accuracy.Gas dynamics,including shocks and radia-tive cooling,can be included too(though of course the resolution isn’t adequate to model turbulence,nor the viscosity in shear layers).Spectacular recent sim-ulations have been able to follow the formation of thefirst stars.But the later stages of galactic evolution,where feedback is important,cannot be modelled without parametrising such processes in a fashion guided by physical intuition and observations.Fortunately,we can expect rapid improvements,from obser-vations in all wavebands,in our knowledge of galaxies,and the high-redshift8universe.Via a combination of improved observations,and ever more refined simulations, we can hope to elucidate how our elaborately structured cosmos emerged from a near-homogeneous early universe.ReferencesBlumenthal,G,Faber,S,Primack,J.R,and Rees,M.J.1984Nature311,517 Davis,M,Efstathiou,G.P,Frenk,C.S.and White,S.D.M.,1985Astrophys.J. 292,371Einasto,J,Kaasik,A and Saar,E,1974Nature250,309Kahn,F and Woltjer,L,1959Astrophys.J.130,705Meszaros,P.1974Astr.Astrophys.37,225Ostriker,J.Peebles,P.J.E.,and Yahil,A,1974Astrophys.J(Lett)193,L1 Pagels,H.and Primack,J.R.1982Phys.Rev.Lett.48,223Peebles,P.J.E.1982Astrophys.J.(Lett)263,L1Roberts,M.S.and Rots,A.H.1973Astr.Astrophys26,483.Rubin,V.C.,Thonnard,N.,and Ford,W.K.,1978Astrophys J.(Lett)225, L107White,S.D.M.,Navarro,J.F.,Evrard,A.E.and Frenk,C.S.1993,Nature366, 429Zwicky,F,1937Astrophys.J86,217910。

英文怪物蔓迪试读范文

英文怪物蔓迪试读范文

英文怪物蔓迪试读范文In the realm of contemporary literature, where captivating narratives and complex characters reign supreme, the emergence of a peculiar and intriguing work of fiction has sparked the interest of avid readers worldwide. "Mandy," the latest literary creation by the enigmatic author, E.L. Wainwright, promises to take its audience on a thrilling journey through the darkest corners of the human psyche, blurring the lines between reality and the supernatural.The story follows the life of Mandy, a seemingly ordinary young woman whose outward appearance belies a haunting and otherworldly presence within. From the very first page, the reader is drawn into Mandy's world, a world where the mundane and the extraordinary coexist in a delicate balance, constantly threatening to tip the scales in favor of the unknown.Wainwright's masterful storytelling immediately captivates the reader, weaving a web of intrigue and suspense that is impossible to escape. The author's command of language is nothing short of remarkable, as they effortlessly navigate the complexities of Mandy'sinner turmoil, painting a vivid and unsettling portrait of a woman torn between her human desires and the dark forces that seem to consume her.One of the most striking aspects of "Mandy" is the author's ability to blend genres seamlessly, creating a narrative that defies easy categorization. It is part psychological thriller, part supernatural horror, and part character study, all woven together with a deft hand that leaves the reader both enthralled and disturbed.The protagonist, Mandy, is a truly captivating and multifaceted character, one who challenges the reader's perceptions and preconceptions at every turn. Wainwright masterfully explores the depths of Mandy's psyche, delving into the shadows of her past and the haunting secrets that lurk within her subconscious. As the story unfolds, the reader is drawn deeper and deeper into Mandy's world, finding it increasingly difficult to discern where the human ends and the monster begins.The supporting cast of characters in "Mandy" are equally compelling, each adding their own unique layers to the overall narrative. From Mandy's well-meaning but ultimately oblivious parents to the enigmatic and unsettling figures who seem to orbit her life, the author weaves a tapestry of relationships that are as complex as they are unsettling.One of the most remarkable aspects of "Mandy" is the way in which Wainwright blends the supernatural and the mundane, creating a world that feels both familiar and profoundly unsettling. The author's attention to detail is meticulous, with every setting, every interaction, and every subtle nuance contributing to the overall sense of unease that permeates the story.The pacing of "Mandy" is masterful, with the author skillfully building tension and suspense throughout the narrative. Just when the reader thinks they have a handle on the story, Wainwright throws in a curveball, leaving them scrambling to keep up with the twists and turns of the plot.The climax of the novel is truly a tour de force, as Wainwright pulls out all the stops, delivering a heart-pounding and deeply unsettling conclusion that will leave the reader both exhilarated and unsettled. The final moments of the story are a testament to the author's storytelling prowess, as they weave together the various threads of the narrative into a seamless and unforgettable finale.One of the most remarkable aspects of "Mandy" is the way in which it challenges the reader's preconceptions about the nature of reality and the human condition. Throughout the story, Wainwright forces the reader to confront their own fears and anxieties, questioning thevery foundations of their beliefs and the boundaries between the natural and the supernatural.The language and style of "Mandy" are equally impressive, with Wainwright's prose striking a delicate balance between the lyrical and the unsettling. The author's command of imagery and metaphor is truly remarkable, as they paint vivid and haunting scenes that linger in the reader's mind long after the final page has been turned.Overall, "Mandy" is a masterful work of fiction that deserves to be hailed as a modern classic of the genre. Wainwright's ability to blend the psychological and the supernatural, the familiar and the terrifying, is truly awe-inspiring, and the result is a novel that is both deeply unsettling and profoundly moving.For those who love a good scare, "Mandy" is a must-read, a captivating and unsettling journey into the darkest corners of the human psyche. But for those who seek something more, a deeper exploration of the human condition and the nature of reality, this novel is an absolute must-read, a work of fiction that will linger in the mind and the heart long after the final page has been turned.。

脑胶质瘤诊疗规范2018年版

脑胶质瘤诊疗规范2018年版

脑胶质瘤诊疗规范(2018年版)一、概述脑胶质瘤是指起源于脑神经胶质细胞的肿瘤,是最常见的原发性颅内肿瘤,世界卫生组织(WHO)中枢神经系统肿瘤分类将脑胶质瘤分为Ⅰ-Ⅳ级,Ⅰ、Ⅱ级为低级别脑胶质瘤,Ⅲ、Ⅳ级为高级别脑胶质瘤。

本规范主要涉及星形细胞、少突胶质细胞和室管膜细胞来源的高、低级别脑胶质瘤的诊治。

我国脑胶质瘤年发病率为5-8/10万,5年病死率在全身肿瘤中仅次于胰腺癌和肺癌。

脑胶质瘤发病机制尚不明了,目前确定的两个危险因素是:暴露于高剂量电离辐射和与罕见综合征相关的高外显率基因遗传突变。

此外,亚硝酸盐食品、病毒或细菌感染等致癌因素也可能参与脑胶质瘤的发生。

脑胶质瘤临床表现主要包括颅内压增高、神经功能及认知功能障碍和癫痫发作三大类。

目前,临床诊断主要依靠计算机断层扫描(CT)及磁共振成像(MRI)检查等影像学诊断,磁共振弥散加权成像(DWI)、磁共振弥散张量成像(DTI)、磁共振灌注成像(PWI)、磁共振波谱成像(MRS)、功能磁共振成像(fMRI)、正电子发射计算机断层显像(PET)等对脑胶质瘤的鉴别诊断及治疗效果评价有重要意义。

脑胶质瘤确诊需要通过肿瘤切除或活检获取标本,进行组织和分子病理学检查,确定病理分级和分子亚型。

目前主要的分子病理标记物包括:异柠檬酸脱氢酶(IDH)突变、染色体1p/19q联合缺失状态(co-deletion)、O6-甲基鸟嘌呤-DNA甲基转移酶(MGMT)启动子区甲基化、α地中海贫血伴智力低下综合征X连锁基因(ATRX)突变、端粒酶逆转录酶(TERT)启动子突变、人组蛋白H3.3(H3F3A)K27M突变、BRAF基因突变、PTPRZ1-MET基因融合、miR-181d、室管膜瘤RELA基因融合等1,2。

这些分子标志物对脑胶质瘤的个体化治疗及临床预后判断具有重要意义。

脑胶质瘤治疗以手术切除为主,结合放疗、化疗等综合治疗方法。

手术可以缓解临床症状,延长生存期,并获得足够肿瘤标本用以明确病理学诊断和进行分子遗传学检测。

Does Dark Matter at the Center and in the Halo of the Galaxy Consist of the Same Particles

Does Dark Matter at the Center and in the Halo of the Galaxy Consist of the Same Particles

a rXiv:as tr o-ph/111536v128Nov21Does Dark Matter at the Center and in the Halo of the Galaxy Consist of the Same Particles?Neven Bili ´c 1,F austin Munyaneza,Gary B.Tupper,and Raoul D.Viollier 2Institute of Theoretical Physics and Astrophysics Department of Physics,University of Cape Town Private Bag,Rondebosch 7701,South Africa After a discussion of the properties of degenerate fermion balls,we analyze the orbits of the star S0-1,which has the smallest projected distance to Sgr A ∗,in the supermassive black hole as well as in the fermion ball scenarios of the Galactic center.It is shown that both scenarios are consistent with the data,as measured during the last six years by Genzel et al.and Ghez et al..We then consider a self-gravitating ideal fermion gas at nonzero temperature as a model for the Galactic halo.The Galactic halo of mass ∼2×1012M ⊙enclosed within a radius of ∼200kpc implies the existence of a supermassive compact dark object at the Galactic center that is in hydrostatic and thermal equilibrium with the halo.The central object has a maximal mass of ∼2.3×106M ⊙within a minimal radius of ∼18mpc or ∼21light-days for fermion masses ∼15keV.We thus conclude that both the supermassive compact dark object and the halo could be made of the same weakly interacting ∼15keV particle.PRESENTED ATCOSMO-01Rovaniemi,Finland,August 29–September 4,20011IntroductionIn the past,self-gravitating degenerate neutrino matter has been suggested as a model for quasars,with neutrino masses in the0.2keV∼<m∼<0.5MeV range[1].Later it was used to describe dark matter in clusters of galaxies and in galactic halos,with neutrino masses in the1∼<m/eV∼<25range[2].More recently,supermassive compact dark objects consisting of weakly interacting degenerate fermionic matter,with fermion masses in the10∼<m/keV∼<20range,have been proposed[3,4,5,6,7]as an alternative to the supermassive black holes that are believed to reside at the centers of many galaxies.It has been pointed out that such degenerate fermion balls could cover[5]the whole range of the supermassive compact dark objects that have been observed so far with masses ranging from106to3×109M⊙[8].Most recently,it has been shown that a weakly interacting dark matter particle in the mass range1∼<m/keV∼<5could solve the problem of the excessive structure generated on subgalactic scales in N-body and hydrodynamical simulations of structure formation in this Universe[9].So far the masses of∼20supermassive compact dark objects at the center of galaxies have been measured using various techniques[8].The most massive compact dark object ever observed is located at the center of M87in the Virgo cluster,and it has a mass of about 3×109M⊙[10].If we identify this object of maximal mass with a degenerate fermion ball at the Oppenheimer-Volkoff(OV)limit[11],i.e.,M OV=0.54M3Pl m−2g−1/2≃3×109M⊙[5],where M Pl=The required weakly interacting fermion of∼15keV mass cannot be an active neu-trino,as it would overclose the Universe by orders of magnitude[14].Moreover,an active neutrino of∼15keV is disfavored by the experimental data on solar and atmospheric neutrinos,as these are most probably oscillating into active neutrinos with smallδm2[15], and theνe mass has been determined to be<3eV[16].However,the∼15keV fermion could very well be a sterile neutrino,contributingΩd≃0.3to the dark matter fraction of the critical density today.Indeed,as has been shown for an initial lepton asymmetry of∼10−3,a sterile neutrino of mass∼10keV may be resonantly produced in the early Universe with near closure density,i.e.Ωd∼1[17].The resulting energy spectrum of the sterile neutrinos is cut offfor energies larger than the resonance energy,thus mimicking a degenerate fermion gas.As an alternative possibility,the∼15keV sterile neutrino could be replaced by the axino[18]or the gravitino[19,20]in soft supersymmetry breaking scenarios.In the recent past,galactic halos have been successfully modeled as a self-gravitating isothermal gas of particles of arbitrary mass,the density of which scales asymptotically as r−2,yieldingflat rotation curves[21].As the supermassive compact dark objects at the galactic centers are well described by a gas of fermions of mass m∼15keV at T=0, it is tempting to explore the possibility that one could describe both the supermassive compact dark objects and their galactic halos in a unified way in terms of a fermion gas atfinite temperature.We will show in this paper that this is indeed the case,and that the observed dark matter distribution in the Galactic halo is consistent with the existence of a supermassive compact dark object at the center of the Galaxy which has about the right mass and size,and is in thermal and hydrostatic equilibrium with the halo.2Dynamics of the Stars Near the Galactic Center We now would like to compare the predictions of the black hole and fermion ball scenarios of the Galactic center,for the stars with the smallest projected distances to Sgr A∗,based on the measurements of their positions during the last six years[7,12].The projected orbits of three stars,S0-1(S1),S0-2(S2)and S0-4(S4),show deviations from uniform motion on a straight line during the last six years,and they thus may contain nontrivial information about the potential.For our analysis we have selected the star,S0-1,because its projected distance from Sgr A∗in1995.53,4.4mpc or5.3light-days,makes it most likely that it could be orbiting within a fermion ball of radius∼18mpc or∼21light-days. We thus may in principle distinguish between the black hole and fermion ball scenarios for this star.The dynamics of the stars in the gravitationalfield of the supermassive compact dark object can be studied solving Newton’s equation of motion,taking into account the initial position and velocity vectors at,e.g.,t0=1995.4yr,i.e., r(t0)≡(x,y,z)and ˙ r(t0)≡(v x,v y,v z).For the fermion ball the source of gravitationalfield is the mass M(r) enclosed within a radius r[3,7]while for the black hole it is M c=M(R c)=2.6×106M⊙.2The x-axis is chosen in the direction opposite to the right ascension(RA),the y-axis inthe direction of the declination,and the z-axis points towards the sun.The black hole and the center of the fermion ball are assumed to be at the position of Sgr A∗which isalso the origin of the coordinate system at an assumed distance of8kpc from the sun.In Figs.1and2the right ascension(RA)and declination of S0-1are plotted as a function of time for various unobservable z’s and v z=0in1995.4,for the black hole andfermion ball scenarios.The velocity components v x=340km s−1and v y=−1190kms−1in1995.4have beenfixed from observations.In the case of a black hole,both RA and declination depend strongly on z in1995.4,while the z-dependence of these quantities inthe fermion ball scenario is rather weak.We conclude that the RA and declination data of S0-1are wellfitted with|z|≈0.25′′in the black hole scenario,and with|z|∼<0.1′′in thefermion ball case(1′′=38.8mpc=46.2light-days at8kpc).Of course,we can also trytofit the data varying both the unknown radial velocity v z and the unobservable radial distance z.The results are summarized in Fig.3,where the z−v z phase-space of1995.4,thatfits the data,is shown.The small range of acceptable|z|and|v z|values in the black hole scenario(solid vertical line)reflects the fact that the orbit of S0-1depend stronglyon z.The weak sensitivity of the orbit on z in the fermion ball case is the reason forthe much larger z−v z phase-spacefitting the data of S0-1[12],as shown by the dashed box.The dashed and solid curves describe the just bound orbits in the fermion ball andblack hole scenarios,respectively.The star S0-1is unlikely to be unbound,because inthe absence of close encounters with stars of the central cluster,S0-1would have to fall in with an initial velocity that is inconsistent with the velocity dispersion of the stars atinfinity.Fig.4shows some typical projected orbits of S0-1in the black hole and fermion ballscenarios.The data of S0-1may befitted in both scenarios with appropriate choices of v x,v y,z and v z in1995.4.The inclination angles of the orbit’s plane,θ=arccos L z/| L| , with L=m r×˙ r,are shown next to the orbits.The minimal inclination angle thatdescribes the data in the black hole case isθ=70o,while in the fermion ball scenario it isθ=0o.In the black hole case,the minimal and maximal distances from Sgr A∗are r min =0.25′′and r max=0.77′′,respectively,for the orbit with z=0.25′′and v z=0which has a period of T0≈161yr.The orbits with z=0.25′′and v z=400km s−1or z=0.25′′and v z=700km s−1have periods of T0≈268yr or T0≈3291yr,respectively.In the fermion ball scenario,the open orbit with z=0.1′′and v z=0has a“period”of T0≈77yr with r min=0.13′′and r max=0.56′′.The open orbits with z=0.1′′and v z=400 km s−1or z=0.1′′and v z=900km s−1have“periods”of T0≈100yr or T0≈1436yr, respectively.In concluding,it is important to note that,based on the data of the star S0-1[12],the fermion ball scenario cannot be ruled out.In fact,in view of the z−v z phase space,that is much larger in the fermion ball scenario than in the black hole case,there is reason to treat the fermion ball scenario of the supermassive compact dark object at the center of our Galaxy with the respect it deserves.33Dark Matter in the Center and the Halo of the GalaxyDegenerate fermion balls are well understood in terms of the Thomas-Fermi theory applied to self-gravitating fermionic matter at T=0[3].Extending this theory to nonzero temperature[22,23,24],it has been shown that at some critical temperature T=T c, a self-gravitating ideal fermion gas,having a mass below the OV limit enclosed in a spherical cavity of radius R,may undergo afirst-order gravitational phase transition from a diffuse state to a condensed state.This is best seen plotting the energy and free energy as functions of the temperature which are three-valued in some temperature interval, exhibiting a Maxwell-Boltzmann branch at high temperatures and the degenerate branch at low temperatures.However,thisfirst-order phase transition can only take place if the Fermi gas is able to get rid of the large latent heat which is due to the binding energy of the fermion ball.As the short-range interactions of the fermions are negligible,the gas cannot release its latent heat;it will thus be trapped for temperatures T<T c in a thermodynamic quasi-stable supercooled state close to the point of gravothermal collapse. The Fermi gas will be caught in the supercooled state even if the total mass of the gas exceeds the OV limit,as a stable condensed state does not exist in this case.The formation of a supercooled state close to the point of gravothermal collapse,may be understood as a process similar to that of violent relaxation,which was introduced to describe rapid virialization of stars of different mass in globular clusters[25,26]with-out invoking binary collisions of the stars,as these would not contribute significantly to thermalization on a scale of the age of the Universe.Through the gravitational collapse of a cold overdensefluctuation,∼1Gyr after the Big Bang,part of gravitational energy transforms into the kinetic energy of random motion of small-scale densityfluctuations. The resulting virialized cloud will thus be well approximated by a gravitationally stable thermalized halo.In order to estimate the mass-temperature ratio,we assume that the cold overdense cloud of the mass of the Galaxy M stops expanding at the time t m,reach-ing its maximal radius R m and minimal average densityρm=3M/(4πR3m).The total energy per particle is just the gravitational energyE=−3R m.(1)Assuming spherical collapse[27]one arrives atρm=9π216Ωdρ0(1+z m)3,(2)where¯ρ(t m)is the background density at the time t m or cosmological redshift z m,and ρ0≡3H20/(8πG)is the present critical density.We now approximate the virialized cloud by a singular isothermal sphere[26]of mass M and radius R,characterized by a constant4circular velocity Θ=(2T/m )1/2and the density profile ρ(r )=Θ2/4πGr 2.Its total energy per particle is the sum of gravitational and thermal energies,i.e.,E =−1R =−15G (6Ωd ρ0M 2)1/3(1+z m ).(4)Taking Ωd =0.3,M =2×1012M ⊙,z m =4,and H 0=65km s −1Mpc −1,we find Θ≃220km s −1,which corresponds to the mass-temperature ratio m/T ≃4×106.Next,we briefly discuss the general-relativistic extension of the Thomas-Fermi theory[23]for a self-gravitating gas of N fermions with mass m and degeneracy factor g at the temperature T enclosed in a sphere of radius R .We denote by p ,ρ,and n the pressure,energy density,and particle number density of the gas,respectively.In the following we use the units in which G =1.The metric generated by the mass distribution is static,spherically symmetric,and asymptotically flat,i.e.,ds 2=ξ2dt 2−(1−2M /r )−1dr 2−r 2(dθ2+sin θdφ2).(5)For numerical convenience,we introduce the parameter α=µ/T and the substitution ξ=(ϕ+1)−1/2µ/m ,where µis the chemical potential associated with the conserved particle number N .The equation of state for a self-gravitating gas may thus be represented in parametric form [28]asn =11+exp {[(y 2+1)1/2/(ϕ+1)1/2−1]α},(6)ρ=11+exp {[(y 2+1)1/2/(ϕ+1)1/2−1]α},(7)p =11+exp {[(y 2+1)1/2/(ϕ+1)1/2−1]α},(8)where appropriate length and mass scales a and b ,respectively,have been chosen such that a =b =(2/g )1/2/m 2.Restoring ¯h ,c ,and G ,we havea =g¯h M Pl2m 2km ,(9)b = g M 3Pl 2m2M ⊙.(10)5Thus fermion mass,degeneracy factor,and chemical potential are eliminated from the equation of state.Einstein’sfield equations for the metric(5)are given bydϕr(r−2M),(11)d Mdr=4πr2(1−2M/r)−1/2n(13) imposing particle-number conservation as a condition at the boundaryN(R)=N.(14) Eqs.(11)-(13)should be integrated using the boundary conditions at the origin,i.e.,ϕ(0)=ϕ0>−1,M(0)=0,N(0)=0.(15) It is useful to introduce the degeneracy parameterη=αϕ/2,which,in the Newtonian limit,approachesηnr=(µnr−V)/T,withµnr=µ−m being the nonrelativistic chemical potential and V the Newtonian potential.Asϕis monotonously decreasing with increas-ing r,the strongest degeneracy is obtained at the center withη0=αϕ0/2.The parameter η0,uniquely related to the central density and pressure,will eventually befixed by the requirement(14).For r≥R,the functionϕyields the usual empty-space Schwarzschildsolutionϕ(r)=µ2r −1−1,(16)withM=M(R)= R0dr4πr2ρ(r).(17) Given the temperature T,the set of self-consistency equations(6)-(13),with the bound-ary conditions(14)-(17)defines the general-relativistic extension of the Thomas-Fermi equation.4Numerical ResultsThe numerical procedure is now straightforward.For afixed,arbitrarily chosenα,wefirst integrate Eqs.(11)and(12)numerically on the interval[0,R]tofind the solutions for various central values of the degeneracy parameterη0.Integrating(13)simultaneously,6yields N(R)as a function ofη0.We then select the value ofη0for which N(R)=N.The chemical potentialµcorresponding to this particular solution is given by Eq.(16)which in turn yields the parametric dependence on the temperature throughα=µ/T.The quantities N,T,and R are free parameters of our model and their range of values are dictated by the physics of the problem at hand.At T=0the number of fermions N is restricted by the OV limit N OV=2.89×109radius is at which the r−2asymptotic behavior of the density begins.Theflattening of the Galactic rotation curve begins in the range1∼<r/kpc∼<10,hence the solution(3’) most likely describes the Galaxy’s halo.This may be verified by calculating the rotational curves in our model.We know already from the estimate(4)that our model yields the correct asymptotic circular velocity of220km/s.In order to make a more realistic com-parison with the observed Galactic rotation curve,we must include two additional matter components:the bulge and the disk.The bulge is modeled as a spherically symmetric matter distribution of the form[31]ρb(s)=e−hs[(u+1)8−1]1/2,(18)where s=(r/r0)1/4,r0is the effective radius of the bulge and h is a parameter.We adopt r0=2.67kpc and h yielding the bulge mass M b=1.5×1010M⊙[32].In Fig.8the mass of halo and bulge enclosed within a given radius is plotted for variousη0.Here,the gravitational backreaction of the bulge on the fermionic halo has been taken into account. The data points,indicated by squares,are the mass M c=2.6×106M⊙within18mpc, estimated from the motion of the stars near Sgr A∗[12],and the mass M50=5.4+0.2−3.6×1011 within50kpc,estimated from the motions of satellite galaxies and globular clusters[30]. Variation of the central degeneracy parameterη0between24and32does not change the essential halo features.In Fig.9we plot the circular velocity components of the halo,the bulge,and the disk. The contribution of the disk is modeled as[33]Θd(r)2=Θd(r o)21.97(r/r o)1.22one important difference:in the Maxwell-Boltzmann case the curve continues to spiral inwards ad infinitum approaching the point of the singular isothermal sphere,that is characterized by an infinite central density.In Fermi-Dirac case the spiral consists of two almost identical curves.The inwards winding of the spiral begins for some negative central degeneracy and stops at the point T=2.3923×10−7m,E=−1.1964×10−7m, whereη0becomes zero.This part of the curve,which basically depicts the behavior of a nondegenerate gas,we call Maxwell-Boltzmann branch.By increasing the central de-generacy parameter further to positive values,the spiral begins to unwind outwards very close to the inwards winding curve.The outwards winding curve will eventually depart from the Maxwell-Boltzmann branch for temperatures T∼>10−3m.Further increase of the central degeneracy parameter brings us to a region,where general-relativistic effects become important.The curve will exhibit another spiral for temperatures and energies of the order of a few10−3m approaching the limiting temperature T∞=2.4×10−3m and energy E∞=3.6×10−3m with both the central degeneracy parameter and the central density approaching infinite values.It is remarkable that gravitationally stable configura-tions with arbitrary large central degeneracy parameters exist atfinite temperature even though the total mass exceeds the OV limit by several orders of magnitude.5ConclusionsIn summary,using the Thomas-Fermi theory,we have shown that a weakly interacting fermionic gas atfinite temperature yields a mass distribution that successfully describes both the center and the halo of the Galaxy.For a fermion mass m≃15keV,a reasonable fit to the rotation curve is achieved with the temperature T=3.75meV and the degen-eracy parameter at the centerη0=28.With the same parameters,we obtain the mass M50=5.04×1011M⊙and M200=2.04×1012M⊙within50and200kpc,respectively. These values agree quite well with the mass estimates based on the motions of satellite galaxies and globular clusters[30].Moreover,the mass of M c≃2.27×106M⊙,enclosed within18mpc,agrees reasonably well with the observations of the compact dark object at the center of the Galaxy.We thus conclude that both the Galactic halo and center could be made of the same fermions.An observational consequence of this unified scenario of fermion ball and fermion halo atfinite temperature could be the direct observation of the radiative decay of the fermion (assumed here to be a sterile neutrino)into a standard neutrino,i.e.,f→νγ.The X-ray luminosity of the compact dark object is most easily observed.If the lifetime for the decay f→νγis0.82×1019yr,the luminosity of a M c=2.6×106M⊙fermion ball would be0.9×1034erg s−1.This is consistent with the upper limit of the X-ray luminosity of∼(0.5 -0.9)×1034erg s−1of the source with radius0.5′′≃23light-days,whose center nearly coincides with Sgr A∗,as seen by the Chandra satellite in the2to7keV band[36].The lifetime is proportional to sin−2θ,θbeing the unknown mixing angle of the sterile with active neutrinos.With a lifetime of0.82×1019yr we obtain an acceptable value for the9mixing angle squared ofθ2=1.4×10−11.The X-rays originating from such a radiative decay would contribute about two orders of magnitude less than the observed diffuse X-ray background at this wavelength if the sterile neutrino is the dark matter particle of the Universe.The signal observed at the Galactic center would be a sharp X-ray line at ∼7.5keV for g=2and∼6.3keV for g=4.This line could be misinterpreted as the Fe Kαline at6.67keV.Scattering with baryonic matter within the Galactic center could distribute the energy more evenly in the2to7keV band.The X-ray luminosity would be tracing the fermion matter distribution,and it could thus be an important test of the fermion ball scenario.Of course the angular resolution would need to be∼<0.1′′and the sensitivity would have to extend beyond7keV.ACKNOWLEDGEMENTSThis research is in part supported by the Foundation of Fundamental Research(FFR) grant number PHY99-01241and the Research Committee of the University of Cape Town. The work of N.B.is supported in part by the Ministry of Science and Technology of the Republic of Croatia under Contract No.00980102.References[1]M.A.Markov,Phys.Lett.10,122(1964).[2]G.Marx and A.S.Szalay,in Neutrino’72,1,191(Technoinform,Budapest,1972);R.Cowsik and J.McClelland,Astrophys.J.180,7(1973);R.Ruffini,Lett.Nuovo Cim.29,161(1980).[3]R.D.Viollier,D.Trautmann and G.B.Tupper,Phys.Lett.B306,79(1993);R.D.Viollier,Prog.Part.Nucl.Phys.32,51(1994).[4]N.Bili´c,D.Tsiklauri and R.D.Viollier,Prog.Part.Nucl.Phys.40,17(1998);N.Bili´c and R.D.Viollier,Nucl.Phys.(Proc.Suppl.)B66,256(1998).[5]N.Bili´c,F.Munyaneza and R.D.Viollier,Phys.Rev.D59,024003(1999).[6]D.Tsiklauri and R.D.Viollier,Astropart.Phys.12,199(1999);F.Munyaneza andR.D.Viollier,astro-ph/9907318.[7]F.Munyaneza,D.Tsiklauri and R.D.Viollier,Astrophys.J.509,L105(1998);ibid.526,744(1999);F.Munyaneza and R.D.Viollier,astro-ph/0103466,Astrophys.J.563,0000(2001).[8]L.C.Ho and J.Kormendy,astro-ph/0003267;astro-ph/0003268.10[9]P.Bode,J.P.Ostriker,and N.Turok,Astrophys.J.556,93(2001),astro-ph/0010389.[10]F.Macchetto et al.,Astrophys.J.489,579(1997).[11]J.R.Oppenheimer and G.M.Volkoff,Phys.Rev.55,374(1939).[12]A.Eckart and R.Genzel,Mon.Not.R.Astron.Soc.284,576(1997);A.M.Ghez,B.L.Klein,M.Morris and E.E.Becklin,Astrophys.J.509,678(1998).[13]R.Mahadevan,Nature394,651(1998).[14]E.W.Kolb and M.S.Turner,The Early Universe(Addison-Wesley,San Francisco,1989).[15]S.Fukuda et al.,Phys.Rev.Lett.85,3999(2000).[16]D.E.Groom et al.,Review of Particle Physics,Eur.Phys.J.C15,1(2000).[17]X.Shi and G.M.Fuller,Phys.Rev.Lett.82,2832(1999);K.Abazajian,G.M.Fuller,and M.Patel,Phys.Rev.D64,023501(2001),astro-ph/0101524;G.B.Tupper,R.J.Lindebaum,and R.D.Viollier,Mod.Phys.Lett.A15,1221(2000).[18]T.Goto and M.Yamaguchi,Phys.Lett.B276,123(1992);L.Covi,J.E.Kim,andL.Roszkowski,Phys.Rev.Lett.82,4180(1999),hep-ph/9905212;L.Covi,H.-B.Kim,J.E.Kim,and L.Roszkowski,hep-ph/0101009.[19]M.Dine and A.E.Nelson,Phys.Rev.D48,1277(1993),hep-ph/9303230;M.Dine,A.E.Nelson and Y.Shirman,Phys.Rev.D51,1362(1995),hep-ph/9408384;M.Dine,A.E.Nelson,Y.Nir and Y.Shirman,Phys.Rev.D53,2658(1996),hep-ph/9507378;D.H.Lyth,Phys.Lett.B488,417(2000),hep-ph/9911257.[20]H.Murayama,Phys.Rev.Lett.79,18(1997),hep-ph/9705271;S.Dimopoulos,G.Dvali,R.Rattazzi and G.F.Giudice,Nucl.Phys.B510,12(1998),hep-ph/9705307;E.A.Baltz and H.Murayama,astro-ph/0108172.[21]S.Cole and cey,Mon.Not.R.Astron.Soc.281,716(1996)and referencestherein.[22]N.Bili´c and R.D.Viollier,Phys.Lett.B408,75(1997).[23]N.Bili´c and R.D.Viollier,Gen.Rel.Grav.31,1105(1999);Eur.Phys.J.B11,173(1999).[24]W.Thirring,Z.Physik235,339(1970);P.Hertel,H.Narnhofer and W.Thirring,Comm.Math.Phys.28,159(1972);J.Messer,J.Math.Phys.22,2910(1981). [25]D.Lynden-Bell,Mon.Not.R.Astron.Soc.136,101(1967).11[26]J.Binney and S.Tremaine,Galactic Dynamics(Princeton University Press,Prince-ton,New Jersey,1987),and references cited therein.[27]T.Padmanabhan,Structure formation in the Universe(Cambridge University Press,Cambridge,1993).[28]J.Ehlers,in Relativity,Astrophysics and Cosmology,edited by W.Israel(D.ReidelPublishing Company,Dordrecht/Boston1973).[29]P.-H.Chavanis and J.Sommeria,Mon.Not.R.Astron.Soc.296,569(1998).[30]M.I.Wilkinson and N.W.Evans,Mon.Not.R.Astron.Soc.310,645(1999).[31]P.J.Young,Astrophys.J.81,807(1976);G.de Vaucouleurs and W.D.Pence,As-trophys.J.83,1163(1978).[32]P.D.Sackett,Astrophys.J.483,103(1997).[33]M.Persic,P.Salucci,and F.Stell,Mon.Not.R.Astron.Soc.281,27(1986).[34]R.P.Olling and M.R.Merrifield,Mon.Not.R.Astron.Soc.311,361(2000).[35]W.Y.Chau,ke,J.Stone,Astrophys.J.281,560(1984).[36]F.K.Baganoffet al.,astro-ph/0102151.12Figure1:Right ascension of S0-1versus time for various|z|and v x=340km s−1, v y=−1190km s−1and v z=0in1995.4.Figure2:Declination of S0-1versus time for various|z|and v x=340km s−1,v y=−1190 km s−1and v z=0in1995.4.Figure3:The z−v z phase-space thatfits the S0-1data.Figure4:Examples of typical orbits of S0-1.Figure5:Number of particles versus central degeneracy parameter for m/T=4×106 (solid),3.5×106(short dashs),4.5×106(long dashs),and5×106(dot-dashed line). Figure6:The density profile of the halo for a central degeneracy parameterη0=0 (dotted line)and for the sixη0-values discussed in the text.Configurations with negative η0((1)-(3))are depicted by the dashed and those with positiveη0((1’)-(3’))by the solid line.Figure7:Mass of the halo M h(r)enclosed within a radius r for various central degeneracy parametersη0as in Fig.6.Figure8:Enclosed mass of halo plus bulge versus radius forη0=24(dashed),28(solid), and32(dot-dashed line).Figure9:Fit to the rotation curve of the Galaxy.The data points are from[34]for R0=8.5kpc andΘ0=220km/s.Figure10:Energy(shifted by12×10−8m)versus temperature(shifted by−24×10−8m), both in units of10−10m,forfixed N=2×1012M⊙/m13。

Clumpy Neutralino Dark Matter

Clumpy Neutralino Dark Matter

a r X i v :a s t r o -p h /9806072v 1 4 J u n 1998USITP/98-08MPI-PhT/98-43June 1998Clumpy Neutralino Dark MatterLars Bergstr¨o mDepartment of Physics,Stockholm University,Box 6730,SE-11385Stockholm,Sweden;lbe@physto.seJoakim Edsj¨oCenter for Particle Astrophysics,University of California,301Le Conte Hall,Berkeley,CA 94720-7304,U.S.A;edsjo@Paolo GondoloMax Planck Institut f¨u r Physik,F¨o hringer Ring 6,80805Munich,Germany;gondolo@mppmu.mpg.dePiero UllioDepartment of Physics,Stockholm University,Box 6730,SE-11385Stockholm,Sweden;piero@physto.seAbstractWe investigate the possibility to detect neutralino dark matter in a sce-nario in which the galactic dark halo is clumpy.We find that under customary assumptions on various astrophysical parameters,the antiproton and contin-uum γ-ray signals from neutralino annihilation in the halo put the strongest limits on the clumpiness of a neutralino halo.We argue that indirect detection through neutrinos from the Earth and the Sun should not be much affected by clumpiness.We identify situations in parameter space where the γ-ray line,positron and diffuse neutrino signals from annihilations in the halo may provide interesting signals in upcoming detectors.I.INTRODUCTIONThe mystery of the dark matter in the Universe remains unsolved.Among the more plausible candidates(not only needed to solve the dark matter problem)can be found the neutralino,the lightest supersymmetric particle in the Minimal Supersymmetric Standard Model(MSSM)(for a review,see[1]).Another candidate is for instance the axion which is still a viable option for a narrow range of axion masses[2].Irrespective of the exact nature of the dark matter,there are reasons to believe that its distribution in the dark halos of galaxies need not be perfectly smooth[3–5].For instance,earlyfluctuations in the dark matter may go non-linear long before photon decoupling,evading the argument of slow, linear growth after recombination.Also,if cosmic strings or other defects exist,they may seed the formation of density-enhanced dark matter clumps.Since very little is known about the inherently non-linear problem of generating dark matter clumps,in this paper we will use a phenomenological approach where we simply assume the existence of clumps with a given density profile,making up a certain fraction of the total mass of the Milky Way halo.We investigate the effect of this clumpiness on the various proposed detection methods for neutralino dark matter.Detection rates depend crucially on the neutralino distribution in momentum and position space.Some detection rates,in particular those of antiprotons and photons generated by neutralino annihilations in the galactic halo,increase substantially compared to the case of a smooth dark matter distribution.For a given set of parameters of the supersymmetric models(such as mass and couplings of the neutralinos)we can then use present experimental limits on thesefluxes to bound the degree of clumpiness allowed in that particular dark matter model.Alternatively, given a positive experimental signature,we can identify regions in the combined parameter space of halo dark matter distribution and supersymmetric models to identify candidates consistent with the data.This approach was used recently by three of us in connection with new data from the EGRET gamma ray detector[6].Some of our results may be of interest also in the standard non-clumpy scenario,which is of course included in our treatment and is easily recovered by putting the fraction of the halo in the form of clumps equal to zero.II.CLUMPINESS IN THE MILKY W AY HALO Present observational data give very poor constraints on the distribution of dark matter in the galaxy.The dynamics of the outer satellites of the galaxy clearly indicates that luminous matter provides just a fraction of the total mass of the Milky Way and that the major contribution must come from a dark matter halo whose size is larger than the radius of the disk.Nevertheless it is not possible to extract from present kinematic information any accurate knowledge of the density profile of the dark matter halo.It is,however,natural to assume that galactic dark matter profiles obey a law of universality.Then,a possible approach is to infer the functional form of the Milky Way halo density profile from the results of N-body simulations of hierarchical clustering in cold dark matter cosmologies,fitting the normalization parameters to known dynamical constraints.This approach hasbeen followed in Ref.[7]:among the general family of spherical density profiles,ρ( x)=ρ0 R01+(| x|/a)α (β−γ)/α,(1)it was considered the case of the Kravtsov et al.profile[8]which is mildly singular towards the galactic centre withγ∼0.2–0.4,of the Navarro et al.profile[9]which is more cuspy (γ=1),and,for comparison the modified isothermal distribution,(α,β,γ)=(2,2,0), extensively used in dark matter detection computations.The dark matter density profile inferred in this way should be regarded as the function that describes the average distribution of dark matter in the galactic halo;the standard assumption which is generally made at this stage is that dark matter particles in the halo form a perfectly smooth‘gas’.This approach is in some way arbitrary:although the dark matter particle distribution has to be regarded as smooth on intermediate length scales, probably around0.01–1kpc,there are reasons to question whether this is true on smaller scales.We here entertain the possibility that at least a fraction of the dark matter in the halo is clustered in substructures with high matter density,‘clumps’of dark matter.Several authors have introduced clumpiness as a generic feature of cold dark matter cosmologies.Silk and Stebbins[4]have considered clump formation in cosmic string,texture and inflationary models,giving also predictions for survival to tidal disruption(see also Ref.[3]).Kolb and Tkachev[5]have studied isothermalfluctuations giving very high-density dark matter clumps.Simulations of structure formation in the early Universe do not yet have the dynamical range to give predictions for the size and density distribution of small mass clumps(we focus here mainly on clumps of less than around106solar masses which avoid the problem of unacceptably heating the disk[4]).The formation of clumps on all scales is however a generic feature of cold dark matter models which have power on all length scales.If self-similarity is a guide,galaxy halos may form hierarchically in a similar way to that of cluster halos(see e.g.Ref.[10]).Rather than examining the different scenarios for clump formation,we take a more phe-nomenological approach and perform a detailed discussion on the implications of clumpiness on neutralino dark matter searches.We thus simply postulate that a fraction f of the total dark matter is concentrated in clumps,which are assumed to be spherical bodies of typical mass M cl and matter density profileρcl( r cl).The total number of clumps inside the halo is given by:f·M hN c∼ParameterµM2tanβm A m0A b/m0A t/m0 Unit GeV GeV1GeV GeV11 M hρ( x)d3x(3)which has the correct normalization p cl( x)d3x=1.It is convenient to introduce the dimensionless parameterδδ=1d3r clρcl( r cl)(4)which gives the effective contrast between the dark matter density in clumps and the local halo densityρ0.For a dark matter density inside the clumps which is roughly constant,ρcl, it reduces to the formδ=ρclWe work in the Minimal Supersymmetric Standard Model(MSSM)as defined in Refs.[11,1].For details on our notation,see Ref.[12].The lightest stable supersymmetric particle is in most models the neutralino,which is a superposition of the superpartners of the gauge and Higgsfields,˜χ01=N11˜B+N12˜W3+N13˜H01+N14˜H02.(6) It is convenient to define the gaugino fraction of the lightest neutralino,Z g=|N11|2+|N12|2(7) For the masses of the neutralinos and charginos we use the one-loop corrections as given in [13].The MSSM has many free parameters,but with some simplifying assumptions,we are left with7parameters,which we vary between generous bounds.The ranges for the parameters are shown in Table I.For the detection rates of neutralino dark matter we have used the rates as calculated in Refs.[6,7,14–17].We will throughout this paper assume that the neutralinos make up most of the dark matter in our galaxy.We only consider therefore MSSM models which are cosmologically interesting,i.e.where the neutralinos can make up a major fraction of the dark matter in the Universe without overclosing it.We will choose this range to be0.025<Ωχh2<0.5. For the relic density calculations we have used the detailed calculations performed in Ref.[12].IV.DETECTION METHODS CONSTRAINING CLUMPINESS Some observational consequences of a clumpy dark matter halo have been pointed out previously,such as the obvious gain in gamma ray signal from annihilation in the halo since theflux from a particular volume element is proportional to the square of the dark matter density there[4,5,18–21].Also,in Ref.[22]it was noted that the antiprotonflux could be enhanced,although the treatment was sketchy and not entirely correct concerning the way the rescaling was done.In Ref.[23],it was investigated whether encounters with dark matter clumps on geophysical time scales could have left imprints in ancient mica.As we show in this section,indirect detection through cosmic antiprotons and gamma rays set the most stringent limits on clumpy neutralino dark matter,therefore we investigate these casesfirst.A.Gamma-raysSince gamma rays produced in neutralino annihilations in the halo travel in straight paths essentially without any absorption,and since the annihilation rate and hence theflux would be enhanced by clumps along a particular line-of-sight,the effects of clumpiness are easy to understand.Neutralino annihilation in the galactic halo may produce both aγ-rayflux with a con-tinuum energy spectrum and monochromaticγ-ray lines.The continuum contribution(see Ref.[1]and references therein)is mainly due to the decay ofπ0mesons produced in jets from neutralino annihilations.To model the fragmenta-tion process and extract information on the number and energy spectrum of theγs produced we have used the Lund Monte Carlo Pythia6.115[24].We have performed the simulation for18neutralino masses between10and5000GeV and for the c¯c,b¯b,t¯t,W+W−,Z0Z0 and gg annihilation states.For eachfinal state and for each neutralino mass we have simu-lated2.5×105events which are tabulated logarithmically in energy.For any given MSSM model,we then sum over the annihilation channels and interpolate in these tables.For the annihilation channels not included in the simulations,like the ones with one gauge and one Higgs boson as well as those with two Higgs bosons theflux is calculated in terms of theflux from the simulated channels.We include all two-bodyfinal states at the tree level (except light quarks and leptons)and the one-loop processes Zγand gg.Forfinal states with Higgs bosons,we let the Higgs bosons decay inflight by summing the contributions to the gammaflux from the Higgs decay products in the Higgs rest system and then boost the spectrum averaging over decay angles.Given the annihilation branching ratios we then get the spectrum for any given MSSM model.The continuum signal lacks distinctive features and it might be difficult to discriminate from other possible sources.It will however be a powerful tool to put constraints on the clumpiness parameters.A much better signature than the continuum contribution is given by monochromatic γ-ray lines which arise from the loop-induced S-wave neutralino annihilations into the2γand Zγfinal states and which have no conceivable background from known astrophysical sources.The amplitude of these two processes in the MSSM was computed only recently at full one loop level[25,26].Large deviations from previous partial results(see Ref.[1]and references therein)were found,in particular it was pointed out that a pure heavy Higgsino has a remarkably high annihilation branching ratio both into2γand Zγ,adding at least a factor of10to previous estimates of the2γline.A detailed phenomenological study is given in Ref.[7]where a smooth halo scenario was considered and it was shown that the monochromatic lines could be detected by the new generation of space-and ground-basedγ-ray experiments,provided that a sensible enhancement of the dark matter density is present towards the galactic centre.We examine here the perspectives of detecting the continuum and the line signals in a given clumpy scenario.Consider a detector with an angular acceptance∆Ωpointing in a direction of galactic longitude and latitude(ℓ,b).The gamma rayflux from neutralino annihilations at a given energy E is given byΦγ(E,∆Ω,ℓ,b)≃1.87·10−8d SdE cont.γ≃ 10GeV10−26cm3s−1 dN FγdE 2γ≃10GeV10−26cm3s−1 δ(E−Mχ)d S Mχ 2 vσZγ4Mχ2 .(9) Here Mχis the neutralino mass,F are the allowedfinal states which contribute to the continuum signal as specified above.For each of these,vσF is the annihilation rate and dN Fγ/dE is the differential energy distribution of produced photons.The product of relative velocity and cross section vσ2γis the annihilation rate into the2γfinal state(as given in Ref.[25]).Similarly,vσZγis the rate into the Zγfinal state(as given in Ref.[26]).In Eq.(8) the dependence of theflux on the dark matter distribution,the direction of observation(ℓ,b) and the angular acceptance of the detector∆Ωis contained in the factor J(ℓ,b) (∆Ω). If we assume a spherical dark matter halo in the form of a perfectly smooth distribution of neutralinos,it is equal toJ(ψ) (∆Ω)=1∆Ω ∆ΩdΩ′line of sight dL ρ(L,ψ′) 3 2/3δ∆Ωf2M clclumps of dark matter if one would detect with an ACT theγ-ray lines from neutralino annihilations.For such a method to be practical,higher overdensitiesδmay be needed.It should also be kept in mind that Eq.(11)gives just a qualitative feature of the possible result;the possibility for the nearest clump of being much further away or a more realistic density profile may change that result by orders of magnitude.Muchfirmer predictions may be formulated in the many small clumps scenario;in this case we assume that most of the clumps cannot be resolved even by a detector with a rather small angular acceptance,say about∆Ω∼10−3sr.There might still be some clumps which are resolvable just because they happen to be nearby and these should be treated as in the previous case.From Eq.(3),the probability for a clump of being at a line of sight distance(L,L+dL), a viewing angle defined by(cosψ,cosψ+d cosψ)and at some azimuthal angle with respect to the direction of the galactic center(φ,φ+dφ)is given byp cl(L,ψ)dL d cosψdφ=18.5kpcN clL2 d3r clρcl( r cl)8.5kpc fδ0.3GeV/cm3 ·· ∆ΩdΩ′ line of sight dL ρ(L,ψ′)10-11101021031040306090| 0 306090L. Bergström, J. Edsjö, P. Gondolo and P. Ullio, 1998latitude b (deg)〈 J (b , l =0) 〉 (∆Ω = 10-3 s r )b) Isothermal sphere:a) Navarro et al.:a = 3.5 kpc ρ0 = 0.3 GeV cm -3R 0 = 8.5 kpc f δ = 20a = 9 kpc ρ0 = 0.3 GeV cm -3R 0 = 8.5 kpc f δ = 20sum smooth clumpsFIG.1.The value of J (ψ)) (∆Ω)for two different halo profiles.The contribution from the smooth and clumpy component are also given.considering the flux towards the galactic centre which as shown in Fig.1is maximal.The modified isothermal profile of Fig.1givesJ (90◦) smooth (0.84sr )+ J (90◦) clumps (0.84sr )≃0.93·(1+1.8·fδ).(15)For simplicity we have made the reasonable assumption that f is small.If that is not true we have to replace 1by (1−f )2in the above equation (as well as Eq.(20)below).The analogous estimates with any of the halo models considered in Ref.[7]are within a factor of 2of the value given in Eq.(15).There is therefore a very weak halo model dependence in these results.In Fig.2(a)we plot the integrated γ-ray flux above the energy threshold E th =1GeV for our set of MSSM models in the smooth halo scenario.Also shown in the figure is the corresponding γ-ray flux measured by the Energetic Gamma Ray Experiment Telescope (EGRET)as inferred from the analysis in Ref.[27]:Φγ(E >1GeV)=(1.0±0.2)×10−6cm −2s −1sr −1.(16)We can compare with this value to obtain a constraint on the allowed values of the parameter fδ.It is however useful to analyse this together with the analogous constraint we can derive in the scenario of many small clumps from neutralino annihilations into cosmic ray antiprotons.B.AntiprotonsNeutralino annihilations of relic neutralinos in the galaxy may produce cosmic ray an-tiprotons ([1]and references therein,[22,28])mainly from jets,in a process which is anal-ogous to the case of continuum γ-rays.To model the fragmentation process and extract information on the number and energy spectrum of the antiprotons produced we have again10-1210-1110-1010-910-810-710-610-510102103104Gaugino-like MixedHiggsino-likeL. Bergström, J. Edsjö, P. Gondolo and P. Ullio, 1998EGRET measured γ fluxSmooth haloE thγ = 1 GeVNeutralino Mass (GeV)Φc o n t . γ (c m -2 s -1 s r -1)1010101010101010101010104Neutralino Mass (GeV)Φ- p (c m -2 s -1 s r -1 G e V -1)FIG.2.The signal of (a)continuum gamma and (b)antiprotons versus the neutralino mass.Only models with 0.025<Ωχh 2<0.5have been included in this and the following figures.used the Lund Monte Carlo Pythia 6.115and applied the same tabulation technique as for the production of photons.Including the same set of final states and treating the Higgs bosons in the same way,for any given MSSM model we can then obtain the energy spectrum of antiproton dark matter sources.If we assume a smooth distribution of WIMPs in the galaxy,the production rate of antiprotons in the volume element d 3x at the galactic position x is given byd R sm ( x )M χ2·FvσFdN F¯p dTd 3x =N cl p cl ( x )d 3r cl ρ2cl ( r cl )·FvσFdN F¯p M χ2·FvσFdN F ¯p11010210310410510610710810910102103104Antiprotons Continuum γL. Bergström, J. Edsjö, P. Gondolo and P. Ullio, 1998Neutralino Mass (GeV)M a x i m a l r e s c a l i n g , f δ10-310-210-111010210102103104Gaugino-like MixedHiggsino-likeL. Bergström, J. Edsjö, P. Gondolo and P. Ullio, 1998Antiprotons more restrictiveCont. γ more restrictiveNeutralino Mass (GeV)(Φ- p / Φl i m i t ) / (Φc o n t . γ / Φl i m i t )FIG.3.The maximal rescaling allowed by the present limits on the antiproton flux and the continuum gamma ray flux.the measured flux at some low value of the kinetic energy,where the ‘trivial’antiproton flux generated by cosmic-ray reactions in the interstellar medium is believed to be less dominant.At T =400MeV the result found by BESS isΦ¯p (T =400MeV)=1.4+0.9−0.6×10−6¯p cm −2s −1sr −1GeV −1.(19)In Fig.2(b)we compare this value with the predictions for antiprotons from neutralino annihilations in a smooth halo scenario (i.e.the source given as in Eq.(17))at the same energy,using for the diffusion model the same set of parameters as in Ref.[28],consider-ing appropriate values of the solar modulation parameters and picking as halo profile the modified isothermal distribution.It is indeed tempting to conclude that some of our models are already excluded by the BESS measurement.However,one has to keep in mind the big uncertainties involved,mainly in the antiproton propagation;for instance it is not clear how large a fraction of antiprotons generated in the halo can penetrate the wind of cosmic rays leaving the disk [29].We introduce in the flux predictions a rescaling factor k which contains the uncertainties deriving from the choice of the parameters which define the propagation model considered and from possible deviations from this simple approach.We consider now the many small clumps scenario.The production rate of antiprotons in this case is given by Eq.(17);the strength of the signal compared to the smooth case is again mainly determined by the product fδ.At T =400MeV and for the same halo profile considered above,we find:Φ¯p =k (1+0.75·fδ)·Φsmooth¯p .(20)We have checked that the coefficient 0.75depends very weakly on the halo profile considered and on T .A conservative limit on the clumpiness parameter fδcan be obtained choosing the uncertainty factor k ask ∈[0.2,5].(21)10101010101010101010101010101010-5Φcont. γ (cm -2 s -1 sr -1)Φ- p (c m -2 s -1 s r -1 G e V -1)FIG.4.The antiproton flux versus the continuum γflux for a smooth halo.We consider a value of fδexcluded if the whole range of possible antiproton fluxes given by Eqs.(20)and (21)exceeds the measured value,Eq.(19).C.Determining the clumpiness factor fδWe have shown that in the many small clumps scenario the signals from dark matter annihilations into γ-rays and antiprotons depend critically on the clumpiness parameter fδ.Focusing on the MSSM,we use the rescalings derived in Eqs.(15)and (20)to determine for each supersymmetric model the maximal value of fδfor which the experimental constraints on the fluxes of continuum photons and antiprotons are not violated.This is shown in Fig.3(a),where the maximal rescaling is given versus the neutralino mass,and where we use different symbols to indicate which of the two bounds is more restrictive.As can be seen,the antiproton flux puts the highest constraints on the clumpiness at low masses,whereas the continuum gammas put better constraints at higher masses.We see that the presentexperimental limits constrain fδ∼<109for all masses.As shown in Fig.4,the two signals are strongly correlated since they are both produced from jets.In this sense the information we get from the two experimental limits is not entirely complementary.At higher masses,both fluxes go down since they are both proportionalto 1/M 2χ,but the correlation also decreases since the antiproton fluxes are only given in a small energy interval while the gamma ray fluxes are integrated above a threshold.Hence the antiproton flux in a given low energy interval decreases more than the gamma ray flux as we go to higher neutralino masses.In Fig.3(b)we analyse how restrictive one detection method is compared to the other.Having derived for each of the MSSM models in our sample the maximal allowed value for the clumpiness parameter fδ,in the next section we analyse the consequences of this result for other indirect detection methods of neutralino dark matter.11010210310410102Gaugino-like MixedHiggsino-likeL. Bergström, J. Edsjö, P. Gondolo and P. Ullio, 1998G L AS T5σ l i m i tMaximally rescaled 2γ linePhoton Energy (GeV)N u m b e r o f p h o t o n s i n 4 y e a r s11010210310410102Gaugino-like MixedHiggsino-likeL. Bergström, J. Edsjö, P. Gondolo and P. Ullio, 1998GLAST 5σ limitMaximally rescaled Z γ linePhoton Energy (GeV)N u m b e r o f p h o t o n s i n 4 y e a r sFIG.5.The number of expected photons in 0.84sr towards b =90◦collected in 4years from (a)the 2γand (b)the Zγfinal states.The expected 5σlimit from the GLAST detector is also shown.V.OTHER DETECTION METHODSIn this section we consider the many small clumps scenario with the highest possible value of fδas given in the previous section and investigate what effect that has on other dark matter searches.We fix again as smooth halo distribution to compare with the modified isothermal distribution,Eq.(1)with (α,β,γ)=(2,2,0),ρ0=0.3GeV cm −3,a =3.5kpc and R 0=8.5kpc.A.Monochromatic γ-ray linesAs we have seen,the same scaling applies to the continuum and the line γ-ray signals,it is therefore straightforward to derive the maximal fluxes of monochromatic photons from neutralino annihilations.We perform this analysis in light of the potential of the next generation of satellite-based γ-ray detectors,and in particular of the proposed Gamma-ray Large Area Space Telescope (GLAST)[31].To prevent uncertainties due to the choice of the dark matter halo profile to play any role in the following discussion,we fix again as field of view a 0.84sr cone in the direction b =90◦.In the actual experiment the detector will collect data with a 4πsr angular acceptance;as for most halo profiles the ratio signal to squared root of the background is greatly enhanced towards the galactic centre,the predictions we show are an underestimate of the possible results.Taking into account the screening of the earth,the useful geometrical acceptance of GLAST towards a fixed point of the sky in a 0.84sr cone is 0.21m 2sr [32];the energy resolution is assumed to be 1.5%.We display in Fig.5the number of expected γs in 4years110102103104105102103104Gaugino-like MixedHiggsino-likeL. Bergström, J. Edsjö, P. Gondolo and P. Ullio, 1998Neutralino Mass (GeV)(Φµ(0)-Φµ(180)) (k m -2 y r -1 s r -1)Vertical, 3σHorizontal, 3σMaximally rescaledE µth = 100 GeVFIG.6.The difference of the diffuse neutrino flux towards the galactic centre to that to the antigalactic centre.The fluxes are averaged over 2.5sr which maximizes signal to noise and they are rescaled maximally as allowed by the antiproton and continuum γfluxes.The limits are for a neutrino telescope with an exposure of 10km 2yr.of exposure time when the fluxes have been maximally rescaled according to Fig.3.Also shown is the curve giving the minimum number of events needed to observe an effect at the 5σlevel,where,in lack of data,we have assumed above 1GeV a 2.7power law fallofffor the diffuse γ-ray background and inferred its normalization from Ref.[27].As can be seen,a fair fraction of our set of supersymmetric models can be probed under these circumstances.Remember that the number of photons given in Fig.5is towards b =90◦and,depending on halo profile,we expect more events towards the galactic centre,with a larger portion of the MSSM parameter space which might be probed.B.Diffuse neutrinosA possibility to get a detectable neutrino flux from WIMP annihilations which has rarely been considered in the literature is neutrinos from annihilation in the galactic halo.Of particular importance is χχ→W +W −,since the W bosons decay in 10%of the cases directly to a muon plus a muon neutrino with a hard neutrino spectrum,which may facilitate detection in neutrino telescopes.This flux would scale in exactly the same way as the gamma flux in the presence of clumps and with future O (km 3)neutrino-telescopes,the diffuse neutrinos might prove more constraining than antiprotons and continuum γs at high masses (several hundred GeV –TeV region)where the rescaling can be high (fδ>103).The flux has been calculated in essentially the same way as for neutralino annihilation in the Sun/Earth [15]with the help of the Lund Monte Carlo Pythia 6.115.The only difference is that some annihilation products will decay and produce neutrinos in the halo,whereas they are stopped before they decay in the Sun/Earth.The neutrino-induced muonflux from neutralino annihilations in a smooth halo is about 10−8–1km−2yr−1sr−pare this with the atmospheric background of about9500km−2yr−1sr−1vertically and30000km−2yr−1sr−1horizontally[33]for this threshold.To be able to distinguish the signal from the background we have to rescale the fluxes by the allowed clumpiness factor derived in the previous section and we also have to make use of the fact that the signal is enhanced towards the centre of the galaxy.The best prospects are probably given by large-area neutrino telescopes with relatively high detection thresholds.We can imagine measuring theflux in a solid angle∆Ωtowards the galactic centre and compare with theflux in the same solid angle in the opposite direction. The limit we can put on theflux is at the3σ-level approximately given by≃3 E∆Ω.(22) [Φµ(0◦)−Φµ(180◦)]limitwhere E is the exposure.For the modified isothermal sphere,it turns out the best limits are obtained with∆Ω=2.5sr,for which we obtain J(0◦) (∆Ω)=4.16and J(180◦) (∆Ω)= 1.09.In Fig.6we show the difference of the diffuse neutrinoflux towards the galactic centre to that in the opposite direction for a muon energy threshold of100GeV.Also shown are the limits that can be reached with an exposure of10km2yr.For different exposures,the limits change as the square root of the exposure.If we increase the threshold from100GeV, we can gain a small factor in sensitivity at higher masses,but lose at intermediate masses.An ideal neutrino detector for this signal would view the galactic center through the center of the Earth(i.e.it should be at29degrees latitude),since then the atmospheric background is minimal.The strength of the signal of course depends on the halo profile, but it is more likely that the halo profile is steeper towards the galactic centre than the isothermal sphere and hence the signal is even bigger then envisioned here.We might have to worry about other sources of high-energy neutrinos at the galactic centre(like neutrinos from the black hole believed to exist in the centre).These other sources can probably be removed by not looking at the very centre of the galaxy.C.PositronsFrom neutralino annihilation in the halo we would also get aflux of positrons which might be detected by satellite[34]or high-flying balloon experiments[35].The propagation of positrons is a more difficult issue than for antiprotons since positrons are so easily deflected and destroyed.We have calculated the positronfluxes using Pythia6.115[24]and have used the propagation model in Ref.[36]with an energy dependent escape time(a more detailed investigation is in preparation[37]).In Fig.7we show the positronfluxes versus the neutralino mass when they have been rescaled with the maximal fδallowed by the antiproton and the continuum gammafluxes.We compare with the measurement by the HEAT experiment[35]at10GeV.Also shown is the prediction of the background at this energy as given in Ref.[38].It would seem that the positrons put more stringent bounds on fδthan the antiprotons and continuumγs at higher masses.The positronfluxes are however even more uncertain than the antiprotonfluxes and can easily be wrong by a factor。

The-Universe

The-Universe

Passage 5The Universe's Invisible HandBy Christopher J. ConseliceDark energy (暗能量) does more than hurry along the expansion of the universe. It also has a stranglehold on the shape and spacing of galaxiesWhat took us so long? Only in 1998 did astronomers discover we had been missing nearly three quarters of the contents of the universe, the so-called dark energy--an unknown form of energy that surrounds each of us, tugging at us ever so slightly, holding the fate of the cosmos in its grip, but to which we are almost totally blind. Some researchers, to be sure, had anticipated that such energy existed, but even they will tell you that its detection ranks among the most revolutionary discoveries in 20th-century cosmology. Not only does dark energy appear to make up the bulk of the universe, but its existence, if it stands the test of time, will probably require the development of new theories of physics.Scientists are just starting the long process of figuring out what dark energy is and what its implications are. One realization has already sunk in: although dark energy betrayed its existence through its effect on the universe as a whole, it may also shape the evolution of the universe's inhabitants--stars, galaxies, galaxy clusters. Astronomers may have been staring at its handiwork for decades without realizing it.暗能量不仅仅会加速宇宙膨胀。

关于mysteries的英语作文

关于mysteries的英语作文

关于mysteries的英语作文Title: The Enigma of Mysteries.In the vast expanse of human existence, mysteries have always been an integral part of our lives. They are the unknown forces, the unexplained phenomena, and theenigmatic secrets that captivate our imaginations andprompt us to delve deeper into the recesses of the unknown. Mysteries have existed throughout history, across cultures, and in every sphere of human endeavour. They are as old as civilization itself and continue to fascinate us even inthe age of advanced technology and scientific understanding.The allure of mysteries lies in their nature of being both intriguing and perplexing. They are the puzzles that challenge our intellectual capabilities and push the boundaries of our understanding. They are the voids in the fabric of reality that beg for explanation, yet oftenremain enigmatic even in the face of the most diligent investigation.One of the oldest and most enduring mysteries is the question of the origin of life itself. How did the complex machinery of life emerge from the primordial soup of chemicals? How did the first cells come to be, and how did they evolve into the diverse array of organisms we see today? This mystery is compounded by the equally enigmatic question of consciousness how does the brain, a collection of neurons and synapses, give rise to the subjective experience of being alive?Another enduring mystery is the question of the universe's origin and ultimate fate. How did the universe begin with a cataclysmic event known as the Big Bang, and what lies beyond its expanding boundaries? What is the nature of dark matter and dark energy, the mysterious forces that seem to shape the universe's destiny? And what will become of the universe in the distant future will it continue to expand indefinitely, or will it collapse in upon itself in a cataclysmic end?Mysteries also abound in the realm of human history andculture. The ancient civilizations of Egypt, Mesopotamia, and Peru, with their monumental temples and intricate hieroglyphics, are repositories of secrets that have perplexed scholars for centuries. The lost cities of Atlantis and Mu, and the enigmatic legends of El Dorado and the Fountain of Youth, continue to captivate the imaginations of adventurers and explorers.The human mind itself is a mystery. How does the brain process information, store memories, and generate thoughts and emotions? Why do we dream, and what do our dreams reveal about the inner workings of the mind? The study of neuroscience and psychology has yielded valuable insights into these questions, but the mysteries of the mind remain as elusive as ever.In the realm of science, there are mysteries that challenge our understanding of the fundamental laws of nature. Quantum mechanics, with its paradoxical nature and counterintuitive predictions, has been described as the "mystery of mysteries" by some physicists. The enigmatic properties of quantum particles, such as superposition andentanglement, have defied our classical understanding of reality and continue to baffle even the most seasoned scientists.The enduring appeal of mysteries lies in theirpotential to reveal deeper truths about the universe and ourselves. They are the gaps in our knowledge that drive us to explore, to question, and to seek answers. They are the engines of scientific inquiry and human progress. And while some mysteries may never be fully resolved, the pursuit of knowledge and understanding remains an essential part of our human nature.In conclusion, mysteries are an integral part of human existence, and their enigma continues to captivate us. They challenge our understanding, prompt us to inquire, and drive us to explore. As we delve deeper into the recesses of the unknown, we not only gain new insights into the universe and ourselves, but we also honour the enduring spirit of curiosity and wonder that is unique to the human species.。

criminalminds名人名言

criminalminds名人名言

criminalminds名人名言第一篇:criminal minds 名人名言Season1◎Episode 1: Extreme Aggressor(2005.09.22)●The belief in a supernatural source of evil is not necessary.Men alone are quite capable of every wickedness.——Joseph Conrad 【约瑟夫·康拉德(波兰出生的英国作家):将邪恶的产生归结于超自然的因素是没有必要的,人类自身就足以实施每一种恶行。

】●Try again.Fail again.Fail better.——Samuel Beckett 【Samuel Beckett(当代最著名的荒诞剧作家):再试,再失败,更好地失败。

】(Gideon片中台词)●Try not.Do or do not.——Yoda 【尤达大师(『星球大战』中的主角):别试。

做或者不做。

】(Morgan片中台词)●All is riddle,and the key to a riddle…is another riddle.——Emerson 【爱默生(美国诗人、散文家、哲学家):所有的事物都是谜团,而解开一个谜的钥匙……是另一个谜。

】●The farther backward you can look,the farther forward you will see.——Winston Churchill 【温斯顿·邱吉尔:你回首看得越远,你向前也会看得越远。

】●When you look long into an abyss,the abyss looks into you.——Nietzsche 【尼采:当你凝视深渊时,深渊也在凝视你。

】◎Episode 2: Compulsion(2005.09.28)●There are certain clues at a crime scene whic h,by their very nature, do not lend themselves to being collected or examined.How does one collect love, rage, hatred, fear?——Dr.James T.Reese 【詹姆斯·瑞斯博士(美国精神创伤压力处理方面的专家):犯罪现场中的某些线索根据它们自己本身的性质,是不容易收集起来检测的。

  1. 1、下载文档前请自行甄别文档内容的完整性,平台不提供额外的编辑、内容补充、找答案等附加服务。
  2. 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
  3. 3、如文档侵犯您的权益,请联系客服反馈,我们会尽快为您处理(人工客服工作时间:9:00-18:30)。

a rXiv:as tr o-ph/73673v127Mar271DARK MATTER:THE CASE OF STERILE NEUTRINO ∗Mikhail Shaposhnikov Institut de Th´e orie des Ph´e nom`e nes Physiques,Ecole Polytechnique F´e d´e rale de Lausanne,CH-1015Lausanne,Switzerland An extension of the Standard Model by three right-handed neutrinos with masses smaller than the electroweak scale (the νMSM)can explain simultaneously dark matter and baryon asymmetry of the Universe,being consistent with the data on neutrino oscilla-tions.A dark matter candidate in this theory is the sterile neutrino with the mass in keV range.We discuss the constraints on the properties of this particle and mechanisms of their cosmological production.Baryon asymmetry generation in this model is reviewed.Crucial experiments that can confirm or rule out the νMSM are briefly discussed.1.Introduction There is compelling evidence that the Minimal Standard Model (MSM)of strong and electroweak interactions is not complete.There are several experimental facts that cannot be explained by the MSM.These are neutrino oscillations,the presence of dark matter in the Universe,the baryon asymmetry of the Universe,its flatness,and the existence of cosmological perturbations necessary for structure formation.Indeed,in the MSM neutrinos are strictly massless and do not oscillate.The MSM does not have any candidate for non-baryonic dark matter.Moreover,with the present experimental limit on the Higgs mass,the high-temperature phase transi-tion,required for electroweak baryogenesis,is absent.In addition,it is a challenge to use CP-violation in Kobayashi-Maskawa mixing of quarks to produce baryonasymmetry in the MSM.Finally,the couplings of the single scalar field of the MSM are too large for the Higgs boson to play the role of the inflaton.This means that the MSM is unlikely to be a good effective field theory up to the Planck scale.In 1–3it was proposed that a simple extension of the MSM by three singlet right-handed neutrinos and by a real scalar field (inflaton)with masses smaller than the electroweak scale may happen to be a correct effective theory up to some high-energy scale,which may be as large as the Planck scale.This model was called “the νMSM”,underlying the fact that it is the extension of the MSM in the neutrino sector.Contrary to Grand Unified Theories,the νMSM does not have any internal2hierarchy problem,simply because it is a theory with a single mass scale.Moreover, as the energy behaviour of the gauge couplings in this theory is the same as in the MSM,the absence of gauge-coupling unification in it indicates that there may be no grand unification,in accordance with our assumption of the validity of this theory up to the Planck scale.As well as the MSM,theνMSM does not provide any explanation why the weak scale is much smaller than the Planck scale.Similarly to the MSM,all the parameters of theνMSM can be determined experimentally since only accessible energy scales are present.As we demonstrated in,1,2theνMSM can explain simultaneously dark matter and baryon asymmetry of the Universe being consistent with neutrino masses and mixings observed experimentally.Moreover,in3we have shown that inclusion of an inflaton with scale-invariant couplings to thefields of theνMSM allows us to have inflation and provides a common source for electroweak symmetry breaking and Majorana neutrino masses of singlet fermions–sterile neutrinos.The role of the dark matter is played by the lightest sterile neutrino with mass m s in the keV range.In addition,the coherent oscillations of two other,almost degenerate,sterile neutrinos lead to the creation of baryon asymmetry of the Universe2through the splitting of the lepton number between active and sterile neutrinos4and electroweak sphalerons.5For review of other astrophysical applications of sterile neutrinos see talk by Peter Biermann at this conference.6In this talk I review the structure of theνMSM and discuss its dark matter candidate–sterile neutrino.The baryogenesis in this model is briefly reviewed. 2.TheνMSMIf three singlet right-handed fermions N I are added to the Standard Model,the most general renormalizable Lagrangian describing all possible interactions has the form:M ILνMSM=L MSM+¯N I i∂µγµN I−FαI¯LαN IǫΦ∗−[M D]T(2)M I3 is valid.Though it is known that the masses of active neutrinos are smaller than O(1)eV,it is clear that the scale of Majorana neutrino masses cannot be extracted. This is simply because the total number of physical parameters describing mνis equal to9(three absolute values of neutrino masses,three mixing angles and three CP-violating phases),which is two times smaller than the number of new parameters in theνMSM.A most popular proposal7is to say that the Yukawa couplings F in the active-sterile interactions are of the same order of magnitude as those in the quark and charged lepton sector.This choice is usually substantiated by aesthetic considera-tions,but is not following from any experiment.Then one has to introduce a new energy scale,M I∼1010−1015GeV,which may be related to grand unification.The model with this choice of M I has several advantages in comparison with the MSM: it can explain neutrino masses and oscillations,and give rise to baryon asymme-try of the Universe through leptogenesis8and anomalous electroweak number non-conservation at high temperatures.5However,it cannot explain the dark matter as the low energy limit of this theory is simply the MSM with non-zero active neutrino masses coming from dimensionfive operators.On a theoretical side,as a model with two very distinct energy scales it suffers from afine-tuning hierarchy problem M I≫M W.Also,since the energy scale which appears in this scenario is so high, it would be impossible to make a direct check of this conjecture by experimental means.Another suggestion is tofix the Majorana masses of sterile neutrinos in1−10eV energy scale9to accommodate the LSND anomaly.10The theory with this choice of parameters,however,cannot explain the baryon asymmetry of the Universe and does not provide a candidate for dark matter particle.Yet another paradigm is to determine the parameters of theνMSM from avail-able observations,i.e.from requirement that it should explain neutrino oscillations, dark matter and baryon asymmetry of the universe in a unified way.It is this choice that will be discussed below.It does not require introduction of any new en-ergy scale,and M I<M W.In this case the Yukawa couplings must be much smaller than those in the quark sector,F<10−6.The theory has a number of directly testable predictions,which can confirm or reject it.3.Dark matterThough theνMSM does not offer any stable particle besides those already present in the MSM,it contains a sterile neutrino with a life-time exceeding the age of the Universe,provided the corresponding Yukawa coupling is small enough.The decay rate of N1to three active neutrinos and antineutrinos(assuming that N1is the lightest sterile neutrino)is given byΓ3ν=G2F M51θ2M1,m20= α=e,µ,τ|M Dα1|2,(3)4where G F is the Fermi constant.For example,a choice of m0∼O(1)eV and of M1∼O(1)keV leads to a sterile neutrino life-time∼1017years.11 The mass of the sterile dark matter neutrino cannot be too small.An application of the Tremaine-Gunn arguments12to the dwarf spheroidal galaxies13gives the lower bound14M1>0.3keV.If the sterile neutrino mass is in the keV region,it may play a role of warm dark matter.15,16Sterile neutrino free streaming length an matter-radiation equality is given byλF S≃1Mps 1keV3.15 (4) and the mass insideλF S isM F S≃3×1010M⊙ 1keV3.15 3,where<p s>(<p a>)is an average momentum of sterile(active)neutrino at the moment of structure formation,M⊙is the solar mass.One normally defines cold dark matter(CDM)as that corresponding to M F S<105M⊙,hot DM as the one with M F S>1014M⊙,and warm DM as anything in between.Potentially, WDM could solve some problems of the CDM scenario,such as the missing satellites problem17,18and the problem of cuspy profiles in the CDM distributions.19,20 Even stronger constraint on the mass of sterile neutrino comes from the analysis of the cosmic microwave background and the matter power spectrum inferred from Lyman-αforest data21,22:M1>M0 <p s>51e-14 1e-131e-12 1e-111e-10Yu ka w ac o u p lings,fm D[e V ]M 1, keVFig.1.Upper bound on Yukawa coupling constant (left vertical axis)and Dirac mass (right vertical axis)of dark matter sterile neutrino,coming from X-ray observations of Large Magellanic Cloud (LMC)and Milky Way (MW)by XMM-Newton and HEAO-1satellites.characterized by parameter θ.In fact,this mixing is temperature dependent:37θ→θM ≃θ1keV 1/3MeV,whichcorresponds to the temperature of the QCD cross-over for keV scale sterile neutri-nos.This fact makes an exact estimate of the number of produced sterile neutrinos to be a very difficult task (see 36for a discussion of the general formalism for com-putation of sterile neutrino abundance),since T peak happens to be exactly at the point where the quark-gluon plasma is strongly coupled and the dilute hadron gas picture is not valid.The chiral perturbation theory works only at T <50MeV.The perturbation theory in QCD works only at T ≫ΛQCD ,and the convergence is very slow.The lattice simulations work very well for pure gluodynamics.However,no results with three light quarks and with reliable extrapolation to continuum limit are available yet.Also,the treatment of hadronic initial and final states in reactions ν+q →ν+q,q +¯q →ν¯νis quite uncertain.In refs.11,15the computation of sterile neutrino production was done with the use of simplified kinetic equations and without accounting for hadronic degrees of freedom.In 16,38some effects related6to existence of quarks and hadrons in the media were included;the same type of ki-netic equations were used.In39a computation of sterile neutrino production based onfirst principles of statistical physics and quantumfield theory has been done and uncertainties related to hadronic dynamics were analyzed.The results are pre-sented in Fig.2.They correspond to the case when there is no entropy production (S=1)due to decay of heavier sterile neutrinos of theνMSM.40The area above dotted line is certainly excluded:the amount of produced dark matter would lead to over-closer of the universe.The region below dashed line is certainly allowed: the amount of sterile neutrinos produced due to active-sterile transitions is smaller than the amount of dark matter observed.Any point in the region between two solid lines(corresponding to the“most reasonable”model for hadronic contribution39) can lead to dark matter generation entirely due to active-sterile transitions.Maxi-mal variation of the hadronic model,defined in39extends this region to the space between dotted and dashed lines.In the case of entropy production with S>1all these four lines simply move up by a factor S.One can see that the active-sterile mixing can accommodate for all dark matter only if M1<3.5keV,if the“most reasonable”hadronic model is taken.The most conservative limit would correspond to M1<6keV,if all hadronic uncertainties are pushed in the same direction and the uncertainty by a factor of2is admitted for the X-ray bounds.Therefore,if Lyman-αconstraints of23,24are taken for granted, the production of sterile neutrinos due to active-sterile neutrino transitions happens to be too small to account for observed abundance of dark matter.In other words, physics beyond theνMSM is likely to be required to produce dark matter sterile neutrinos.Another option is to assume that the universe contained relatively large lepton asymmetries.41In3it was proposed the theνMSM may be extended by a light inflaton in order to accommodate inflation.To reduce the number of parameters and to have a common source for the Higgs and sterile neutrino masses the inflaton-νMSM couplings can be taken to be scale invariant on the classical level:LνMSM→LνMSM[M→0]+12¯NIc NIχ+h.c.−V(Φ,χ),(5)where the Higgs-inflaton potential is given by:V(Φ,χ)=λ Φ†Φ−α4χ4−171010M 1 / keV1010101010si n 22θFig.2.X-ray constraints from 28,32versus required mixing of sterile neutrino in Dodelson-Widrow scenario.It is assumed that no entropy production from decays of heavier sterile neutrinos of the νMSM is taking place.The area between two solid lines corresponds to all possible variations of mixing angles to different leptonic families for “best choice”hadronic dynamics.39The area between dotted and dashed lines corresponds to most conservative estimate of hadronic uncertain-ties.39neutrino abundance due to inflaton decays:χ→NN is given byΩs ≃0.26ΓM 0m sζ(3).So,for m I ∼300MeV (m I ∼100GeV)the correct Ωs is obtained for m s ∼16−20keV (m s ∼O (10)MeV).A sterile neutrino in this mass range is perfectly consistent with all cosmological and astrophysical observations.As for the bounds on mass versus active–sterile mixing coming from X-ray observations of our galaxy and its dwarf satellites,they are easily satisfied since the production mechanism of sterile neutrinos discussed above has nothing to do with the active–sterile neutrino mixing leading to the radiative mode of sterile neutrino decay.5.Baryon Asymmetry of the UniverseThe baryon (B)and lepton (L)numbers are not conserved in the νMSM.The lep-ton number is violated by the Majorana neutrino masses,while B +L is broken by8the electroweak anomaly.As a result,the sphaleron processes with baryon number non-conservation are in thermal equilibrium for100GeV<T<1012GeV.As for CP-breaking,theνMSM contains6CP-violating phases in the lepton sector and a Kobayashi-Maskawa phase in the quark sector.This makes two of the Sakharov conditions43for baryogenesis satisfied.Similarly to the MSM,this theory does not have an electroweak phase transition with allowed values for the Higgs mass,44mak-ing impossible the electroweak baryogenesis,associated with the non-equilibrium bubble expansion.However,theνMSM contains extra degrees of freedom-sterile neutrinos-which may be out of thermal equilibrium exactly because their Yukawa couplings to ordinary fermions are very small.The latter fact is a key point for the baryogenesis in theνMSM,ensuring the validity of the third Sakharov condition.In4it was proposed that the baryon asymmetry can be generated through CP-violating sterile neutrino oscillations.For small Majorana masses the total lepton number of the system,defined as the lepton number of active neutrinos plus the total helicity of sterile neutrinos,is conserved and equal to zero during the Universe’s evolution.However,because of oscillations the lepton number of active neutrinos becomes different from zero and gets transferred to the baryon number due to rapid sphaleron transitions.Roughly speaking,the resulting baryon asymmetry is equal to the lepton asymmetry at the sphaleron freeze-out.The kinetics of sterile neutrino oscillations and of the transfers of leptonic num-ber between active and sterile neutrino sectors has been worked out in.2The effects to be taken into account include oscillations,creation and destruction of sterile and active neutrinos,coherence in sterile neutrino sector and its lost due to interaction with the medium,dynamical asymmetries in active neutrinos and charged leptons. The corresponding equations are written in terms of the density matrix for sterile neutrinos and concentrations of active neutrinos and are rather lengthy and will not be presented here due to the lack of space.They can be found in the original work.2The corresponding equations are to be solved with the choice of theνMSM parameters consistent with the experiments on neutrino oscillations and with the requirement that dark matter neutrino has the necessary properties.The value of baryon to entropy ratio n B≃1.7·10−10δCP 10−53 M33,swhere M2,3are the masses of the heavier sterile neutrinos,∆M232=M23−M22,and the CP-breaking factorδCP is expressed through the different mixing angles and CP-violating phases,parameterizing the Dirac neutrino masses,and can be O(1), given the present experimental data on neutrino oscillations.This shows that the correct baryon asymmetry of the Universe n B9 It is interesting to note that for masses of sterile neutrinos>100GeV the mechanism does not work as the sterile neutrinos equilibrate.Also,the temperature of baryogenesis is rather low,T L≃(∆M2M P l)11011. A.D.Dolgov and S.H.Hansen,Astropart.Phys.16(2002)339.12.S.Tremaine and J.E.Gunn,Phys.Rev.Lett.42(1979)407.13. D.N.C.Lin and S.M.Faber,Astrophys.J.266(1983)L21.14.J.J.Dalcanton and C.J.Hogan,Astrophys.J.561(2001)35.15.S.Dodelson and L.M.Widrow,Phys.Rev.Lett.72(1994)17.16.K.Abazajian,G.M.Fuller and M.Patel,Phys.Rev.D64(2001)023501.17. B.Moore et al.,Astrophys.J.524(1999)L19.18.P.Bode,J.P.Ostriker and N.Turok,Astrophys.J.556(2001)93.19.T.Goerdt et al.,Mon.Not.Roy.Astron.Soc.368(2006)1073.20.G.Gilmore et al.,arXiv:astro-ph/0608528.21.S.H.Hansen,J.Lesgourgues,S.Pastor and J.Silk,Mon.Not.Roy.Astron.Soc.333(2002)544.22.M.Viel,J.Lesgourgues,M.G.Haehnelt,S.Matarrese and A.Riotto,Phys.Rev.D71(2005)063534.23.U.Seljak,A.Makarov,P.McDonald and H.Trac,Phys.Rev.Lett.97(2006)191303.24.M.Viel,J.Lesgourgues,M.G.Haehnelt,S.Matarrese and A.Riotto,Phys.Rev.Lett.97(2006)071301.25.K.Abazajian,G.M.Fuller and W.H.Tucker,Astrophys.J.562(2001)593.26. A.Boyarsky,A.Neronov,O.Ruchayskiy and M.Shaposhnikov,Mon.Not.Roy.As-tron.Soc.370(2006)213.27. A.Boyarsky,A.Neronov,O.Ruchayskiy and M.Shaposhnikov,Phys.Rev.D74(2006)103506.28. A.Boyarsky,A.Neronov,O.Ruchayskiy,M.Shaposhnikov and achev,Phys.Rev.Lett.97(2006)261302.29.S.Riemer-Sorensen,S.H.Hansen and K.Pedersen,Astrophys.J.644(2006)L33.30. C.R.Watson,J.F.Beacom,H.Yuksel and T.P.Walker,Phys.Rev.D74(2006)033009.31.S.Riemer-Sorensen,K.Pedersen,S.H.Hansen and H.Dahle,astro-ph/0610034.32. A.Boyarsky,J.Nevalainen and O.Ruchayskiy,astro-ph/0610961.33. A.Boyarsky,O.Ruchayskiy and M.Markevitch,astro-ph/0611168.34.K.N.Abazajian,M.Markevitch,S.M.Koushiappas and R.C.Hickox,arXiv:astro-ph/0611144.35. A.Boyarsky,J.W.d.Herder,A.Neronov and O.Ruchayskiy,arXiv:astro-ph/0612219.36.T.Asaka,ine and M.Shaposhnikov,JHEP0606(2006)053.37.R.Barbieri and A.Dolgov,Phys.Lett.B237(1990)440.38.K.Abazajian,Phys.Rev.D73(2006)063513.39.T.Asaka,ine and M.Shaposhnikov,JHEP0701(2007)091.40.T.Asaka,M.Shaposhnikov and A.Kusenko,Phys.Lett.B638(2006)401.41.X.Shi and G.M.Fuller,Phys.Rev.Lett.82(1999)2832.42. A.D.Linde,Phys.Lett.B129(1983)177.43. A.D.Sakharov,Pisma ZhETF5(1967)32.44.K.Kajantie,ine,K.Rummukainen and M.E.Shaposhnikov,Phys.Rev.Lett.77(1996)2887.45.M.Shaposhnikov,Nucl.Phys.B763(2007)49.46. A.Boyarsky,A.Neronov,O.Ruchayskiy and M.Shaposhnikov,JETP Lett.83(2006)133.47.G.Bernardi et al.,Phys.Lett.B203(1988)332.48.P.Astier et al.[NOMAD Collaboration],Phys.Lett.B506(2001)27.49. F.Bezrukov and M.Shaposhnikov,Phys.Rev.D75(2007)053005.。

相关文档
最新文档