Higgs boson production at hadron colliders in the k_T-factorization approach
希格斯玻色子解读
希格斯说希格斯玻色子将很快被发现据新华社日内瓦2008年4月12日电在40多年前预言了希格斯玻色子存在的英国物理学家彼得·希格斯，日前在参观欧洲核子研究中心的大型强子对撞机（LHC）时对媒体说：“几乎可以确定，很快就可以发现希格斯玻色子。
”希格斯玻色子被认为是物质的质量之源，它是“标准模型”这一粒子物理学理论中最后一种未被证实的粒子，但是它的存在却是整个“标准模型”的基石。
因此，它被称为粒子物理学的“圣杯”，也被称为“上帝粒子”，充满了神秘色彩。
自从希格斯预言这一粒子存在以来，科学家们就一直试图在实验中发现该粒子从而证实其存在，但至今所有努力均告失败。
于2003年开始兴建的欧洲大型强子对撞机位于法国和瑞士边境地区地下100米深、约27公里长的环形隧道中，耗资总计约20亿美元，预计将于今年6月正式开始运行。
届时，它将凭借能使单束粒子流能量达到7万亿电子伏特而成为世界上能级最高的对撞机。
科学家普遍期望在这一对撞机的帮助下，能够在前所未有的对撞能量下取得包括发现希格斯玻色子在内的新发现。
不过希格斯认为，发现希格斯玻色子未必一定需要大型强子对撞机的帮助。
他说，迄今已运行多年的美国费米实验室的万亿电子伏特加速器（Tevatron）可能已经获得了希格斯玻色子存在的数据，“这是可能的……希格斯玻色子的身影可能已存在于他们获得的数据中了，只是还没有从数据分析中找到而已”。
新闻资料粒子物理学的“圣杯”——希格斯玻色子人们早已发现，自然界中物体之间千差万别的相互作用，可以简单划分为4种力：即引力、电磁力、维持原子核的强作用力和产生放射衰变的弱作用力。
在爱因斯坦的相对论解决了重力问题后，人们开始尝试建立一个统一的模型，以期解释通过后3种力相互作用的所有粒子。
经过长期研究和探索，科学家们建立起被称为“标准模型”的粒子物理学理论，它把基本粒子（构成物质的亚原子结构）分成3大类：夸克、轻子与玻色子。
“标准模型”的出现，使得各种粒子如万鸟归林般拥有了一个共同的“家园”。
物理专业英语词汇(H)
物理专业英语词汇(H)h maser 氢微波激射器氢脉泽h parameter h参数h region h 区h theorem h 定理haag araki theory 哈格荒木理论haag kastler theorem 哈格卡斯特勒定理hadamard transform spectrometer 阿达玛德变换光谱仪hadron 强子hadron electron storage ring 强子电子存储环hadron multiplet 强子多重态hadronic atom 强子原子hafnium 铪hagen poiseuille's law 哈根泊肃叶定律hair hygrometer 毛发湿度计halation 晕光half integral spin 半整数自旋half life 半衰期half life period 半周期half shadow apparatus 半影装置half shadow polarimeter 半影偏光计half tone 半音half value layer 半值层half value period 半衰期half wave dipole 半波偶极子half wave line 半波长线half wave rectification 半波整流half wavelength plate 半波片halftime 半周期halfwidth 半值宽度hall coefficient 霍耳系数hall constant 霍耳常数hall effect 霍耳效应hall generator 霍耳发生器hall mobility 霍耳迁移率halley's comet 哈雷彗星halo 晕halogen 卤halogen counter 卤计数管halogen leak detector 卤探漏器hamilton jacobi's equation 哈密顿雅可比方程hamilton's principle 哈密顿原理hamiltonian 哈密顿算符hamiltonian dynamics 哈密顿动力学hamiltonian formalism 哈密顿形式论hamiltonian function 哈密顿函数hamiltonian operator 哈密顿算符hard component 硬性成分hard landing 硬着陆hard magnetic material 硬磁材料hard superconductor 硬超导体hard x rays 硬 x 射线hardening 硬化hardness 硬性hardware 硬件harmonic 谐音harmonic analysis 低解析harmonic analyzer 低解析器低分析器harmonic component 谐波分量harmonic function 低函数harmonic motion 谐运动harmonic oscillation 谐振荡harmonic oscillator 谐振子harmonic vibration 谐振荡harmonic wave 谐波harmonics 低函数hartley oscillator 哈脱莱振荡器hartmann diaphragm 哈特曼光栏hartmann flow 哈特曼流hartmann number 哈特曼数hartmann's dispersion formula 哈特曼色散公式hartree approximation 哈特里近似hartree fock approximation 哈特里福克近似hausdorff dimension 豪斯多夫维数hawking effect 霍金效应hawking penrose theorem 霍金彭罗塞定理hayashi phase 林相位he cd laser 氦镉激光器he counter 氦计数器he ne laser 氦氖激光器head 磁头head on collision 对头碰撞health physics 保健物理学hearing 听觉heat 热heat accumulator 回热器heat balance 热平衡heat budget 热平衡heat capacity 热容heat capacity at constant pressure 恒压热容heat conduction 热传导heat conductivity 热导率heat conductor 热导体heat content 焓heat convection 热对流heat effect 热效应heat emission 热发射heat energy 热能heat engine 热机heat equilibrium 热平衡heat exchange 热交换heat exchanger 换热器热交换器heat flux 热通量heat index 热指数heat insulation 热绝缘heat loss 热损失heat of adsorption 吸附热heat of atomization 原子化热heat of combustion 燃烧热heat of condensation 凝结热heat of crystallization 结晶热heat of dissociation 离解热heat of evaporation 蒸发热heat of fusion 融解热heat of hydration 水合热heat of ionization 电离热heat of mixing 混合热heat of phase transition 相转移热heat of reaction 反应热heat of solidification 凝固热heat of solution 溶解热heat of vaporization 汽化热heat output 热功率heat pattern 温度记录图heat pipe 热管heat quantity 热量heat radiation 热辐射heat rays 热射线heat release 放热heat reservoir 热库heat resistant 耐热性的heat source 热源heat test 加热试验heat tight 不透热的heat transfer 传热heat transmission 传热heat treatment 热处理heat wave 热浪heating 加热heating curve 加热曲线heating element 加热体heating surface 加热面heating unit 加热体heavenly body 天体heavenly twins 双子座heaviside layer 亥维赛层heaviside lorentz's system of units 亥维赛洛伦兹单位制heavy atom method 重原子法heavy current 强电流heavy electron 重电子heavy fermion 重费密子heavy hydrogen 氘heavy ion 重离子heavy ion accelerator 重离子加速器heavy ion beam 重离子束heavy ion nuclear reaction 重离子核反应heavy ion reaction 重离子反应heavy lepton 重轻子heavy metal 重金属heavy nucleus 重核heavy particle 重粒子heavy particle collision 重粒子碰撞heavy water 重水heavy water homogeneous reactor 重水型均匀堆heavy water reactor 重水堆hecto 百heisenberg force 海森伯力heisenberg model 海森伯模型heisenberg pauli method 海森伯泡利法heisenberg picture 海森伯绘景heisenberg uncertainty principle 海森伯测不准原理heisenberg's equation of motion 海森伯方程heisenberg's representation 海森伯表示heitler london theory 海特勒伦敦理论helical antenna 螺旋天线helical dislocation 螺形位错helical magnetic structure 螺旋形磁结构helical motion 螺旋运动helical spin structure 螺纹自旋结构helical spring 螺旋弹簧helical structure 螺旋形结构helicity 螺旋性helicoid 螺旋面helicon wave 螺旋形波heliocentric coordinates 日心坐标heliocentric system 日心系heliocentric theory 日心说heliograph 日照计heliographic coordinates 日面坐标heliostat 定日镜helium 氦helium cadmium laser 氦镉激光器helium fusion process 氦聚变反应helium leak detector 氦探漏器helium liquefaction 氦液化helium liquefier 氦液化器helium neon laser 氦氖激光器helium star 氦星helix accelerator 螺旋波导直线加速器helmholtz resonator 亥姆霍兹共振器helmholtz's vortex theorem 亥姆霍兹涡旋定理hemihedral form 半面晶形hemihedry 半面象hemimorphy 异极象henry 亨henry draper catalog 亨利德雷伯分光星表hercules 武仙座hermann mauguin notation 赫曼莫金记号hermitian form 厄密形式hermitian matrix 厄密矩阵hermitian operator 厄密算符herschel type reflector 赫谢耳望远镜hertz 赫hertz oscillator 赫兹振荡器hertzian vector 赫兹矢量hertzian wave 赫兹波hertzsprung russel diagram 赫罗图heterochromatic photometer 异色光度计heterochromatic photometry 多色光度学heterodyne 外差heterodyne reception 外差接收法heterodyne spectroscopy 外差光谱学heteroepitaxial growth 异质外延生长heteroepitaxy 异质外延法heterogeneity 非均匀性heterogeneous 非均匀的heterogeneous equilibrium 多相平衡heterogeneous radiation 非单色辐射heterogeneous reactor 非均匀堆heterogeneous system 非均匀系heterojunction laser 异质结激光器heterolaser 异质结激光器heteronuclear molecule 异核分子heterophase structure 非均匀相结构heteropolar bond 异极键heteropolar compound 异极化合物heteropolar crystal 异极晶体heterotope 异位素heusler alloy 赫斯勒合金hexadecapole deformation 十六极形变hexagonal close packed structure 六角密积结构hexagonal lattice 六方晶格hexagonal system 六角系hexahedron 六方体hexode 六极管hf laser 氟化氢激光器hf 激光器hidden parameter 隐参量higgs boson 希格斯玻色子higgs mechanism 希格斯机制higgs particle 希格斯粒子high altitude rocket 高空火箭high atmosphere 上层大气high definition television 高清嘶度电视high density exciton 高密度激子high density nuclear matter 高密度核物质high elasticity 高弹性high energy electron diffraction 高能电子衍射high energy nuclear physics 高能核物理学high energy radiation 高能辐射high energy region 高能区域high flux neutron beam reactor 高通量中子束堆high frequecy choke 高频扼力high frequency 高频high frequency ammeter 高频安培计high frequency amplifier 高频放大器high frequency furnace 高频炉high frequency heating 高频加热high frequency oscillator 高频振荡器high frequency resistor 高频电阻器high frequency transformer 高频变换器high frequency wattmeter 高频瓦特计high magnetic fields 强磁场high molecular compound 高分子化合物high polymer 高分子聚合物high polymer physics 高聚合体物理学high power laser 高功率激光器high pressure 高压high pressure arc discharge 高压电弧放电high pressure area 反气旋区域high pressure electronic phase transition 高压电子相变high pressure gage 高压计high pressure gas 高压气体high pressure physics 高压物理学high reflectance film 高反射膜high resolution nuclear magnetic resonance 高分辨率核磁共振high speed camera 高速照相机high speed flow 快速怜high speed scanning spectroscopy 高速扫描光谱学high tc superconductor 高 tc 超导体high technology 高技术high temperature expansion 高温展开high temperature gas cooled reactor 高温气冷堆high temperature superconductor 高温超导体high tension 高压high vacuum 高真空high vacuum technique 高真空技术high velocity stars 高速星high voltage accelerator 高压加速器high voltage electron microscope 高压电子显微镜higher harmonic 高次谐波highly excited atom 高度受激原子highly excited level 高激发态highly ionized ion 高度电离离子highly sensitive 高灵敏度的hilbert space 希耳伯特空间hilbert transform 希耳伯特变换hildebrand rule 希尔得布兰德定则hill's equation 希耳方程histogram 直方图hodograph 速度图hodograph method 速度面法hodoscope 描迹器hohlraum 腔holding pump 保持泵hole 空腔hole burning 烧孔hole conduction 空穴传导hole diffusion 空穴扩散hole hole interaction 空穴空穴相互酌hole mobility 空穴迁移率hole theory 空穴理论hollow cathode discharge 空心阴极放电hollow space radiation 空腔辐射hologram 全息照相holographic diffraction grating 全息衍射光栅holographic interferometry 全息干涉度量学holographic microscope 全息显微镜holography 全息学holohedral form 全面形holohedry 全面象holomorphic function 全纯函数holon 霍伦holonomic system 完整力系holonomy group 完整群homocentric pencil 共心光束homogeneity 均匀性homogeneous broadening 均匀增宽homogeneous distribution 均匀分布homogeneous field 均匀场homogeneous function 齐次函数homogeneous medium 均匀介质homogeneous reactor 均匀堆homogeneous turbulence 同的流homogeneous universe 均匀宇宙homology 同调homometric structure 同 x 光谱结构homomorphism 同晶形homonuclear molecule 同核分子homopolar bond 同极键homotopy 同伦hook on ammeter 钳式安培表hooke's law 胡克定律hopf bifurcation 霍普夫分岐hopping conductivity 跳动传导horizon 地平horizontal coordinates 地平坐标horizontal intensity 水平磁力强度horizontal parallax 地平视差horizontal resolution 水平分辨率horn antenna 喇叭天线horologium 时钟座horse power 马力horse shoe magnet 蹄形磁铁host crystal atom 基质晶体原子hot atom 热原子hot band 热带hot cathode 热阴极hot cathode ionization gage 热阴极电离真空计hot cathode magnetron gage 热阴极磁控管真空计hot cathode mercury vapour rectifier 热阴极汞汽整淋hot cathode x ray tube 热阴极 x 射线管hot cave 高放射性物质工琢蔽室hot cell 高放射性物质工琢蔽室hot electron 热电子hot junction 热结hot laboratory 强放射性物质实验室hot universe 热宇宙hot wave 热浪hot wire ammeter 热线安培计hot wire galvanometer 热线检疗hot working 热加工hour 小时hour angle 时角hubbard model 哈费模型hubble constant 哈勃常数hubble space telescope 哈勃空间望远镜hubble's classification of galaxies 哈勃分类法hubble's law 速距关系hubble's time 哈勃年龄hue 色彩hum 哼鸣human counter 全身计数器human engineering 人类工程学humidity 湿度hund rule 洪德定则hunting 摆动huygens eyepiece 惠更斯目镜huygens fresnel principle 惠更斯菲涅耳原理huygens' principle 惠更斯原理hybrid bubble chamber 混合气泡室hybrid orbital 杂化轨道hybrid reactor 混合反应堆hybrider 混合反应堆hybridization of atomic orbits 原子轨道的杂化hydra 长蛇座hydrated electron 水化电子hydration 水化hydraulic radius 水力半径hydraulics 水力学hydroacoustics 水声学hydrodynamic drag 铃动力学阻力hydrodynamic instability 铃动力学不稳定性hydrodynamical model 铃动力学模型hydrodynamics 铃动力学hydroelasticity 水弹性hydrogen 氢hydrogen atom 氢原子hydrogen bomb 氢弹hydrogen bond 氢键hydrogen bubble chamber 氢气泡室hydrogen chloride laser 氯化氢激光器hydrogen electrode 氢电极hydrogen embrittlement 氢脆化hydrogen fluoride laser 氟化氢激光器hf 激光器hydrogen helium cycle 氢氦循环hydrogen laser 氢激光器hydrogen like atom 类氢原子hydrogen maser 氢微波激射器氢脉泽hydrogen scale 氢温标hydrogen spectrum 氢光谱hydrogen star 氢星hydrogenated amorphous semiconductor 氢化非晶态半导体hydrolysis 水解hydromagnetic wave 磁铃波hydromagnetics 磁铃动力学hydromechanics 铃力学hydrometer 比重计hydrophily 亲水性实用文档hydrophobic bond 疏水键hydrophoby 疏水性hydrophone 水听器hydrosphere 水圈hydrostatic balance 比重天平hydrostatic pressure 铃静压力hydrostatics 铃静力学hydrothermal synthesis method 水热合成法hydrus 水蛇座hygrograph 湿度记录仪hygrometer 湿度表hyper abrupt junction 超突变结hyper raman scattering 超喇曼散射hypercharge 超荷hyperconjugation 超共轭hyperfine interaction 超精细相互酌hyperfine structure 超精细结构hyperfragment 超裂片hyperfunction 超函数hypergeometric function 超几何函数hypermetropia 远视hypermicroscope 超倍显微镜hypermultiplet 超多重谱线hyperon 超子hyperopia 远视hyperquantization 超量子化hypersonic 特超声的hypersonic flow 特超声速流hypersonic velocity 特超声速hypersonic wave 特超声波hypocenter 震源hypochromatic shift 蓝移hypochromism 减色性hypothesis 假设hypothetical accident 假设事故hypsochromic effect 浅色效应hypsometer 沸点测定器沸点测高器hysteresis 滞后hysteresis constant 滞后常数hysteresis curve 滞后曲线hysteresis loop 滞后回线hysteresis loss 滞后损耗。
希格斯玻色子 考研英语
希格斯玻色子考研英语In the realm of particle physics, the Higgs boson stands as a pivotal element in the Standard Model, which serves as the most widely accepted framework for understanding the fundamental particles and forces that shape our universe. The discovery of the Higgs boson at CERN's Large Hadron Collider (LHC) in 2012 was a monumental milestone, confirming the existence of the last predicted particle in the Standard Model and providing crucial insights into the mechanism that gives particles their mass.The Higgs boson, often referred to as the "God particle," is unique because it is associated with the Higgs field, an energy field that permeates the entire universe. According to the theory proposed by Peter Higgs and others in the 1960s, particles acquire mass by interacting with this field. The more strongly a particle interacts with the Higgs field, the heavier it becomes. Conversely, particles that do not interact with the Higgs field remain massless, such as photons, the particles of light.Understanding the Higgs boson is not only a matter of scientific curiosity but also has profound implications for our comprehension of the universe. For instance, without the Higgs mechanism, atoms would not exist, as the elementary particles they are made of would zip around at the speed of light without ever coming together to form atoms. The Higgs field is thus essential for the formation of complex structures, including stars, planets, and ultimately life itself.The search for the Higgs boson was a decades-long quest that involved thousands of scientists and engineers from around the world. It required the construction of the LHC, the most powerful and complex machine ever built, capable of accelerating protons to near the speed of light and smashing them together at unprecedented energy levels. The detection of the Higgs boson was achieved through the observation of the particles that result from its decay, as the Higgs boson itself is highly unstable and disintegrates almost immediately after being created.The confirmation of the Higgs boson's existence has opened up new avenues of research in particle physics. Scientists are now probing the properties of the Higgs bosonwith greater precision, seeking to uncover any deviations from the Standard Model predictions that could hint at new physics beyond our current theories. Such discoveries could potentially lead to a deeper understanding of the universe's early moments and the conditions that led to the formation of matter as we know it.Moreover, the study of the Higgs boson has broader implications for fields such as cosmology and astrophysics. It plays a significant role in theories of cosmic inflation, the rapid expansion of the universe that occurred fractions of a second after the Big Bang. The Higgs field's interaction with other fields and particles during this period could have shaped the large-scale structure of the universe, influencing the distribution of galaxies and the evolution of cosmic structures.In conclusion, the Higgs boson is a cornerstone of modern physics, providing a key to unlocking the mysteries of mass and the fundamental structure of matter. Its discovery is a testament to human ingenuity and the collaborative spirit of the scientific community. As research continues, the Higgs boson will undoubtedly remain at the forefront of our quest to understand the deepest secrets of the universe.(Note: This document is a creative composition intended for educational purposes and does not contain any direct quotations or copyrighted material.)。
Signals of Doubly-Charged Higgsinos at the CERN Large Hadron Collider
Signals of Doubly-Charged Higgsinos at the CERN Large Hadron Collider
Durmu¸ s A. Demir1,2 , Mariana Frank3 , Katri Huitu4 , Santosh Kumar Rai4 , and Ismail Turan3
Department of Physics, Izmir Institute of Technology, IZTECH, TR35430 Izmir, Turkey. 2 Deutsches Elektronen - Synchrotron, DESY, D-22603 Hamburg, Germany. 3 Department of Physics, Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec, CANADA H4B 1R6. and 4 Department of Physics, University of Helsinki and Helsinki Institute of Physics, P.O. Box 64, FIN-00014 University of Helsinki, Finland. Several supersymmetric models with extended gauge structures, motivated by either grand unification or by neutrino mass generation, predict light doubly-charged Higgsinos. In this work we study productions and decays of doubly-charged Higgsinos present in left-right supersymmetric models, and show that they invariably lead to novel collider signals not found in the minimal supersymmetric model (MSSM) or in any of its extensions motivated by the µ problem or even in extra dimensional theories. We investigate their distinctive signatures at the Large Hadron Collider (LHC) in both pair– and single–production modes, and show that they are powerful tools in determining the underlying model via the measurements at the LHC experiments.
Single production of doubly charged Higgs bosons at hadron colliders
hee · hµµ < 0.44 TeV−1 .
(1)
M∆++
The tightening of these limits makes the study of the high-energy phenomenology of the triplet Higgs bosons at future hadronic colliders interesting and well motivated.
work of the left-right symmetric model and the Higgs triplet model.
We show that in the left-right symmetric model the production of
∆+R+ by Drell-Yan contribution. The
arXiv:hep-ph/0201196v3 4 Mar 2002Leabharlann HIP-2002-02TH
Single production of doubly charged Higgs bosons at hadron colliders
J.Maalampia and N. Romanenkob
a Department of Physics, University of Jyva¨skyla¨, Finland, and Helsinki Institute of Physics, Helsinki, Finland
The origin of neutrino masses is quite difficult to figure out just by looking at the low-energy phenomenology of neutrinos. The phenomena like neutrino oscillations, leptonic decays of particles and the neutrinoless double beta decay are quite independent of the mechanism by which neutrino masses are created. Indirect information could, however, be obtained by studying the physics related to the mass generation mechanism in high-energy collision process. Particularly, indirect information on the see-saw mechanism can be obtained through the phenomenology of the triplet Higgs fields.
20个关于科学突破的英语作文
20个关于科学突破的英语作文Scientific breakthroughs have revolutionized our world, shaping the way we live, work, and understand the universe. In this article, we will explore 20 remarkable scientific breakthroughs that have had a profound impact on various fields of study.1. Discovery of Penicillin。
In 1928, Alexander Fleming discovered the antibiotic properties of penicillin, paving the way for the development of modern antibiotics that have saved countless lives.2. Theory of Relativity。
Albert Einstein's theory of relativity, published in 1915, revolutionized our understanding of space, time, and gravity, providing a new framework for physics.3. DNA Structure。
James Watson and Francis Crick's discovery of the double helix structure of DNA in 1953 laid the foundation for modern genetics and our understanding of inheritance.4. Moon Landing。
Peskin量子场论习题解答(第二学期)
Physics 331–Problem Set #2(due Wednesday,February 1)1.Peskin and Schroeder,Problem 9.1.2.Let Φbe a linear combination of free fields:Φ= d 4xg (x )φ(x ),where g (x )is a fixed function and φ(x )is a free Klein-Gordon field.(a)First,look at the evaluation of products of Φ’s in canonicalquantization.Time-ordered expectation values of Φare evaulated as sums of contractions.Show that Φ4 =3· Φ2 2 Φ4 =5·3· Φ2 3etc .(1)where ··· denotes the time-ordered expectation value and Φ2 is the ing these results,show that exp[Φ] =exp[ Φ2 /2](2)(b)Rederive (2)using the functional integral to define the expectation values of φ(x ).3.Peskin and Schroeder,Problem pare these results to Problem 2of the previous problem set.4.Peskin and Schroeder,Problem 15.4.The formula at the top of p.504should read:D F (x,y )= ∞0dT D x exp i dt 12(−(dx μdt )2−m 2)−ie dt dx μdt A μ(x ) (3)which is correct,because (d x /dt )2(the square of the space components of x μ)should have a positive coefficient.1Physics 331–Problem Set #3(due Wednesday,February 8)1.Peskin and Schroeder,Problem 9.2.2.In class,we computed the matrix element for the process qq→gg ,where q is a massless fermion in the representation r of a Yang-Mills gauge group G and g is the Yang-Mills gauge boson.Our result had the form:i M =v (p )γ· ∗(k 1)t a ···γ· ∗(k 2)t b u (p )+···(1)In QED,we were typically interested in cross sections summed over final spins and averaged over initial spins.In Yang-Mills theory,we might also wish to sum over final gauge indices (‘colors’)and average over initial colors.(a)For the term written out in (1),show that the group theory factor corresponding to this color average and sum of the squared matrix elements is 1d 2r tr[t a t b t b t a ](2)(b)Show that this factor evaluates to 1d r [C 2(r )]2(3)(c)Evalute 1d 2r tr[t a t b t a t b ](4)pute the differential cross section dσ/d cos θfor qq →gg ,averaged over initial spins and colors and summed over final spins and e the method of Peskin and Schroeder,Problem 17.3(a).Use the same explicit spinors and polarization vectors that appeared in the Problem Sets 6and 7of Physics pute the color averages and sums using the results of Problem 2.1Physics 331–Problem Set #4(due Wednesday,February 15)1.In the previous problem set,you computed the differentialcross section for qq →gg in a general Yang-Mills theory with massless fermions.Specialize your answer to QCD and show that it produces eq.(17.75)of Peskin and ing crossing appropriately (being careful to average over initial state colors but sum over final state colors),derive eqs.(17.76)and (17.77).2.The various fermion-fermion scatting cross sections in QCD can be derived from QED results by multiplying by appropriate color ing this strategy,derive eqs.(17.64),(17.65),(17.70),and (17.71)of Peskin and pute the differential cross section dσ/d cos θfor gg →gg ,averaged over initial spins and colors and summed over final spins and e the method ofPeskin and Schroeder,Problem 17.3(b).Derive eq.(17.78)of Peskin and Schroeder.This completes the set of 2→2parton cross sections needed to compute the cross sections for hard-scattering processes at hadron colliders.1Physics 331–Problem Set #5(due Wednesday,February 22)1.The effective interaction used in class to compute the crosssection for neutrino deep inelastic scattering can be tested in purely leptonic processes,in particular,in muon decay μ−→e −νe νμ.From the vertex ΔL =4G F √2eγμP L νe νμγμP L μ(1)where P L =(1−γ5)/2,and ignoring the masses of the electron and the neutrinos:(a)Compute the muon decay rate Γμ.The measured muon lifetime,τμ=2.19703(4)×10−6sec,gives the most accurate determination of G F .Compute G F (2significant figures suffice).(b)Compute the electron energy distribution d Γ/dE (e −)in the muon rest frame.(c)(extra credit)For a muon at rest with spin oriented along the +ˆz axis,compute the electron energy and angular distribution.When this distribution is averaged with that for a muon with spin oriented in the −ˆz direction,you should find an angle-independent result that agrees with the answer in (b).Parts (a)and (b)are quite straightforward with the use of the tricks for 3-body phase space described in Problem Set #8of Physics 330.Part (c)is more difficult;I have made it optional.It might be useful to use the identity for integrating over the phase space of massless vectors k and q such that (k +q )=P : d 3k (2π)32k d 3q (2π)32q (2π)4δ(4)(k +q −P )·k αq β=196π(2P αP β+g αβP2)(2)2.Peskin and Schroeder,Problem 17.4.3.Peskin and Schroeder,Problem 17.5.Work out both the total cross section and the differential cross section E dσd 3p (3)where p ,E are the energy and momentum of the heavy quark Q .You can work inthe γ-p CM frame,though the quantity in (3)is actually invariant to longitudinal boosts.1。
英语中同位语从句的用法归纳总结
英语中同位语从句的用法归纳总结全文共3篇示例，供读者参考篇1The Versatile Appositive Clause: A Student's Guide to Mastering This Nifty ConstructionAs an English student, I've come to appreciate the sheer versatility and expressiveness of our language. One construction that has particularly caught my attention is the appositive clause – a nifty little tool that can add depth, clarity, and flair to our writing and speech. In this essay, I'll delve into the nitty-gritty of appositive clauses, exploring their various forms, functions, and proper usage.What's an Appositive Clause, Anyway?Before we dive in, let's establish a clear definition. An appositive clause is a dependent clause that further describes or clarifies a noun or noun phrase that precedes it. It's like a little side note or extra bit of information that helps the reader better understand what or who you're referring to.For example, "My friend, who is an avid hiker, loves exploring the mountains." In this sentence, "who is an avid hiker" is anappositive clause that provides additional details about "my friend."The Many Faces of Appositive ClausesAppositive clauses come in various shapes and sizes, each serving a unique purpose. Here are some of the most common types:Restrictive Appositive ClausesThese bad boys are essential for clarifying or identifying the noun they modify. Without the appositive clause, the sentence would be ambiguous or confusing. For instance, "The student who aced the exam received a scholarship." The clause "who aced the exam" is crucial in specifying which student we're talking about.Non-Restrictive Appositive ClausesUnlike their restrictive counterparts, non-restrictive appositive clauses provide additional, non-essential information about the noun. They're like little bonus tidbits that enhance our understanding but aren't strictly necessary. For example, "My brother, who is a professional chef, makes the best lasagna."Appositive Clauses with PrepositionsSometimes, appositive clauses follow prepositions, adding even more depth and nuance to our sentences. "The painting, with its vibrant colors and bold brushstrokes, caught my eye." Here, "with its vibrant colors and bold brushstrokes" is an appositive clause that modifies "the painting."Using Appositive Clauses EffectivelyNow that we've covered the basics, let's talk about how to wield these bad boys like a pro:Punctuation is KeyProper punctuation is crucial when using appositive clauses. Restrictive clauses don't require commas, but non-restrictive clauses do. For example:Restrictive: "The student who studied diligently passed the exam."Non-restrictive: "My friend, who is a grammar enthusiast, always notices my appositive clause usage."Placement MattersWhile appositive clauses typically follow the noun they modify, they can sometimes precede it for emphasis or stylisticeffect. "Beaming with pride, my little sister received her diploma."Avoid AmbiguityAppositive clauses can sometimes create ambiguity if not used carefully. For instance, "I met my friend's sister, who is a doctor, at the park." Is the sister or the friend a doctor? Rephrase for clarity when needed.Use Them JudiciouslyWhile appositive clauses are undoubtedly useful, overusing them can lead to clunky, convoluted sentences. Strike a balance, and use them only when they genuinely enhance your writing.In ConclusionAppositive clauses are a powerful tool in the English language, allowing us to add depth, clarity, and richness to our communication. By mastering their various forms and usages, we can elevate our writing and speech to new heights. So, the next time you find yourself needing to provide additional details or clarification, don't hesitate to reach for that trusty appositive clause. Just remember to use them wisely, punctuate correctly, and avoid ambiguity. With practice and attention to detail, you'll be an appositive clause extraordinaire in no time!篇2The Versatile Appositive Clause: A Student's GuideAs an English student, you've probably encountered those pesky clauses that seem to provide additional information but leave you scratching your head about their purpose. Fear not, my fellow learners, for today we'll dive into the world of appositive clauses and explore their multifaceted roles in the English language.First things first, what exactly is an appositive clause? Simply put, it's a dependent clause that provides extra details or clarification about a noun or pronoun in the main clause. These clauses are set off by commas, dashes, or parentheses, acting as a sort of grammatical sidekick to the main clause.Now, let's break down the different types of appositive clauses and how they can be used to enhance your writing and speaking skills.Defining Appositive ClausesThese clauses are essential for adding crucial information about the noun or pronoun they're referring to. Without them, the sentence might lack clarity or context. For example:"My friend, who is a talented artist, just had her first exhibition."In this case, the appositive clause "who is a talented artist" provides a defining detail about the noun "friend."Non-defining Appositive ClausesUnlike their defining counterparts, non-defining appositive clauses offer additional, non-essential information. They're like little trivia tidbits that enrich the sentence but aren't strictly necessary for understanding the main point. For instance:"John, whose passion for cooking knows no bounds, prepared a delectable meal for us."Here, the clause "whose passion for cooking knows no bounds" gives us a fun fact about John, but the sentence would still make sense without it.Appositive Clauses for EmphasisSometimes, appositive clauses can be used to add emphasis or draw attention to a particular detail. This can be especially useful in persuasive writing or public speaking:"The new tax policy, which will undoubtedly burden the middle class, has faced widespread criticism."In this example, the appositive clause highlights the anticipated impact of the tax policy, underscoring its importance.Appositive Clauses in Narrative WritingIn creative writing, appositive clauses can help bring characters to life and provide depth to their descriptions:"Sarah, whose eyes sparkled with mischief, had a knack for getting into trouble."This appositive clause not only describes Sarah's physical appearance but also hints at her personality, making her character more vivid and engaging.Appositive Clauses in Technical WritingEven in technical or academic writing, appositive clauses can be invaluable for clarifying complex concepts or providing additional context:"The Higgs boson, which was theorized in the 1960s, was finally discovered at the Large Hadron Collider in 2012."This clause offers background information about the Higgs boson, helping readers better understand its significance.Now, as with any grammatical construct, there are a few rules and considerations to keep in mind when using appositive clauses:Punctuation is crucial: Appositive clauses must be set off from the main clause with appropriate punctuation (commas, dashes, or parentheses) to avoid confusion.Parallelism matters: If you have multiple appositive clauses modifying the same noun or pronoun, be sure to maintain parallel structure for clarity and coherence.Avoid ambiguity: Appositive clauses should clearly refer to the noun or pronoun they're modifying. Ambiguous placement can lead to misunderstanding.Use them judiciously: While appositive clauses can enhance your writing, overusing them can make your sentences overly complex and difficult to follow.As you can see, appositive clauses are versatile tools that can enrich your writing and speaking in numerous ways. Whether you're aiming for precision, emphasis, or narrative flair, mastering the art of the appositive clause can elevate your command of the English language.So, the next time you encounter an appositive clause, don't shy away from it. Embrace it as a valuable addition to your linguistic arsenal, and use it to add depth, clarity, and personality to your communication. With practice and a keen eye for detail, you'll soon be wielding appositive clauses like a seasoned pro.Happy learning, and may your journey through the world of English grammar be enlightening and enriching!篇3Sure, here's a 2000-word essay on the usage of appositive clauses in English, written in a student's tone:The Lowdown on Appositive Clauses: A Student's GuideAs a student grappling with the intricacies of English grammar, one concept that can leave you scratching your head is the appositive clause. These little buggers can be a real headache, but fear not, my fellow scholars! I'm here to break it down for you in a way that won't make your brain hurt (too much).First things first, let's define what an appositive clause is. Simply put, it's a group of words that provides additional information about a noun or pronoun that precedes it. Sounds simple enough, right? Well, hold on to your hats, because there's more to it than meets the eye.Appositive clauses can be either essential or non-essential, and this distinction is crucial. Essential appositive clauses are, well, essential. They provide information that is necessary for identifying the noun or pronoun they're modifying. Without this information, the sentence would be incomplete or unclear.For example:"The book that won the Pulitzer Prize was a best-seller."In this case, "that won the Pulitzer Prize" is an essential appositive clause because it specifies which book we're talking about. If we remove it, the sentence becomes ambiguous.On the other hand, non-essential appositive clauses offer additional, but non-crucial, information about the noun or pronoun. They're like the cool cousin who shows up with fun stories but isn't really necessary for the party to happen.For instance:"My friend, who loves to dance, won the talent show."Here, "who loves to dance" is a non-essential appositive clause. It provides extra information about your friend, but the sentence would still make sense without it.Now, here's where things get a little tricky. Non-essential appositive clauses need to be set off with commas (or, in some cases, dashes or parentheses) to separate them from the rest of the sentence. Essential appositive clauses, on the other hand, shouldn't be set off with commas because they're, well, essential.I know, I know, it's a lot to keep track of. But fear not, my fellow pupils, for I have a nifty little trick to help you remember: Think of non-essential appositive clauses as little asides or side notes. They're like the friend who leans over and whispers a juicy tidbit in your ear during a conversation – you can ignore them, and the conversation will still make sense, but they add a little extra something.。
Large extra dimension effects in Higgs boson production at linear colliders and Higgs facto
a r X i v :h e p -p h /0303259v 2 3 O c t 2003HIP-2003-19/TH ROME1-1352/2003Large extra dimension effects in Higgs boson production at linear colliders and Higgs factoriesAnindya Datta 1,Emidio Gabrielli 1,and Barbara Mele 21Helsinki Institute of Physics,POB 64,University of Helsinki,FIN 00014,Finland 2Istituto Nazionale di Fisica Nucleare,Sezione di Roma,and Dip.di Fisica,Universit`a La Sapienza,P.le A.Moro 2,I-00185Rome,Italy1IntroductionIn recent years much attention has been paied to theories where the weakness of thegravitational coupling is explained by the presence of large compact extra spatial dimensions,as shown in [1].In such theories,while standard model (SM)fields are confined in the usual 4-dimensional space,the gravity can propagate in the full high dimensional space,and its intensity is diluted in the large volume of the extra dimensions.1The Newton’s constant G N in the3+1dimensional space is then related to the corresponding Planck scale M D in the D=4+δdimensional space by(1)G−1N=8πRδM2+δDwhere R is the radius of a compact manifold assumed to be on a torus.According to the present limits on Newton’s law[2],one could have M D∼1TeV if the number of extra dimensions isδ≥2.A crucial consequence of this framework is that quantum gravity effects could become strong at the TeV scale and measurable at future high-energy colliders.Af-ter integrating out the compact extra dimensions,the effective Einstein theory in 3+1dimensions reliably describes the interactions of the extra-dimensional gravitons with gauge and matterfields[3,4,5].An essentially continuum spectrum of massive Kaluza-Klein(KK)excitations of the standard gravitonfield arises,forδnot larger than about6.When summing over the allowed spectrum of KK states either in the inclusive production or in the exchange of virtual KK gravitons,the small coupling (E/M P)2associated to a single graviton production/exchange(where E is the typ-ical energy of the process and M P is the Plank mass)is replaced by the quantity (E/M D)2+δ.Then,for M D∼1TeV,processes involving gravitons could well be detected at present and future high-energy colliders.This possibility has been quite thoroughly explored in a number of papers[3]-[8].Regarding processes with virtual KK graviton exchange,it is well known that in general the corresponding amplitude is divergent and not computable in the effective theory[3].In particular,the real part of the amplitude,Re[A],needs an ultraviolet cut-off.This means that in general the theory is not predictive in the sector of virtual KK graviton exchange.On the other hand,the imaginary part of the amplitude, Im[A],isfinite and cutoffindependent,being connected to the branch-cut singularity of real graviton emission[3].In a recent paper[8],we stressed that this can have important consequences,when considering standard model(SM)resonant processes interfering with virtual KK graviton exchange graphs.In fact,the corresponding interference,that is dominated by Im[A],turns out to befinite,and predictable in terms of the fundamental Plank scale M D and the number of extra dimensionsδ.In[8],we applied this observation to LEP physics,and computed the effects on the e+e−→f¯f physical observables of the interference of the virtual KK graviton-exchange amplitude with the resonant SM amplitude at the Z boson pole.We found that,although the corresponding impact on total cross-sections vanishes,there are finite modifications of different asymmetries,whose relative effect amounts,in the most favorable cases,to about10−4.2In the present paper,we want to extend this approach to the case of a heavy Higgsboson(H)production at future linear e+e−colliders andµµcolliders.By heavy,wewill imply m H≥200GeV.Graviton interference effects on cross-sections turns out to be proportional to the ratio of the total width over the mass of the resonance state,dueto the imaginary part of the SM amplitude[8].Then,one expects tofind remarkablymore conspicuous graviton interference effects in a heavy Higgs boson productionthan in the Z0boson pole physics,due to the rapidly growing Higgs width with theHiggs mass.One can compare,e.g.,ΓZ/M Z≃0.027withΓH/m H≃0.072,0.29 for m H=400,700GeV,respectively.Moreover,the imaginary part of the graviton amplitude grows quite rapidly with the process c.o.m.energy.+P_P e+W+W−e−W +e+W −Σn He−P_Pνν−νν−G Sn n,Figure1:Feynman diagrams of the processes in Eq.(2).At linear e+e−colliders[9],we consider the Higgs production via vector boson fusion with the subsequent H decay into pairs of heavy particlese+e−(W W)→ν¯νH→ν¯νW W,ν¯νZZ,ν¯νt¯t.(2)Feynman diagrams for these processes are presented in Figure1.This process is one of the dominant H production mechanism at linear colliders,and becomes the main one at√S≫M W can be reliably treated in the effective-W approximations[11],by convoluting the cross-sections for the subprocessesW W→H→W W,ZZ,t¯t,(4)andn{W W→G∗n,S∗n→W W,ZZ,t¯t}(5)with the appropriate W distributions in the electron beam(same for ZZ initiated processes).On the Higgs boson resonance,the interference of the processes eqs.(4)and(5) will be dominated by the imaginary part of the graviton/graviscalar amplitude,that, as discussed above,isfinite and predictable in terms of M D andδ.The aim of the present paper is to determine the amount by which the Higgs production cross-sections and distributions can be affected by the interference with the KK graviton/graviscalar amplitude.We then discuss the possibility to measure such an effect(and,hence,tofind a footprint of a large extra dimension theory)at realistic linear collider machines.In the last part of the paper we also analyze KK graviton/graviscalar interference effects in Higgs production at a possibleµµcollider acting as a Higgs boson factory [12],through the channelsµ+µ−→H→W W,ZZ,t¯t,(6)andn µ+µ−→G∗n,S∗n→W W,ZZ,t¯t .(7)This process would presumably be affected by smaller theoretical uncertainty,and could provide an even more sensitive probe to large extra dimension effects.2The virtual-graviton exchange amplitudeWe are interested in computing the interference of the exchange of a virtual KK spin-2graviton and a virtual KK spin-0graviscalar with a resonant SM scattering amplitude.Hence,we will analyze in particular an s-channel KK exchange amplitude. We will follow in this section the approach of[3].The graviton-mediated scattering amplitude in the momentum space is obtained by summing over all KK modesA=1s−m2n Tαβ+1δ+2 TµµTνν8π),and Tµνis the energy-momentum tensor of the scatteringfields.Thefirst and second terms in Eq.(8) corresponds to graviton and graviscalar exchanges respectively(here m n represents4both the graviton and graviscalar masses without loss of any generality).In the unitary gauge,the projector of the graviton propagator,Pµναβ,is given byPµναβ=13ηµνηαβ+ (9)whereηµνis the Minkowski metric.Dots represent terms proportional to the graviton momentum qµ,that,being qµTµν=0,give a vanishing contribution to the amplitude. The trace of Tµνis nonvanishing only for massive initial andfinal states.Since the energy-momentum tensors do not depend on KK indices,one can per-form the sum(over n)irrespective of the scattering process,and Eq.(8)becomesA=S(s)T,S(s)=1s−m2n,T=TµνTµν−1M2+δD dδq T 122) −s2−1(11)where we assumed m2n=q2T,with q T the graviton momentum orthogonal to the brane.In the interference with a resonant amplitude,only Im[S(s)]will contribute,withIm[S(s)]=−π2sδ−22),with n integer.Hence,imaginary part of the amplitude isfinite and predictable,only depending on the D-dimensional Plank scale M D and on the number of extra dimensionsδ.It also grows quite rapidly with√3Interference effects in the W W partonic cross-sectionsIn this section,we determine the effects on the angular distributions and cross-sections of the W W fusion Higgs production processes in Eq.(2)arising from their interfer-ences with the corresponding KK graviton/graviscalar exchange processes in Eq.(3). We start from the partonic W W initiated amplitude for the processesW W→H→W W,ZZ,t¯t,(13)andn{W W→G∗n,S∗n→W W,ZZ,t¯t},(14)we compute their interferences,and then convolute them(along with the correspond-ing SM cross sections as in Eq.(13)with the effective-W distributions in the initial electron/positron beams.We notice that due to the different spin properties of the Higgs(s=0),graviton (s=2)and graviscalar(s=0)intermediate states,only the graviton will have a nontrivial impact on the angular distribution.On the other hand,the latter effect will vanish in the total cross section,since different spin amplitudes turn out to be orthogonal.An analogous effect can be observed in the Z boson-graviton interference in[8].The initial W polarizations that are relevant for Higgs production are the ones where both the W’s are either transverse(with opposite polarization projection)or longi-tudinal.We call the two combinations,λ=T andλ=L,respectively.If P stands for one of the possiblefinal particles W,Z and t in Eq.(13),the polarization dependent angular distribution for the process W+W−→P¯P via Higgs exchange plus interference effects with the graviton/graviscalar mediated scattering reads,near the Higgs boson pole(i.e.,for|√d cosθ=¯σPλ†Contributions coming from the real part of the amplitudes are suppressed by terms of order |ˆs−m2H|/m2H in this case.6Higgs-exchange total cross section for the process W +W −→P ¯P,¯σPλ=1(ˆs −m 2H )2+m 2H Γ2Hˆs −4m 2WρP λˆs ˆs is thetotal energy of the initial W ’s in their c.o.m.frame,and ξP are numerical coefficients (ξt =ξW =1,and ξZ =14ρt T (x ),ρt T (x )=34ρV T (x ),ρV T (x )=(x 2−4xr V +12r 2V )δ+2,∆P 2,λ=R δf Pλˆs 4√ˆs ˆs(17)where c P are numerical coefficients (c W =43,and c t =42x +43f VL (x )=−1x −2f VT (x ),f VT (x )=2(x 2−4xr V +12r 2V ).(18)We recall that interference effects arising from the real part of the amplitudes (thatwe are neglecting)are suppressed by terms of order |ˆs −m 2H |/m 2H on the Breit-Wigner resonance.When convoluting the partonic W W cross sections with the W ’s effective fluxes in the collider beams,it will be useful to approximate the Breit-Wigner propagator in Eq.(16)by a Dirac delta function1m H ΓH δ(ˆs −m 2H ).(19)7A few basic features of the distribution in Eq.(15)can be discussed even beforemaking the convolution with the W’sfluxes.First of all,as anticipated,the spinstructure of the intermediate states determine aflat(Higgs-like)angular distributionfor the graviscalar interference contribution,affecting the total cross section by anamount∆P0×σSM.On the other hand,the spin-2gravitons give rise to a(1−3cos2θ) angular distribution in the W W c.o.m frame,that gives a vanishing result on the to-tal cross section.Nevertheless,an angular analysis of thefinal state will reflect thenontrivial impact of the(1−3cos2θ)distribution in the W W c.o.m system on thelaboratory-frame angular characteristics.For instance,some angular cut on the direc-tions of thefinal states P with respect to the electron/positron beams will originatea non null effect(weighted by the coefficients∆P2,L and∆P2,T)in the integrated crosssections.In order to establish the general relevance of the present effects,it is of coursecrucial to analyze the numerical values of the coefficients∆P0and∆P2,λfor interestingcases of the model parameters.In Tables1and2the most favorable(experimentallyallowed)case of M D=1TeV withδ=2is presented for the processes W+W−→W+W−and W+W−→t¯t,respectively.The coefficients∆P0and∆P2,λhave been √evaluated atΓH(GeV)∆W2,L2005.9×10−52.8×10−58.5−5.1×10−44002.8×10−31.1×10−367.−4.4×10−36001.6×10−27.3×10−3200.−1.6×10−28005.2×10−22.4×10−2Table1:Numerical values of∆2,T,∆2,L and∆0for various Higgs masses ifδ=2and M D=1TeV,for the process W+W−→W+W−.The leading dependence on the Higgs mass of the coefficients∆P0and∆P2,λarises from the Rδbehavior as a function of m H andΓH.In general,from Eq.(17),on the8m H(GeV)∆t2,T∆t029.2.7×10−3500−1.3×10−23.3×10−3 123.1.6×10−2700−5.6×10−21.4×10−2 309.5.0×10−2G F M2D m H m H .(20)Atδ=2,R2∼m HΓH,and this largely explains the increase of∆P0and∆P2,λwith m H observed in Tables1and2.One can note that for m H>500GeV most of the coefficients are quite large,and could have an impact on the measurable cross-sections.At m H=800GeV,all the coefficients amount to a few percent.The most striking one seems to be the graviton-interference case in the top quark channel,that gives∆t2,T≃−0.1at m H≃800GeV.On the other hand,increasing the Planck scale M D can quite affect the coefficient values considered above.From Eq.(20),one has Rδ∼1/M2+δD.Increasing M D by a factor2would imply,for instance,a reduction by a factor about1/16on the coefficients values shown in Tables1and2.4Interference effects in the e+e−cross-sectionsIn the previous section,we have shown that,after integrating over the full range of cosθthe W+W−→P¯P angular distribution,the graviton interference,weighted by the function(1−3cos2θ),vanishes.Only graviscalar-interference effects survive, affecting the total cross sections by a factor(1+∆P0).The latter will modify the cor-responding total cross-sections in e+e−collisions.In order to pin down the graviton-interference coefficients∆P2,λ,one should instead optimize the angular analysis of the process by defining proper strategies(like angular cuts or new asymmetries)that can enhance the graviton contribution(cf.[8]).To this end,it is crucial to consider the laboratory-frame angular distribution for the complete process e+e−(W W)→ν¯νP¯P, that can be obtained by properly boosting the subprocess W+W−→P¯P according to the initial W Wfluxes in the electron/positron beams.9In a laboratory frame where the initial W W systems moves with velocityβ,the W+W−→P¯P angular distribution in Eq.(15)becomesdσPλ2 1+∆P0+∆P2,λF(θL,β) J(θL,β),(21) whereF(θL,β)≡1−3 cosθL−β(1−βcosθL)2,(22) andθL is the P scattering angle in laboratory frame.Above,we have neglected terms of order m2W/E2e.We then fold the above partonic cross sections with the probabilities P Wλ(x)of emitting from an e+(e−)beam a real W with polarizationλand fraction of the beam momentum x.The e+e−(W W)→ν¯νP¯P differential cross-section can be written as dσP ee(S)d cosθL (23) whereˆs=x1x2S and√64π2x2+2(1−x)m2WP W L(x)=g2x .(24)We now can have the laboratory-frame angular distribution for the complete pro-cess e+e−(W W)→ν¯νP¯P,by convoluting Eq.(21)with the W-fluxes.By introduc-ing the variablesτ=m2Hx2+τ,r H=m2H32Sm3HΓhr H−4ρP T(r H),(26)and,by making use of Eq.(19),one has from Eqs.(21)and(23) dσP eexP W T(x)P W T τ-0.006-0.004-0.00200.0020.004-1-0.500.51d σ/d c o s θL (f b )cos θL ∆2∆0m H = 300 GeV√s ee = 0.5 TeV(a)-0.06-0.04-0.0200.020.04-1-0.500.51d σ/d c o s θL (f b )cos θL ∆2∆0m H = 300 GeV m H = 500 GeVm H = 500 GeV↑√s ee = 1 TeV ↓↓↑(b)Figure 2:Graviton (solid line)and graviscalar (dashed line)contributions to the an-gular distribution in the laboratory frame [Eq.(27)]for e +e −center-of-mass energies (a)500GeV and (b)1TeV.I L 0(θL )=(r H −2)2x P W L (x )P W L τxP W T (x )P W T τ4 1τdx x J (θL ,β)F (θL ,β),(31)where the factor 2in the transverse functions I T 0,2(θL )comes from the two differentinitial W polarization transverse projections that contribute to a spin-0state.For the graviton component,the zeros of the (1−3cos 2θ)distribution in the W W c.o.m.frame are in general shifted by the W W boosts to higher values of |cos θ|.In Figure 2a,we show (by the symbol ∆0)the graviscalar contribution and (by the symbol ∆2)the graviton contribution (including both the longitudinal and the trans-verse part)to the total interference with the SM amplitude in the angular distribution in Eq.(27),at√αǫλ= ǫ−ǫd cosθL Iλ2(θL)S=1TeV case(cf.Figure2b),one has,for m H=300GeV,ǫ≃0.86withαT≃0.18andαL≃0.09.For m H=500GeV,one can selects the central range where the graviton distribution keeps negative values, and setǫ≃0.60.Correspondingly,one hasαT≃0.13andαL≃0.43.Hence,one in general expects that the graviton coefficients in Table1will con-tribute to the measured cross section with reduction factors of a few tens percent according to Eq.(32).At the same time,the graviscalar contribution,having the sameflat distribution as the SM signal,will always contribute by the total relative amount∆0to both the total and the cut cross section.5Gravity interference effects atµ+µ−collidersA cleaner framework where to study gravity interference effects on the Higgs boson pole is clearly given by a Higgs boson factory.Although presently challenging from a technological point of view,aµ+µ−collider with c.o.m.energies around m H is the natural place where to realize a Higgs boson factory[12].One then should consider the gravity interference with the Higgs exchange diagram for the processµ+µ−→P¯P,(34) with P=t,W,Z.For unpolarized initial states,the cross section for the latter process,including interference contributions with the graviscalar and graviton exchange graphs,can be expressed near the Higgs pole as:dσP2 1+∆P0+∆P2(1−3cos2θ) ,(35)12where¯σP=d P(s−m2H)2+m2HΓ2hs−4m2µ(s−4m2µ)ρP s2(x2−4x+12),(37)is the SM total cross section for the process in Eq.(34).Here,√2. The coefficients∆P0are the same as in Eq.(17)∆P0=Rδc P δ−13and c Z=23Rδ,∆W,Z2=Rδ2x2−4x+12,(39)with x=s/m2W,Z.Note that∆t,W2=∆t,W2,T,with coefficients∆t,W2,Tdefined as in Eq.(17).As aconsequence of the above identities,a few numerical interesting values of∆t,Wand∆t,W2,for M D=1TeV andδ=2,can be found back in the Tables1and2. Even in the processµ+µ−→P¯P the gravity interference effects can be quite large for high Higgs boson masses.Also in this case,in order to enhance the graviton contribution(that vanishes in the total cross section)it would be sufficient to properly exclude in the measured cross-section the forward-backward direction.This can be straightforwardly done in this case by properly cutting theθrange in Eq.(34).6ConclusionsIn this paper,we computed gravity interference effects in Higgs boson production at future colliders in the framework of the models based on large compact extra di-mensions proposed in[1].In particular,we considered the Higgs production channel via W W fusion at linear colliders(that we treat in the effective W approximation) with a subsequent Higgs decay into pairs of heavy particles(W W,ZZ,t¯t).We also analyzed Higgs production and decay channels atµ+µ−Higgs factories.The interfer-ence of graviton/graviscalar exchange diagrams with resonant Higgs production and decay channels has the advantage with respect to usual virtual graviton/graviscalar13exchange channels to lead to a completely predictive determination in terms of the Planck scale M D and number of extra dimensionsδ.The effect on the SM angular distribution in general increases with the Higgs boson mass(forδ=2,the effect is proportional to m HΓH).The graviscalar interference,that does not alter the shape of the distributions,changes its normalization by a few percent for m H>500GeV, if M D≃1TeV andδ=2.On the other hand,due to the different spin properties of the graviton and Higgs boson amplitude,the graviton interference alters the angular shape by a universal (1−3cos2θ)distribution(in the W+W−orµ+µ−c.o.m.frame)with a coefficient that is again of the order of a few percent for m H>500GeV.The latter distribution is averaged to zero in the total cross section.Hence,in order to select a graviton effect, we suggest angular-cut strategies that enhance the graviton interference contribution in the measured cross section.In order to detect such indirect graviton effects in Higgs cross section measure-ments,it is crucial that the actual experimental set up will be able to reach the required sensitivity.While assessing thefinal precision of muon colliders is prema-ture at the moment,quite a few studies on this subject have been carried out for the linear e+e−colliders[9].In particular,the precision expected on the measurement of the cross section for Higgs boson production via W W fusion has been considered in [14](see also[15])for a light Higgs decaying predominantly into b quark pairs,and is of the order of a few percent.A detailed study for heavier Higgs bosons(that are the relevant ones for our study)is presently missing,to our knowledge.Anyhow,a percent precision in the cross section measurements should allow to detect some effect at least in the most favorable case of M D≃1TeV andδ=2at both linear colliders and Higgs factories.The effect scales as∼1/M2+δwith the Planck mass scale.DA complete treatment(i.e.,beyond the effective W approximation)of the cross-section in the W W fusion process at linear colliders is not expected to alter our conclusions.Note that,by the time experiments at linear colliders should be operating,the LHC will have presumably observed the direct production of gravitons in the range of parameters that could be relevant for our precision measurements.In particular, a direct graviton signal is expected,forδ=2,3,4,for M D up to a few TeV’s[16,17]. The information derived from the direct graviton production and observation at LHC will definitely help in disentangling the deviations in the Higgs cross sections and distributions analyzed in the present paper.14AcknowledgmentsWe would like to thank M.Giovannini,M.Porrati,and M.Testa for useful discussions.E.G.and A.D.would also like to thank the Physics Department of University of Roma “La Sapienza”,while E.G.thanks also the CERN Theory Division,for their kind of hospitality during the preparation of this work.A.D.and E.G.also thank Academy of Finland(project number48787)forfinancial support.References[1]N.Arkani-Hamed,S.Dimopoulos and G.Dvali,Phys.Lett.B429(1998)263;I.Antoniadis,N.Arkani-Hamed,S.Dimopoulos,and G.Dvali,Phys.Lett.B436 (1998)257.[2]S.Dimopoulos and G.F.Giudice,Phys.Lett.B379(1996)105;J.C.Long,H.W.Chan and J.C.Price,Nucl.Phys.B539:23-34,1999.[3]G.F.Giudice,R.Rattazzi and J.D.Wells,Nucl.Phys.B544(1999)3.[4]E.A.Mirabelli,M.Perelstein and M.E.Peskin,Phys.Rev.Lett.82(1999)2236.[5]T.Han,J.D.Lykken and R.Zhang,Phys.Rev.D59(1999)105006.[6]N.Arkani-Hamed,S.Dimopoulos and G.Dvali,Phys.Rev.D59(1999)086004;J.L.Hewett,Phys.Rev.Lett.82(1999)4765;C.Bal´a zs,H.-J.He,W.W.Repko and C.-P.Yuan,Phys.Rev.Lett.83(1999)2112;E.Dudas and J.Mourad,Nucl.Phys.B575(2000)3;E.Accomando,I.Antoniadis and K.Benakli,Nucl.Phys.B579(2000)3;S.Cullen,M.Perelstein and M.E.Peskin,Phys.Rev.D62 (2000)055012;W.D.Goldberger and M.B.Wise,Phys.Lett.B475(2000)275;B.Grzadkowski and J.F.Gunion,Phys.Lett.B473(2000)50;G.F.Giudice,R.Rattazzi and J.D.Wells,Nucl.Phys.B630(2002)293;Nucl.Phys.B595(2001) 250;H.Davoudiasl,J.L.Hewett and T.G.Rizzo,Phys.Rev.Lett.84(2000) 2080;Phys.Lett.B473(2000)43;Phys.Rev.D63(2001)075004;T.G.Rizzo, Phys.Rev.D64(2001)095010;E.Gabrielli and B.Mele,Nucl.Phys.B647 (2002)319;J.Hewett,M.Spiropulu,Ann.Rev.Nucl.Part.Sci.52(2002)397;E.Dvergsnes,P.Osland and N.Ozturk,hep-ph/0207221;T.G.Rizzo,eConf15C010630(2001)P301,hep-ph/0108235;M.Cavagli´a,hep-ph/0210296;T.G.Rizzo,JHEP0302(2003)008;G.C.Nayak,hep-ph/0211395;G.F.Giudice,A.Strumia,hep-ph/0301232;N.G.Deshpande,D.K.Ghosh,hep-ph/0301272.[7]ndsberg,arXiv:hep-ex/0105039,and references therein.[8]A.Datta,E.Gabrielli and B.Mele,Phys.Lett.B552(2003)237.[9]J.A.Aguilar-Saavedra et al.[ECFA/DESY LC Physics Working Group Collab-oration],‘TESLA Technical Design Report Part III:Physics at an e+e-Linear Collider,hep-ph/0106315.[10]See,for instance,M.Spira and P.M.Zerwas,hep-ph/9803257.[11]S.Dawson,Nucl.Phys.B249(1985)42.[12]see,e.g.,HIGGS FACTORY2001SNOWMASS REPORT,/hep/hfactory/index.html[13]K.Hagiwara et al.,Phys.Rev.D6*******(2002),/.[14]K.Desch and N.Meyer,LC-PHSM-2001-025In*2nd ECFA/DESY Study1998-2001*1694-1704.[15]S.Dawson and S.Heinemeyer,Phys.Rev.D66(2002)055002.[16]L.Vacavant and I.Hinchliffe,J.Phys.G27(2001)1839.[17]L.Vacavant,“Search for extra dimensions at LHC”,talk given at the Inter-national Europhysics Conference on High Energy Physics EPS,July17th-23rd, 2003,Aachen,Germany.16。
当代科学家的英语作文
当代科学家的英语作文题目，The Role of Contemporary Scientists in Shaping Our Future。
Contemporary scientists play a pivotal role in shaping the trajectory of our future. Through their relentless pursuit of knowledge, groundbreaking discoveries, and innovative solutions, they have the power to address pressing global challenges, foster technological advancements, and enhance the quality of human life. In this essay, we will explore the multifaceted roles of contemporary scientists and their profound impact on society.First and foremost, contemporary scientists serve as pioneers of discovery, pushing the boundaries of human understanding across various disciplines. From unraveling the mysteries of the cosmos to delving into the complexities of the human genome, their research efforts expand the frontiers of knowledge and pave the way fortransformative breakthroughs. For instance, the discoveryof the Higgs boson particle by physicists at the Large Hadron Collider not only validated fundamental theories in particle physics but also opened new avenues for exploring the origins of the universe.Moreover, contemporary scientists play a crucial rolein addressing pressing global challenges, such as climate change, pandemics, and resource scarcity. Through interdisciplinary collaboration and evidence-based research, they develop innovative solutions to mitigate environmental degradation, combat infectious diseases, and promote sustainable development. For instance, climate scientists contribute invaluable insights into the causes and impactsof climate change, informing policymakers and drivingefforts to reduce greenhouse gas emissions and transitionto renewable energy sources.In addition to their role as researchers, contemporary scientists also serve as educators and communicators, fostering scientific literacy and public engagement. Through outreach initiatives, science communicationplatforms, and educational programs, they inspire curiosity, critical thinking, and a deeper appreciation for the scientific method. By demystifying complex scientific concepts and promoting evidence-based reasoning, they empower individuals to make informed decisions and participate in discussions on scientific issues that affect society.Furthermore, contemporary scientists play a centralrole in driving technological innovation and economic growth. Their research fuels the development of new technologies, products, and industries, driving progress in fields such as biotechnology, artificial intelligence, and clean energy. By fostering an environment of innovation and entrepreneurship, they stimulate economic activity, create jobs, and enhance global competitiveness. For instance, advances in genetic engineering have led to the development of life-saving medical treatments, agricultural improvements, and bioremediation solutions.However, it is essential to recognize that contemporary scientists also face numerous challenges and ethicaldilemmas in their pursuit of knowledge and innovation. Issues such as research integrity, responsible use of emerging technologies, and equitable access to scientific resources require careful consideration and proactive measures. Furthermore, the increasing commercialization and politicization of science pose threats to academic freedom, scientific integrity, and public trust in the scientific enterprise.In conclusion, contemporary scientists play a vitalrole in shaping our future by advancing knowledge, addressing global challenges, fostering innovation, and promoting scientific literacy. Their contributions havefar-reaching implications for society, economy, and the environment, making it imperative to support and nurture the scientific community. By embracing the values of curiosity, collaboration, and integrity, we can harness the power of science to create a more prosperous, sustainable, and equitable world for future generations.。
teamwork英语作文有例子
teamwork英语作文有例子Teamwork: The Key to SuccessTeamwork is the foundation upon which many successful endeavors are built. It is the collaborative effort of individuals working towards a common goal, each contributing their unique skills and perspectives to achieve a greater outcome. In today's fast-paced and interconnected world, the ability to work effectively as part of a team has become increasingly crucial for both personal and professional success.One of the primary benefits of teamwork is the synergy it creates. When individuals with diverse backgrounds and expertise come together, they can leverage their collective knowledge and skills to tackle complex problems more effectively than if they were working alone. This shared understanding and complementary abilities allow teams to arrive at innovative solutions that may not have been possible through individual efforts.Furthermore, teamwork fosters a sense of camaraderie and mutual support among team members. When individuals feel valued and respected for their contributions, they are more likely to be engaged,motivated, and invested in the team's success. This positive work environment can lead to increased job satisfaction, higher levels of productivity, and a stronger commitment to the team's objectives.Another key advantage of teamwork is the opportunity for personal growth and development. By collaborating with others, individuals can learn from their teammates, gain new perspectives, and develop critical skills such as communication, problem-solving, and conflict resolution. This exposure to diverse viewpoints and experiences can broaden one's understanding of the world and enhance their overall professional competence.One example of the power of teamwork can be seen in the field of scientific research. Researchers often work in collaborative teams to tackle complex scientific problems, combining their expertise and resources to push the boundaries of human knowledge. For instance, the discovery of the Higgs boson, a fundamental particle in particle physics, was the result of the efforts of thousands of scientists from around the world working together as part of the Large Hadron Collider (LHC) project at CERN.Another example of successful teamwork can be found in the world of sports. In team sports such as soccer, basketball, or rugby, players must work together seamlessly, anticipating each other's moves and supporting one another to achieve victory. The best teams are thosethat have developed a strong sense of unity, communication, and trust, allowing them to perform at the highest level.In the business world, effective teamwork is equally crucial for success. Companies that foster a culture of collaboration and teamwork often outperform their competitors. For instance, the success of tech giants like Google and Apple can be attributed, in part, to their ability to assemble talented teams that work together to develop innovative products and services.However, it is important to note that effective teamwork does not come without its challenges. Differences in personalities, communication styles, and work preferences can sometimes lead to conflicts and misunderstandings within a team. Successful teams must be able to navigate these challenges by developing strong interpersonal skills, practicing active listening, and embracing a spirit of compromise and understanding.In conclusion, teamwork is a crucial component of success in various aspects of life, from scientific research to sports and business. By leveraging the collective strengths and diverse perspectives of team members, individuals can achieve far more than they could on their own. As we navigate the complexities of the modern world, the ability to work effectively as part of a team will continue to be a valuable asset for personal and professional growth.。
科学探索宇宙的英语作文
科学探索宇宙的英语作文Title: Exploring the Universe: A Journey into the Unknown。
The universe, with its vast expanse and endless mysteries, has captivated human curiosity for centuries. Through the lens of science, humanity has embarked on an extraordinary journey to explore and understand the cosmos. From ancient astronomers gazing at the stars to modern space missions probing distant galaxies, our quest for knowledge about the universe knows no bounds.One of the fundamental questions driving scientific exploration of the cosmos is the search forextraterrestrial life. The discovery of exoplanets, planets orbiting stars beyond our solar system, has opened new possibilities in this quest. Through telescopes like the Hubble Space Telescope and the Kepler Space Telescope, scientists have identified thousands of exoplanets, some of which may harbor the conditions necessary for life as weknow it.Furthermore, advancements in astrobiology have led to a deeper understanding of the potential habitats for life in our own solar system. Moons like Europa, orbiting Jupiter, and Enceladus, orbiting Saturn, have subsurface oceans that could potentially support microbial life. Missions such as NASA's Europa Clipper and ESA's JUICE (JUpiter ICy moons Explorer) are poised to explore these tantalizing worlds in the coming years, searching for signs of life beyond Earth.In addition to the search for life, scientists are also unraveling the mysteries of the universe's origins and evolution. The Big Bang theory, supported by a wealth of observational evidence, suggests that the universe began as an infinitely dense and hot point nearly 13.8 billion years ago. Since then, the universe has been expanding and evolving, giving rise to galaxies, stars, planets, and ultimately, life.Cosmological observations, such as the cosmic microwave background radiation, provide crucial insights into theearly universe and its subsequent evolution. By studying the distribution of galaxies and the dynamics of cosmic structures, astronomers can trace the history of cosmic expansion and the formation of large-scale structures in the universe.Moreover, the quest to understand the fundamental forces and particles that govern the universe has led to groundbreaking discoveries in particle physics and cosmology. Experiments conducted at particle accelerators, such as the Large Hadron Collider, have revealed the existence of fundamental particles like the Higgs boson, shedding light on the nature of mass and the fundamental forces of nature.Furthermore, the study of dark matter and dark energy, which together make up the majority of the universe's mass-energy content, continues to be a major focus of cosmological research. Although their exact nature remains elusive, their gravitational effects on visible matter provide compelling evidence for their existence, challenging our understanding of the universe's compositionand evolution.In conclusion, the scientific exploration of the universe represents a journey into the unknown, driven by humanity's insatiable curiosity and thirst for knowledge. From the search for extraterrestrial life to the unraveling of the universe's origins and fundamental laws, each discovery brings us closer to understanding our place in the cosmos. As we continue to push the boundaries of exploration and discovery, we embark on a voyage of discovery that will shape our understanding of the universe for generations to come.。
它是如何被发现的英语作文
As a high school student with a keen interest in history and discovery, I have always been fascinated by the stories of how significant things were found. These discoveries often lead to a better understanding of the world, and they can be as diverse as unearthing ancient artifacts, uncovering scientific principles, or stumbling upon natural wonders. Here, I recount a personal journey of discovery that has left a lasting impression on me.It all began with a book I found in our school library. The book, titled Great Discoveries of Our Time, was a compilation of stories about various discoveries that changed the course of history. One story, in particular, caught my eye: the discovery of the Rosetta Stone.The Rosetta Stone, as I learned, was a key to deciphering ancient Egyptian hieroglyphs. Found by a French soldier named PierreFrançois Bouchard in 1799 during the Napoleonic Wars, the stone had inscriptions in three different scripts: Greek, Demotic, and Hieroglyphic. The Greek text provided scholars with a means to translate the other two, ultimately unlocking the secrets of a longlost language.This story sparked my curiosity, and I decided to delve deeper into the world of discoveries. I started with the internet, reading articles and watching documentaries about various discoveries, from the structure of DNA by Watson and Crick to the Higgs boson particle by the Large Hadron Collider team. Each discovery was a testament to human ingenuity and the relentless pursuit of knowledge.One discovery that particularly intrigued me was the story of penicillin.Alexander Fleming, a Scottish biologist, discovered the antibiotic properties of the Penicillium mold in 1928. His accidental finding revolutionized medicine and saved countless lives. It was a reminder that sometimes, the most significant discoveries come from the most unexpected places.My fascination with discoveries led me to a local museum where an exhibition on ancient civilizations was being held. There, I saw artifacts that had been unearthed from archaeological sites, each telling a story of a different time. The curator explained how these artifacts were often found by chance, during construction projects or by farmers tilling their land. It was a humbling reminder of the vastness of human history and the many secrets it still holds.One artifact that stood out to me was a small, intricately carved figurine from the ancient Mayan civilization. The curator explained that such artifacts were often found in burial sites, indicating the importance of the afterlife in Mayan culture. It was a stark contrast to the Rosetta Stone, which was discovered during a military campaign. The contrast between these two discoveries highlighted the diverse circumstances under which historys secrets are revealed.As I continued my exploration, I came across the story of the discovery of the Dead Sea Scrolls. Found in a series of caves near the Dead Sea, these ancient texts provided invaluable insights into Jewish history and the origins of Christianity. The discovery was made by a Bedouin shepherd who was looking for a lost goat. It was a perfect example of howserendipity can play a role in the most significant of finds.These discoveries have not only expanded our knowledge of the world but have also inspired me to think about the potential for discovery in my own life. Whether its a new perspective on a familiar subject or an unexpected insight during a routine task, I believe that there is always something new to learn and discover.In conclusion, the process of discovery is a journey that can be as exciting as it is unpredictable. From the Rosetta Stone to the Dead Sea Scrolls, each discovery is a testament to the human spirits curiosity and drive to understand the world around us. As a high school student, I am inspired by these stories and look forward to the many discoveries that await me in the future.。
SUSY-QCD Corrections to $W^{pm}H^{mp}$ Associated Production at the CERN Large Hadron Colli
mq0 = mq + δmq ,
q 2 q 2 ψq0 = (1 + δZL ) ψqL + (1 + δZR ) ψqR .
1 1
(2) (3)
After calculating the self-energy diagram in Fig. 1, we obtain the explicit expressions of all the renormalization constants as follows: δmq = − αs 2 2 2 2 2 2 2 2 mq [B1 (m2 ˜ sin 2θq ˜[B0 (mq , mg q , mg ˜ , mq ˜1 ) + B1 (mq , mg ˜ , mq ˜2 )] + mg ˜ , mq ˜1 ) (4) 3π 2 2 −B0 (m2 q , mg ˜ , mq ˜2 )] , 2αs ˜ 1 2 2 2 ˙1 ˙ 2 mg ˙1 ˙2 cos2 θq sin 2θq (5) ˜B1 + sin θq ˜B1 + mq [B1 + B1 + ˜(B0 − B0 )] , 3π mq 2αs ˜ 1 2 2 2 ˙1 ˙ 2 mg ˙1 ˙2 sin2 θq sin 2θq (6) ˜B1 + cos θq ˜B1 + mq [B1 + B1 + ˜(B0 − B0 )] , 3π mq
B.
Analytical Results
We consider the associated production of W + H − from the collision of the two protons with momentum P1 and P2 at the LHC. First, we define the Mandelstam variables of the subprocess b(p1 )¯ b(p2 ) → W + (p4 )H − (p3 ) as s = (p1 + p2 )2 = (p3 + p4 )2 , t = (p1 − p3 )2 = (p2 − p4 )2 , u = (p1 − p4 )2 = (p2 − p3 )2 .
Higgs Boson Mass From Gauge-Higgs Unification
Theory Division, KEK, Tsukuba 305-0801, Japan
Abstract In certain five dimensional gauge theories the Standard Model Higgs doublet is identified, after compactification on the orbifold S 1 /Z2 , with the zero mode of the fifth component of the gauge field. An effective potential for the Higgs field is generated via quantum corrections, triggered by the breaking of the underlying gauge symmetry through boundary conditions. The quartic Higgs coupling can be estimated at low energies by employing the boundary condition that it vanishes at the compactification scale Λ, as required by five dimensional gauge invariance. For Λ 1013 − 1014 GeV, the Standard Model Higgs boson mass is found to be mH = 125± 4 GeV, corresponding to a top quark pole mass Mt = 170.9 ± 1.8 GeV. A more complete (gaugeHiggs-Yukawa) unification can be realized for Λ ∼ 108 GeV, which happens to be the scale at which the SU(2) weak coupling and the top quark Yukawa coupling have the same value. For this case, mH = 117 ± 4 GeV.
Search for Standard Higgs Boson at Supercolliders
The Standard Model which describes within an unprecendental scale of energies and distances the strong and electroweak interactions of elementary particles relays on a few basic principles - the renormalizability, the gauge invariance and the spontaneous breaking of the underlying gauge symmetry. The principle of the renormalizability which is considered often as something lying beyond the limits of experimental test is in fact one of the most important (if not the major) ingredients of the quantum field theory. The requirement of renormalizabilty which content and deep meaning were uncovered in the fundamental textbook by N.N.Bogolyubov and D.V.Shirkov [1] plays the central role in the construction and classification of the field theoretic models. They split in general on two classes. In the renormalizable models the ultraviolet divergences of the radiative corrections are under mathematically rigorous control due to the famous Bogolyubov-Parasiuk theorem [2]. These models which preserve their locality in all orders of the perturbation theory are characterised by a finite number of relevant dimensionless coupling constants whose dependence on an arbitrary dimensional normalization parameter is described by the renormalization group [1]. These so-called the “running” coupling constants depending on the model may have or the asymptotic freedom behaviour at large momenta (as for non-abelian gauge theories) or like in quantum electrodynamics with an abelian gauge symmetry reveal the growth of the effective coupling constant in the ultraviolet region. The second class of field theoretical models - the non-renormalizable models have a very serious drawback which makes them useless for description of particle interactions at the present level of knowledge. First of all, the non-renormalizable models have infinite number of divergent matrix elements that requires as a consequence an introduction of 3
二十一世纪的新发现作文
二十一世纪的新发现作文英文回答：In the 21st century, there have been numerous groundbreaking discoveries in various fields, from science and technology to medicine and space exploration. One of the most significant discoveries is the detection of gravitational waves, which was first announced in 2016. This discovery confirmed a major prediction of Albert Einstein's general theory of relativity and opened up a new window to observe the universe.Another remarkable discovery in the 21st century is the development of CRISPR gene-editing technology. This revolutionary tool allows scientists to precisely edit DNA, leading to potential breakthroughs in treating genetic diseases and creating genetically modified organisms.Furthermore, the discovery of exoplanets outside of our solar system has expanded our understanding of the universeand the possibility of extraterrestrial life. With the advancement of telescopes and space exploration technology, astronomers have identified thousands of exoplanets, someof which may have the conditions to support life.In the field of medicine, the development of immunotherapy has transformed cancer treatment byharnessing the body's immune system to target and destroy cancer cells. This has led to significant improvements inthe survival rates of patients with certain types of cancer.In addition, the discovery of the Higgs boson particleat the Large Hadron Collider in 2012 provided crucial evidence for the mechanism of mass generation in the universe, as proposed by the Standard Model of particle physics.These discoveries have not only advanced human knowledge and understanding of the world around us, butthey have also opened up new possibilities for scientific and technological advancements in the future.中文回答：在21世纪，各个领域都取得了许多突破性的发现，从科学技术到医学和太空探索。
学科学爱科学的作文600到1千字
学科学爱科学的作文600到1千字英文回答:I love science because it allows me to explore the wonders of the world and understand how things work. It satisfies my curiosity and fuels my desire to learn.Science is like a language that helps us communicate with nature and unravel its secrets.Science is not just about memorizing facts and formulas. It is a way of thinking and problem-solving. It teaches usto observe, experiment, and analyze data to draw logical conclusions. For example, when I was studying biology, I learned about the process of photosynthesis. By understanding the chemical reactions involved, I could explain why plants need sunlight to grow and produce oxygen.Moreover, science has practical applications that improve our lives. It has led to the development of new technologies and medicines that save lives and make ourdaily tasks easier. For instance, the invention of the internet has revolutionized communication, allowing us to connect with people from all over the world in an instant.Science also encourages critical thinking and creativity. It challenges us to question existing theories and come up with innovative solutions. One famous example is Albert Einstein's theory of relativity, which revolutionized our understanding of space and time. His groundbreaking ideas were initially met with skepticism, but they eventually changed the course of physics.In addition, science fosters collaboration and global cooperation. Scientists from different countries work together to tackle complex problems and share knowledge. This international collaboration has led to major breakthroughs in various fields, such as the discovery of the Higgs boson particle at the Large Hadron Collider.中文回答：我热爱科学，因为它让我能够探索世界的奇迹，理解事物的运作方式。
Higgs Boson Production and Decay at the Tevatron
DESY 98-159 hep-ph/9810289 October 1998Higgs Boson Production and Decay at the Tevatron∗arXiv:hep-ph/9810289v1 8 Oct 1998Michael SpiraII. Institut f¨r Theoretische Physik† , Universit¨t Hamburg, Luruper Chaussee 149, u a D–22761 Hamburg, GermanyAbstractThe theoretical status of Higgs boson production and decay at the Tevatron within the Standard Model and its minimal supersymmetric extension is reviewed. The focus will be on the evaluation of higher-order corrections to the production cross sections and their phenomenological implications.Contribution to the Workshop Physics at Run II – Supersymmetry/Higgs, 1998, Fermilab, USA Supported by Bundesministerium f¨ r Bildung und Forschung (BMBF), Bonn, Germany, under Conu tract 05 7 HH 92P (5), and by EU Program Human Capital and Mobility through Network Physics at High Energy Colliders under Contract CHRX–CT93–0357 (DG12 COMA).†∗1IntroductionThe search for Higgs bosons is of primary interest for present and future experiments. In the Standard Model [SM] the existence of a single Higgs particle is predicted as a consequence of electroweak symmetry breaking by means of the Higgs mechanism [1]. The direct search at the LEP experiments leads to a lower bound of ∼ 90 GeV [2] on the value of the Higgs mass, while triviality and unitarity constraints require the Higgs mass to be smaller than O(1 TeV). At the upgraded Tevatron experiment, a p¯ collider with p √ a c.m. energy s = 2 TeV, SM Higgs bosons will mainly be produced via gluon fusion gg → H and the Drell–Yan like production q q → W ∗ → W H. Since an intermediate mass ¯ ¯ pairs, the QCD background of b¯ production Higgs boson will dominantly decay into bb b will be too large to allow for a detection of the Higgs boson produced in the gluon fusion process. Recently it has been shown that a detection of the Higgs boson from W fusion W W → H seems to be impossible due to the overwhelming QCD background [3]. Thus, the primary possibility to find the SM Higgs boson at the Tevatron will be via the Drell– Yan like process. Careful studies have shown that a discovery of the SM Higgs boson at the upgraded Tevatron might be possible for Higgs masses up to about 120 GeV [4]. Apart from the dominant b¯ decay [4] it turned out that a discovery may also be feasible via the b + − H → τ τ decay [5] in H + W/Z production, while the gold-plated mode of the LHC, gg → H → ZZ ∗ → 4ℓ± , is hopeless at the Tevatron [4]. Recently it has been found that there is also the possibility to detect the processes gg → H → W ∗ W ∗ → ℓνjj, ℓ+ ℓ− ν ν by ¯ using the strong angular correlations among the final state leptons [6]. The SM Higgs mass is unstable against quantum fluctuations in the context of grand unified theories, which force the Higgs mass to be of the order of the GUT scale MGU T ∼ 1016 GeV. The most attractive solution to this hierarchy problem is provided by the introduction of supersymmetry. The minimal supersymmetric extension of the SM [MSSM] requires two Higgs doublets, leading to the existence of 5 elementary Higgs particle, two neutral CP-even (h, H), one neutral CP-odd (A) and two charged ones (H ± ). At treelevel the mass of the light scalar Higgs boson h is restricted to be smaller than the Z mass MZ . However, radiative corrections to the MSSM Higgs sector are large, since they increase with the fourth power of the large top quark mass mt . They enhance the upper < bound on the light scalar Higgs mass to Mh ∼ 135 GeV [7]. For the discovery at the Tevatron the light scalar Higgs boson h will mainly be produced via q q → W/Z + h analogously to the SM case. However, for large tgβ the associ¯ ated production meachanisms q q , gg → b¯ + h/A become competitive due to the enhanced ¯ b Yukawa couplings to b quarks. Finally, similar to the LHC the light scalar Higgs may be detectable in SUSY particle production process via the decay χ0 → χ0 h in the final state ˜2 ˜1 cascade decays [8]. Charged Higgs bosons can also be searched for at the Tevatron [9]. They will be produced in top quark decays t → bH + , if their masses are light anough. At the Tevatron ¯ the process p¯ → tt with t → bH + is sensitive to charged Higgs bosons for large tgβ. The p Drell–Yan like charged Higgs pair production p¯ → H + H − and gluon fusion gg → H + H − p processes seem to be difficult to detect, while the analysis of the associated production 2p¯ → W ± H ∓ requires a more careful background study in order to investigate its relevance p for charged Higgs searches at the Tevatron. Finally gluon-gluon fusion gg → t¯ − , bH − ′ ± gluon-bottom fusion gb → tH and quark-bottom fusion qb → q bH provide additional possibilities to search for charged Higgs bosons at the Tevatron.2Higgs Boson Decays¯ φ → ffIn the intermediate Higgs mass range the SM Higgs decay H → b¯ is dominating, while the b decay H → τ + τ − reaches a branching ratio of O(10%), see Fig. 1. In the past the QCD1Standard Model BR(HSM)10-1bb WW* *_ττ cc_+ −gg10-2ZZ* *100105110115120125130135140MH [GeV]Figure 1: Branching ratios of the dominant decay modes of the SM Higgs particle. All relevant higher order corrections are taken into account. The shaded bands represent the 2 variations due to the uncertainties in the input parameters: αs (MZ ) = 0.120 ± 0.003, mb (Mb ) = (4.22 ± 0.05) GeV, mc (Mc ) = (1.22 ± 0.06) GeV, Mt = (174 ± 5) GeV. corrections have been evaluated [10]. They turn out to be moderate for the decay mode ¯ H → tt in the threshold region, while they are large for the H → b¯ c¯ decays due to large b, c logarithmic contributions. These can be absorbed in the running quark mass by replacing the scale by the Higgs mass. In order to gain a consistent prediction of the partial decay widths one has to use direct fits of the MS masses mQ (MQ ) to experimental data. The evolution of mQ (MQ ) to mQ (MH ) is controlled by the renormalization group equations b for the running MS masses. As a result the QCD corrections reduce the H → b¯ decay width by ∼ 50% and the H → c¯ width by ∼ 75% relative to the Born term expressed in c terms of the quark pole masses MQ . In the MSSM the decay modes h, H, A → b¯ τ + τ − dominate the neutral Higgs decay b, < modes for large tgβ, while for small tgβ they are important for Mh,H,A ∼ 150 GeV as can be inferred from Figs. 2a–c. The dominant decay modes of the charged Higgs particles are H + → τ + ντ , t¯ [see Fig. 2d]. Analogous to the SM case the QCD corrections reduce b the partial decay widths into b, c quarks by about 50–75% as a result of the running quark masses, while they are moderate for decays into top quarks. 31 BR(h) tgβ = 3 10-1bb_1bb BR(h) tgβ = 30_1_ bb (tgβ=30) BR(H) _ bb tgβ=3 τ τ (tgβ=30)+ −1hhhhtt BR(H) tgβ=3ττ+ −10-1ττ+ −WW→←gg ←cc_WW 10-110-1ZZ10-2gg cc_WW10-2ττ ←ZZ gg ←γγ 10 90 100 110 Mh [GeV] 120-2+ −gg ZA _ cc 100 200 300 500 MH [GeV] 1000 10-2γγ 10-310 85 90 95 Mh [GeV] 100 105-38080100200 300 500 MH [GeV]1000Fig. 2a1 bb BR(A) tgβ = 3 10-1_Fig. 2bbb_tt Zh_1 BR(A) tgβ = 30 10-11τνtb1 BR(H ) tgβ = 3±τνtbBR(H ) tgβ = 30±ττ+ −ττ+ −10-1Wh10-1WA 10-210-210 tt_-2cb cs µν 10cb-2cs µνgg 10-3gg 200 500 MA [GeV] 1000 10-3100100200 500 MA [GeV]100010-3100200 300 MH± [GeV]50010-3100200 300 MH± [GeV]500Fig. 2cFig. 2dFigure 2: Branching ratios of the MSSM Higgs bosons h(a), H(b), A(c), H ± (d) for nonSUSY decay modes as a function of their masses for two values of tgβ = 3, 30 and vanishing mixing. The common squark mass has been chosen as MS = 1 TeV. Below the corresponding thresholds the decays A → t∗ t and H + → t∗¯ into off-shell b top quarks turn out to be important, since they reach branching ratios of O(1%) already far below the thresholds for on-shell top quarks [11]. H → W W, ZZ> In the SM the decays H → W W, ZZ are dominant for MH ∼ 140 GeV, since they increase with the third power of the Higgs mass for large Higgs masses, see Fig. 1. Decays into > off-shell W, Z bosons H → W ∗ W ∗ , Z ∗ Z ∗ are sizeable already for Higgs masses MH ∼ 100 GeV, i.e. significantly below the W W/ZZ thresholds [11, 12]. In the MSSM the decays h, H → W W, ZZ are suppressed by kinematics and, in general, by SUSY couplings and are thus less important than in the SM. Their branching ratios turn out to be sizeable only for small tgβ or in the decoupling regime, where the light scalar Higgs particle h reaches the upper bound of its mass. The gluonic (photonic) decays of the Higgs bosons h, H, A → gg(γγ) reach branching ratios of ∼ 10% (∼ 10−3 ) in the SM and MSSM and are unimportant at the Tevatron. 4The decay mode H → hh is dominant in the MSSM for small tgβ in a wide range of ¯ heavy scalar Higgs masses MH below the tt threshold, see Fig. 2b. The dominant radiative corrections to this decay arise from the corrections to the self-interaction λHhh in the MSSM and are large [7]. The decay mode H → AA is only important at the lower end of the heavy scalar Higgs mass range. φ → φ′ + W/ZH → hh, AA¯ The decay modes H → AZ and A → hZ are important for small tgβ below the tt thresh+ ∗ (∗) old, see Figs. 2b,c. Similarly the decays H → W A, W h are sizeable for small tgβ and MH + < mt + mb , see Fig. 2d. The dominant higher-order corrections can be absorbed into the couplings and masses of the Higgs sector. Below the corresponding thresholds decays into off-shell Higgs and gauge bosons turn out to be important especially for small tgβ [11], see Figs. 2b–d. Decays into SUSY particles Higgs decays into charginos, neutralinos and third-generation sfermions can become important, once they are kinematically allowed [13] as can be inferred from Fig. 3, which shows the branching ratios of the heavy Higgs bosons into gauginos and squarks as functions of their masses for a special SUSY scenario. Thus they could complicate the Higgs search at the Tevatron, since the decay into the LSP will be invisible.1 bb BR(h) tgβ = 30* _χ0χ0 1 1 WW*10-1ττ+ −ggZZ-2* *cc_108090100 Mh [GeV]110120130Figure 3: Branching ratios of the light scalar MSSM Higgs boson h decays into charginos/neutralinos as a function of its mass for tgβ = 30. The mixing parameters have been chosen as µ = 150 GeV, At = 2.45 TeV, Ab = 0 and the squark masses of the first two generations as MQ = 1000 GeV. The gaugino mass parameter has been set to M2 = 136 GeV. The masses of the lightest gauginos are mχ0 = 56.5 GeV and mχ± = 94.1 ˜1 ˜1 GeV.53Higgs Boson ProductionThe most relevant SM Higgs production mechanism at the Tevatron is Higgs-strahlung off W, Z bosons q q → W ∗ /Z ∗ → W/Z + H. The cross section reaches values of 10−1 – ¯ < 1 pb in the relevant Higgs mass range MH ∼ 120 GeV, where this production process may be visible at the Tevatron [4], see Fig. 4. The QCD corrections coincide with those of the Drell-Yan process and increase the cross sections by about 30% [14, 15]. The theoretical uncertainty can be estimated as ∼ 15% from the remaining scale dependence. The dependence on different sets of parton densities is rather weak and leads to a variation of the production cross sections by about 15%.10 2 σ(pp→H+X) [pb] √s = 2 TeV Mt = 175 GeV gg→H 1-1_ _q q → V ∗ → V H [V = W, Z] ¯10CTEQ4M10qq→Hqq-2qq’→HW qq→HZ gg,qq→Htt_ _ _ _1010-310-4gg,qq→Hbb 80 100 120 140 MH [GeV] 160 180 200_√ Figure 4: Higgs production cross sections at the Tevatron [ s = 2 TeV] for the various production mechanisms as a function of the Higgs mass. The full QCD-corrected results for the gluon fusion gg → H, vector boson fusion qq → V V qq → Hqq, Higgs-strahlung ¯ q q → V ∗ → HV and associated production gg, q q → Htt, Hb¯ are shown. The QCD ¯ ¯ b corrections to the last process are unknown and thus not included. In the MSSM the Higgs-strahlung processes are in general suppressed by the SUSY couplings. However, the process q q → W ∗ /Z ∗ → W/Z + h can be important in the ¯ decoupling regime, where the light scalar Higgs particle h exhibits SM Higgs properties, see Fig. 5a,b. ¯ b q q , gg → φtt, φb¯ ¯In the SM both processes of Higgs radiation off top and bottom quarks are unimportant due to the small event rates, see Fig. 4. However, in the MSSM Higgs radiation off bottom quarks becomes important for large tgβ with cross sections exceeding 10 pb for the light scalar (h) and the pseudoscalar (A) Higgs particles, see Fig. 5. Thus, the theoretical prediction is crucial for the large tgβ regime in the MSSM. 610 2σ(pp→h/H+X) [pb] √s = 2 TeV Mt = 175 GeV gg→h CTEQ4 tgβ = 3_101-110hW hZ hqq HW hbb _ htt_gg→H10-2Htt_10-3Hqq h H 80 100 120 H H Hbb_HZ 160 180 20010-4140 Mh/H [GeV]Fig. 5a10 4 103σ(pp→h/H+X) [pb] √s = 2 TeV gg→h__10 2 10 1 10 10 10 10-1 -2 -3 -4Mt = 175 GeV CTEQ4 tgβ = 30hbb gg→H Hbb hW hZ hqq h H 80_ _htt 100HW Htt_H H HZ 140 Mh/H [GeV]←Hqq 160 180 200120Fig. 5b √ Figure 5: Neutral MSSM Higgs production cross sections at the Tevatron [ s = 2 TeV] for gluon fusion gg → Φ, vector-boson fusion qq → qqV V → qqh/qqH, vector-boson ¯ bremsstrahlung q q → V ∗ → hV /HV and the associated production gg, q q → Φb¯ ¯ ¯ b/Φtt including all known QCD corrections. (a) h, H production for tgβ = 3, (b) h, H production for tgβ = 30, (c) A production for tgβ = 3, (d) A production for tgβ = 30.7σ(pp→A+X) [pb] 10 √s = 2 TeV Mt = 175 GeV 1-1_CTEQ4 gg→A tgβ = 31010-2gg,qq→Abb__10-310-480100120140 MA [GeV]160180200Fig. 5cσ(pp→A+X) [pb] 10 3 √s = 2 TeV Mt = 175 GeV CTEQ4 102_gg→Atgβ = 3010 gg,qq→Abb 1_ _10-180100120140 MA [GeV]160180200Fig. 5d Figure 5: Continued.8Until now the full QCD corrections are unknown so that the cross sections are only known within about a factor of 2. However, the QCD corrections are known in the limit ¯ of light Higgs particles compared with the heavy quark mass, which is applicable for tt + h ¯ production [16]. In this limit the cross section factorizes into the production of a tt pair, which is convoluted with a splitting function for Higgs radiation t → t + h. This reults in an increase of the cross section by about 20–60%. However, since this equivalent Higgs approxiamtion is only valid within a factor of 2 the result may not be sufficiently reliable. Moreover, it is not valid for bottom quarks, which are more relevant for the Tevatron. 2 2 In the opposite limit of large Higgs masses MH ≫ MQ large logarithms log MH /MQ arise due to quasi-on-shell t-channel quark exchanges, which can be resummed by absorbing them into the heavy quark parton densities. After adding the processes q q , gg → b¯ ¯ b+φ, gb → b + φ and b¯ → φ, after the logarithms have been subtracted accordingly, the final b result turns out to be about a factor of 2 larger than the pure q q , gg → b¯ + φ processes ¯ b [17]. However, there are additional sources of large logarithms, e.g. Sudakov logarithms from soft gluon radiation and large logarithms related to the Yukawa coupling, which will appear in the NLO cross section. Thus, a full NLO calculation is needed in order to gain a satisfactory theoretical prediction of these production processes. In this analysis the scales of the parton densities have been identified with the invariant mass of the final state ¯ QQφ triplet and the bottom Yukawa coupling in terms of the bottom pole mass Mb = 5 GeV. gg → φThe gluon fusion processes are mediated by heavy top and bottom quark triangle loops and in the MSSM by squark loops in addition [18–20]. Gluon fusion is the dominant neutral Higgs production mechanism at the Tevatron, even for large tgβ, with cross sections of b 1–103 pb, see Figs. 4, 5. However, the dominant b¯ final states are overwhelmed by the huge ¯ production and thus hopeless for a detection of the Higgs bosons QCD background of bb via gluon fusion. Only the τ + τ − decay modes may be promising for large tgβ, especially if the Higgs bosons are produced in association with a jet [21]. Moreover, similar to the LHC it may be possible to detect the H → W ∗ W ∗ decay mode in a significant Higgs mass range due to the strong angular correlations of the final state leptons [6]. The two-loop QCD corrections enhance the gluon fusion cross sections by about 60– 100% and are thus large [19]. They are dominated by soft and collinear gluon radiation in the SM and for small tgβ in the MSSM [22]. The remaining scale dependence yields an estimate of ∼ 15% for the theoretical uncertainty. The dependence of the gluon fusion cross section on different parton densities amounts to about 15%. The K factor remains nearly the same after including squark loops, since the dominant soft and collinear gluon effects are universal, thus suppressing the (s)quark mass dependence [20]. Recently the analytical QCD corrections to Higgs + jet production have been evaluated in the limit of heavy top quarks, but there is no numerical analysis so far [23].9Vector boson fusion W W/ZZ → H in the SM leads to a sizeable cross section at the Tevatron, see Fig. 4. Since there are two forward jets in the full process qq → W W/ZZ + qq → H + qq, one may hope to be able to suppress the QCD backgrounds by appropriate cuts. Unfortunatly it turned out that this is not possible [3]. The QCD corrections can easily be obtained in the structure function approach from deep inelastic scattering. They are small enhancing the cross section by about 10% [15, 24]. In the MSSM vector boson fusion is additionally suppressed by SUSY couplings and thus unimportant at the Tevatron. Higgs pairs Light scalar Higgs pair production gg → hh yields a sizeable cross section at the Tevatron > with σ ∼ 10f b [25, 26]. The cross section for q q , gg → hA is of similar size in some regions ¯ of the MSSM paramater space [see Fig. 6]. Since the process gg → H → hh is sensitive to the trilinear coupling λHhh it is important for a partial reconstruction of the Higgs potential. One may hope that the dominant b¯ ¯ b¯ + τ − final states can be extracted bbb, bτ from the QCD backgrounds due to the different event topologies. The two-loop QCD corrections have recently been calculated [for gg initial states in the limit of heavy top quarks, thus leading to a reliable result for small tgβ]. They enhance the gg → hh, hA production cross sections by about 70–90% and the Drell–Yan-like q q → hA cross section ¯ by about 30% [26].123.5 67.1 103W W/ZZ → H131.6 77.7_143.3 85.0157.9 89.6174.4 92.4192.0 94.3210.3 MH [GeV] 95.5 Mh [GeV]10 2σ(pp → hh/hA + X) [fb] √s=2 TeVmt = 175 GeV tgβ = 310 qq,gg → hA 1-1_gg → hh1010-280100120140 MA [GeV]160180200√ Figure 6: QCD corrected production cross sections of hh, hA pairs at the Tevatron [ s = 2 TeV] as a function of the pseudoscalar Higgs mass for tgβ = 3. The secondary axis exhibits the corresponding values of the light and heavy scalar Higgs masses Mh , MH . The bump in the gg → hh cross section originates from resonance gg → H → hh production.104ConclusionsAll relevant NLO QCD corrections to Higgs boson decays within the SM and MSSM areknown so that the theoretical uncertainties are sufficiently small.At the Tevatron thedecay modesφ0→b¯b,τ+τ−,W∗W∗are relevant for the Higgs boson search in Run II.All corrections beyond LO are contained in the program HDECAY1[15,27],which calculatesthe branching ratios of SM and MSSM Higgs bosons.For neutral Higgs boson production most QCD corrections are known leading to anearly complete theoretical status.The only processes,which are known at LO,are Higgsradiation offtop and bottom quarks,the latter being important for large tgβin the MSSM.The known corrections to the important processes are moderate and thus well under control.The remaining theoretical uncertainties are less than∼15%2. 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a r X i v :h e p -p h /0501172v 1 18 J a n 2005Higgs boson production at hadron collidersin the k T -factorization approachA.V.Lipatov,N.P.ZotovFebruary 2,2008D.V.Skobeltsyn Institute of Nuclear Physics,M.V.Lomonosov Moscow State University,119992Moscow,Russia Abstract We consider the Higgs boson production at high energy hadron colliders in the framework of the k T -factorization approach.The attention is focused on the dominant gluon-gluon fu-sion subprocess.We calculate the total cross section and transverse momentum distributions of the inclusive Higgs production using unintegrated gluon distributions in a proton obtained from the full CCFM evolution equation.We show that k T -factorization gives a possibility to investigate the associated Higgs boson and jets production.We calculate the transverse mo-mentum distributions and study the Higgs-jet and jet-jet azimuthal correlations in the Higgs +one or two jet production processes.We demonstrate the importance of the higher-order corrections within the k T -factorization approach.These corrections should be developed and taken into account in the future applications.1IntroductionIt is well known that the electroweak symmetry breaking in the Standard Model of elementary particle interactions is achieved via the Higgs mechanism.In the minimal model there are a single complex Higgs doublet,where the Higgs boson H is the physical neutral Higgs scalar which is the only remaining part of this doublet after spontaneous symmetry breaking.In non-minimal models there are additional charged and neutral scalar Higgs particles.The search for the Higgs boson takes important part at the Fermilab Tevatron experiments and will be one of the main fields of study at the CERN LHC collider [1].The experimental detection of the H will be great triumph of the Standard Model of electroweak interactions and will mark new stage in high energy physics.At LHC conditions,the gluon-gluon fusion gg→H is the dominant inclusive Higgs production mechanism[2,3].In this process,the Higgs production occurs via triangle heavy(top)quark loop.The gluon fusion and weak boson fusion(qq→qqH subprocess via t-channel exchange of a W or Z bosons)are also expected to be the dominant sources of semi-inclusive Higgs production(in association with one or two hadronic jets)[4].The detailed theoretical studies of such processes are necessary,in particular,to determine an optimal set of cuts on thefinal state particles.It is obvious that the gluon-gluon fusion contribution to the Higgs production at LHC is strongly dependend on the gluon density xG(x,µ2)in a ually gluon density are described by the Dokshitzer-Gribov-Lipatov-Altarelli-Parizi(DGLAP)evolution equa-tion[5]where large logarithmic terms proportional to lnµ2are taken into account.The cross sections can be rewritten in terms of hard matrix elements convoluted with gluon density functions.In this way the dominant contributions come from diagrams where the parton emissions in the initial state are strongly ordered in virtuality.This is called collinear fac-torization,as the strong ordering means that the virtuality of the parton entering the hard scattering matrix elements can be neglected compared to the large scaleµ2.However,at the√LHC energies,typical values of the incident gluon momentum fractions x∼m H/the gluons to the Higgs via top-quark loop can be replaced by an effective coupling.Thus it reduces the number of loops in a given diagram by one.The large m t approximation isvalid to an accuracy of∼5%in the intermediate Higgs mass range m H<2m t,as long as transverse momenta of the Higgs orfinal jets are smaller than of the top quark mass (p T<m t)[16].Within this approach,the total cross section for gg→H+X is knownto next-to-next-to-leading order(NNLO)accuracy[18].Higher-order QCD corrections to inclusive Higgs production were found to be large:their effect increases the leading ordercross section by about80−100%[19](see also[20]).A particularly interesting quantity is the transverse momentum distribution of the pro-duced Higgs boson.The precise theoretical prediction of the dσ/dp T at the LHC is importantfor quantitative evaluation of the required measurement accuracies and detector performance. It is well-known that thefixed-order perturbative QCD is applicable when the Higgs trans-verse momentum is comparable to the m H.Hovewer,the main part of the events is expectedin the small-p T region(p T≪m H),where the coefficients of the perturbative series inαs are enhanced by powers of large logarithmic terms proportional to ln m2H/p2T.Thereforereliable predictions at small p T can only be obtained if these terms will be resummed to all orders.Such procedure is called soft-gluon resummation[21-23]and has been performed in collinear calculations at leading logarithmic(LL),next-to-leading logarithmic(NLL)[24] and next-to-next-to-leading logarithmic(NNLL)[25]levels.Recently it was shown[26]that in the framework of k T-factorization approach the soft gluon resummation formulas are the result of the approximate treatment of the solutions of the CCFM evolution equation(in the b-representation).There are several additional motivations for our study of the Higgs production in the k T-factorization approach.First of all,in the standard collinear approach,when the transverse momentum of the initial gluons is neglected,the transerse momentum of thefinal Higgs boson in gg→H subprocess is zero.Therefore it is necessary to include an initial-state QCD radi-ation to generate the p T distributions.It is well known at present that the k T-factorization naturally includes a large part of the high-order perturbative QCD corrections[27].This fact is illustrated more detailed in Figure1,which is a schematical representation of a typ-ical Higgs+jet production process.Figure1(a)shows thefixed-order perturbative QCD picture where the upper part of the diagram(above the dash-dotted line)corresponds to the gg→gH subrocess,and the lower part describes the gluon evolution in a proton.As the incoming gluons are assumed to have zero transverse momentum,the transverse momentum distributions of the produced Higgs and jet are totally determined by the properties of the O(α3s)matrix element.In the k T-factorization approach(Figure1(b)),the underlying par-tonic subprocess is gg→H,which is formally of order O(α2s).Some extra powers ofαs are hidden in the gluon evolution represented by the part of the diagram shown below the dash-dotted line.In contrast with the collinear approximation,the k T-factorization takes into account the gluon transverse motion.Since the upper gluon in the parton ladder is not included in the hard interaction,its transverse momentum is now determined by the properties of the evolution equation only.It means that in the k T-factorization approach the study of transverse momenta distributions in the Higgs production via gluon-gluon fusion will be direct probe of the unintegrated gluon distributions in a proton.In this case the transverse momentum of the produced Higgs should be equal to the sum of the transverse momenta of the initial gluons.Therefore future experimental studies at LHC can be usedas further test of the non-collinear parton evolution.In the previous studies[26,28,29]the k T-factorization formalism was applied to cal-culate transverse momentum distribution of the inclusive Higgs production.The simplified solution of the CCFM equation in single loop approximation[30](when small-x effects can be neglected)were used in[26].In such approximation the CCFM evolution is reduced to the DGLAP one with the difference that the single loop evolution takes the gluon trans-verse momentum k T into account.Another simplified solution of the CCFM equation was proposed in Ref.[31],where the transverse momenta of the incoming gluons are generated in the last evolution step(Kimber-Martin-Ryskin prescription).The calculations[26,29] were done using the on-mass shell(independent from the gluon k T)matrix element of the gg→H subprocess and rather the similar results have been obtained.In Ref.[28]in the framework of MC generator CASCADE[32]the off-mass-shell matrix element obtained by F.Hautmann[33]has been used with full CCFM evolution.In present paper we investigate Higgs production at hadron colliders using the full CCFM-evolved unintegrated gluon densities[28].We obtain the obvious expression for the g∗g∗→H off-mass-shell matrix element in the large m t limit apart from Ref.[33].After that, we calculate the total cross section and transverse momentum distribution of the inclusive Higgs production at Tevatron and LHC.To illustrate the fact that in the k T-factorization approach the main features of collinear higher-order pQCD corrections are taken into account effectively,we give theoretical predictions for the Higgs+one jet and Higgs+two jet production processes using some physically motivated approximation.In Section2we recall the basic formulas of the k T-factorization formalism with a brief review of calculation steps.In Section3we present the numerical results of our calculations and discussion.Finally,in Section4,we give summary of our results.2Basic formulasWe start from the effective Lagrangian for the Higgs boson coupling to gluons[16]:L eff=αs2 1/2G aµνG aµνH,(1)where G F is the Fermi coupling constant,G aµνis the gluonfield strength tensor and H is the Higgsfield.The triangle vertex Tµν(k1,k2)for two off-shell gluons having four-momenta k1 and k2and color indexes a and b respectively,can be obtained easily from the Lagrangian(1):Tµν(k1,k2)=iδab αs2 1/2[kµ2kν1−(k1·k2)gµν].(2)To calculate the squared off-mass-shell matrix element for the g∗g∗→H subprocess it is necessary to take into account the non-zero virtualities of the initial gluons k21=−k21T=0, k22=−k22T=0.We have obtained1|¯M|2(g∗g∗→H)=α2s(µ2)2 m2H+k21T+k22T+2|k1T||k2T|cosφ 2cos2φ,(3)whereφis the azimuthal angle between transverse momenta k1T and k2T,the transverse momentum of the produced Higgs boson is p T=k1T+k2T and the virtual gluon polarization tensor has been taken in the form[7,8]ǫµǫ∗ν=kµT kνTx1A(x1,k21T,µ2)d k21Tdφ1x2A(x2,k22T,µ2)d k22Tdφ2dy H= α2s(µ2)22π,(6)where y H is the Higgs rapidity in the proton-proton c.m.frame.The longitudinal momentumfractions x1and x2are given byx1= s exp(y H),x2= s exp(−y H).(7) If we average the expression(6)over transverse momenta k1T and k2T and take the limitk21T→0,k22T→0,we obtain well-established expression[2]for Higgs production cross section in leading-order perturbative QCD:dσ(p¯p→H+X)=α2s(µ2)2m2H2See Refs.[15,34]for more details. 3lipatov@theory.sinp.msu.ru3Numerical results and discussion3.1Inclusive Higgs productionWe now are in a position to present our numerical results.First we describe our theoret-ical input and the kinematical conditions.Besides the Higgs mass m H,the cross section(6) depend on the uninterated gluon distribution A(x,k2T,µ2)and the energy scaleµ.The new fits of the unintegrated gluon density(J2003set1—3)have been recently presented[28]. The full CCFM equation in a proton was solved numerically using a Monte Carlo method. The input parameters werefitted to describe the proton structure function F2(x,Q2).Since these gluon densities reproduce well the forward jet production at HERA,charm and bot-tom production data at Tevatron[28]and charm and J/ψproduction at LEP2energies[35], we use it(namely J2003set1)in our calculations.As is often done for Higgs production, we choose the renormalization and factorization scales to beµ=ξm H,and vary the scale parameterξbetween1/2and2about the default valueξ=1.Also we use LO formula for the strong coupling constantαs(µ2)with n f=4active quarkflavours andΛQCD=200 MeV,such thatαs(M2Z)=0.1232.In Figure2and3we display our prediction for the transverse momentum and rapidity√distributions of the inclusive Higgs production at the LHC(s=1.96TeV) and LHC conditions as function Higgs mass are plotted in Figure5and6in the mass range m H=100−200GeV.The solid lines are obtained byfixing both the factorization and renormalization scales at the default valueµ=m H.In order to estimate the theoretical uncertainties in our predictions,we vary the unphysical parameterξas indicated above. These uncertainties are presented by upper and lower dashed lines.Wefind that our default predictions agree very well with recent NNLO results[18].For example,when Higgs bosonmass is m H=120GeV,our calculations giveσ=0.84pb at Tevatron andσ=35.9pbat LHC.However,the scale dependences are rather large.At LHC energy,it changes from about20%when m H=100GeV,to about50%when m H=200GeV.At Tevatron,it rangefrom40%to50%,respectively.This fact indicates the necessarity of high-order correctionsinclusion in the k T-factorization formalism.But one should note that in the k T-factorization the role of such correction is very different in comparison with the corrections in the collinearapproach,since part of the standard high-order corrections are already included at LO level in k T-factorization4.At the same time the theoretical uncertainties of the collinear QCDcalculations,after inclusion of both NNLO corrections and soft-gluon resummation at theNNLL level,are about10%in the low mass range m H<200GeV[18].3.2Higgs production in association with jetsNow we demonstrate how k T-factorization approach can be used to calculate the semi-inclusive Higgs production rates.The produced Higgs boson is accompanied by a number of gluons radiated in the course of the gluon evolution.As it has been noted in Ref.[38],on the average the gluon transverse momentum decreases from the hard interaction blocktowards the proton.As an approximation,we assume that the gluon k′closest to the Higgs compensates the whole transverse momentum of the virtual gluon participating in the gluonfusion,i.e.k′T≃−k T(see Figure1).All the other emitted gluons are collected together in the proton remnant,which is assumed to carry only a negligible transverse momentumcompared to k′T.This gluon gives rise to afinal hadron jet with p jet T=k′T.From the two hadron jets represented by the gluons from the upper and lower evolution ladder we choose the one carrying the largest transverse momentum,and then compute Higgs with an associated jet cross sections at the LHC energy.We have applied the usual cut on thefinal jet transverse momentum|p jet T|>20GeV.Our predictions for the transverse momentum distribution of the Higgs+one jet production are shown in Figure7.As in the inclusive Higgs production case,we test four different m H values in the transverse momentum ditributions.All curves here are the same as in Figure2.One can see the shift of the peak position in the p T distributions in comparison with inclusive production,which is direct consequence of the|p jet T|>20GeV cut.We note that the rapidity interval between the jet and the Higgs boson is naturally large.It is because there is angular ordering in the CCFM evolution,which is equivalent to an ordering in rapidity of the emitted gluons.The investigation of the different azimuthal correlations betweenfinal particles in semi-inclusive Higgs production provides many interesting insights.In particular,studying ofthese quantities are important to clean separation of weak-boson fusion and gluon-gluon fusion contributions.To demonstrate the possibilities of the k T-factorization approach,we present here the two azimuthal angle distributions.First,we calculate azimutal angle dis-tribution between the Higgs boson andfinal jet transverse momenta in the Higgs+one jet production process.Second,we calculate azimuthal angle distributions between the two final jet transverse momenta in the Higgs+two jet production process.In this case the Higgs boson is centrally located in rapidity between the two jets and it is very far from either jet,and the kinematical cut|p jet T|>20GeV was applied for bothfinal jets.We set nocuts on the jet-jet invariant mass.Our results are shown in Figure8and9,respectively. Figure8demonstrated roughly the back-to-back Higgs+one jet production.In Figure9 we obtained a dip at90degrees in jet-jet azimuthal correlation,which is characteristic for loop-induced Higgs coupling to gluons[39].Thefixed-order perturbative QCD calculations of the gg→ggH subprocess give the similar result[16].However,as it was already men-tioned above,such calculations are very cumbersome even at leading order.The evaluation of the radiative corrections at O(αs)to Higgs+two jet production would imply the calcula-tion of up to hexagon quark loops and two-loop pentagon quark loops,which are at present unfeasible[20].We note that contribution from the weak-boson fusion to the Higgs+two jet production hasflat behavior of the jet-jet angular distribution[16,20].To illuminate the sensitivity of the Higgs production rates to the details of the uninte-grated gluon distribution,we repeated our calculations for jet-jet angular correlations using J2003set2gluon density[28](dashed line in Figure9).This density takes into account the singular and non-singular terms in the CCFM splitting function,where the Sudakov and non-Sudakov form factors were modified accordinly.We note that J2003set1takes into ac-count only singular terms.Both these sets describe the proton structure function F2(x,Q2) at HERA reasonable well.However,one can see the very large discrepancy(about order of magnitude)between predictions of J2003set1and set2unintegrated gluon densities.The similar difference was claimed[28]for charm and bottom production at Tevatron also.This fact clearly indicates again that high-order corrections to the leading order k T-factorization are important and should be developed for future applications.4ConclusionsWe have considered the Higgs boson production via gluon-gluon fusion at high energy hadron colliders in the framework of the k T-factorization approach.Our interests were fo-cused on the Higgs boson total cross section and transverse momenta distributions at Teva-tron and LHC colliders.In our numerical calculations we use the J2003set1unintegrated gluon distribution,which was obtained recently from the full CCFM evolution equation.Wefind that k T-factorization gives the very close to NNLO pQCD results for the inclusive Higgs production total cross sections.It is because the main part of the high-order collinear pQCD corrections is already included in the k T-factorization.Also we have demonstrated that k T-factorization gives a possibility to investigate the associated Higgs boson and jets production in much more simple manner,than it can be done in the collinear factorization. Using some approximation,we have calculated transverse momentum distributions and in-vestigated the Higgs-jet and jet-jet azimuthal correlations in the Higgs+one or two jet production processes.However,the scale dependence of our calculations is rather large(of the order of20−50%),which indicates the importance of the high-order correction within the k T-factorization approach.These corrections should be developed and taken into account in the future applications.We point out that in this paper we do not try to give a better prediction for Higgs production than thefixed-order pQCD calculations.The main advantage of our approach is that it is possible to obtain in straighforward manner the analytic description whichreproduces the main features of the collinear high-order pQCD calculations5.But in any case,the future experimental study of such processes at LHC will give important information about non-collinear gluon evolution dynamics,which will be useful even for leading-order k T-factorization formalism.5AcknowledgementsThe authors are very grateful to H.Jung for possibility to use the CCFM code for unintegrated gluon distributions in our calculations,for reading of the manuscript and useful discussion.We thank S.P.Baranov for encouraging interest and helpful discussions.N.Z. thanks P.F.Ermolov for support and the DESY directorate for the hospitality and support. 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