New Evaluation of the QED Running Coupling and of the Muonium Hyperfine Splitting
国际经济学第九版英文课后答案第7单元
CHAPTER 7ECONOMIC GROWTH AND INTERNATIONAL TRADEOUTLINE7.1 Introduction7.2 Growth of Factors of Production7.2a Labor Growth and Capital Accumulation Over Time7.2b The Rybczynski Theorem7.3 Technical Progress7.3a Neutral, Labor-Saving, and Capital-Saving Technical Progress7.3b Technical Progress and the Nation's Production FrontierCase Study 7-1: Changes in Relative Resource Endowments of Various Countries and Regions Case Study 7-2: Change in Capital-Labor Rations in Selected Countries7.4 Growth and Trade: The Small Country Case7.4a The Effects of Growth on Trade7.4b Illustration of Factor Growth, Trade, and Welfare7.4c Technical Progress, Trade, and WelfareCase Study 7-3: Growth of Output per Worker from Capital Deepening, TechnologicalChange, and Improvements in Efficiency7.5 Growth and Trade: The Large-Country Case7.5a Growth and the Nation's Terms of Trade and Welfare7.5b Immiserizing Growth7.5c Illustration of Beneficial Growth and TradeCase Study 7-4: Growth, Trade, and the Giants of the Future7.6 Growth, Change in Tastes, and Trade in Both Nations7.6a Growth and Trade in Both Nations7.6b Change in Tastes and Trade in Both NationsCase Study 7-5: Change in the Revealed Comparative Advantage of Various Countries orRegionsCase Study 7-6: Growth, Trade, and Welfare in the Leading Industrial NationsAppendix: A7.1 Formal Proof of Rybczynski TheoremA7.2 Growth with Factor ImmobilityA7.3 Graphical Analysis of Hicksian Technical ProgressKey TermsComparative statics Antitrade production and consumptionDynamic analysis Neutral production and consumptionBalanced growth Normal goodsRybczynski theorem Inferior goodsLabor-saving technical progress Terms-of-trade effectCapital-saving technical progress Wealth effectProtrade production and consumption Immiserizing growthLecture Guide1.This is not a core chapter and it is one of the most challenging chapters in international tradetheory. It is included for more advanced students and for completeness.2.If I were to cover this chapter, I would present two sections in each of three lectures.Time permitting, I would, otherwise cover Sections 1 and 2, paying special attention to theRybczynski theorem.Answer to Problems1. a) See Figure 1.b) See Figure 2c) See Figure 3.2. See Figure 4.3. a) See Figure 5.b) See Figure 6.c) See Figure 7.4. Compare Figure 5 to Figure 1.Compare Figure 6 to Figure 3. Note that the two production frontiers have the same vertical or Y intercept in Figure 6 but a different vertical or Y intercept in Figure 3.Compare Figure 7 to Figure 2. Note that the two production frontiers have the samehorizontal or X intercept in Figure 7 but a different horizontal or X intercept in Figure 2.5. See Figure 8 on page 66.6. See Figure 9.7. See Figure 10.8. See Figure 11.9. See Figure 12.10. See Figure 13 on page 67.11. See Figure 14.12. See Figure 15.13.The United States has become the most competitive economy in the world since the early-1990 period.1990’s while the data in Table 7.3 refers to the 196514.The data in Table 7.4 seem to indicate that China had a comparative advantage incapital-intensive commodities and a comparative disadvantage in unskilled-laborintensive commodities in 1973. This was very likely due to the many traderestrictions and subsidies, which distorted the comparative advantage o f China.Its true comparative advantage became evident by 1993 after China had started to liberalize its economy.App. 1a. See Figure 16.1b. For production and consumption to actually occur at the newequilibrium point after the doubling of K in Nation 2, we mustassume either than commodity X is inferior or that Nation 2 is toosmall to affect the relative commodity prices at which it trades.1c. Px/Py must rise (i.e., Py/Px must fall) as a result of growth only.Px/Py will fall even more with trade.1. If the supply of capital increases in Nation 1 in the production of commodity Yonly, the VMPLy curve shifts up, and w rises in both industries. Some labor shifts to the production of Y, the output of Y rises and the output of X falls, r falls, and Px/Py is likely to rise.2. Capital investments tend to increase real wages because they raise the K/L ratioand the productivity of labor. Technical progress tends to increase K/L and realwages if it is L-saving and to reduce K/L and real wages if it is K-saving.Multiple-Choice Questions1. Dynamic factors in trade theory refer to changes in:a. factor endowmentsb. technologyc. tastes*d. all of the above2. Doubling the amount of L and K under constant returns to scale:a. doubles the output of the L-intensive commodityb. doubles the output of the K-intensive commodityc. leaves the shape of the production frontier unchanged*d. all of the above.3. Doubling only the amount of L available under constant returns to scale:a. less than doubles the output of the L-intensive commodity*b. more than doubles the output of the L-intensive commodityc. doubles the output of the K-intensive commodityd. leaves the output of the K-intensive commodity unchanged4. The Rybczynski theorem postulates that doubling L at constant relative commodity prices:a. doubles the output of the L-intensive commodity*b. reduces the output of the K-intensive commodityc. increases the output of both commoditiesd. any of the above5. Doubling L is likely to:a. increases the relative price of the L-intensive commodityb. reduces the relative price of the K-intensive commodity*c. reduces the relative price of the L-intensive commodityd. any of the above6.Technical progress that increases the productivity of L proportionately more than the productivity of K is called:*a. capital savingb. labor savingc. neutrald. any of the above7. A 50 percent productivity increase in the production of commodity Y:a. increases the output of commodity Y by 50 percentb. does not affect the output of Xc. shifts the production frontier in the Y direction only*d. any of the above8. Doubling L with trade in a small L-abundant nation:*a. reduces the nation's social welfareb. reduces the nation's terms of tradec. reduces the volume of traded. all of the above9. Doubling L with trade in a large L-abundant nation:a. reduces the nation's social welfareb. reduces the nation's terms of tradec. reduces the volume of trade*d. all of the above10.If, at unchanged terms of trade, a nation wants to trade more after growth, then the nation's terms of trade can be expected to:*a. deteriorateb. improvec. remain unchangedd. any of the above11. A proportionately greater increase in the nation's supply of labor than of capital is likely to result in a deterioration in the nation's terms of trade if the nation exports:a. the K-intensive commodity*b. the L-intensive commodityc. either commodityd. both commodities12. Technical progress in the nation's export commodity:*a. may reduce the nation's welfareb. will reduce the nation's welfarec. will increase the nation's welfared. leaves the nation's welfare unchanged13. Doubling K with trade in a large L-abundant nation:a. increases the nation's welfareb. improves the nation's terms of tradec. reduces the volume of trade*d. all of the above14. An increase in tastes for the import commodity in both nations:a. reduces the volume of trade*b. increases the volume of tradec. leaves the volume of trade unchangedd. any of the above15. An increase in tastes of the import commodity of Nation A and export in B:*a. will reduce the terms of trade of Nation Ab. will increase the terms of trade of Nation Ac. will reduce the terms of trade of Nation Bd. any of the aboveADDITIONAL ESSAYS AND PROBLEMS FOR PART ONE1.Assume that both the United States and Germany produce beef and computer chipswith the following costs:United States Germany(dollars) (marks)Unit cost of beef (B) 2 8Unit cost of computer chips (C) 1 2a) What is the opportunity cost of beef (B) and computer chips (C) in each country?b)In which commodity does the United States have a comparative cost advantage?What about Germany?c)What is the range for mutually beneficial trade between the United States andGermany for each computer chip traded?d)How much would the United States and Germany gain if 1 unit of beef isexchanged for 3 chips?Ans. a) In the United States:the opportunity cost of one unit of beef is 2 chips;the opportunity cost of one chip is 1/2 unit of beef.In Germany:the opportunity cost of one unit of beef is 4 chips;the opportunity cost of one chip is 1/4 unit of beef.b) The United States has a comparative cost advantage in beef with respect toGermany, while Germany has a comparative cost advantage in computer chips.c)The range for mutually beneficial trade between the United States and Germanyfor each unit of beef that the United States exports is2C < 1B < 4Cd) Both the United States and Germany would gain 1 chip for each unit of beeftraded.2.Given: (1) two nations (1 and 2) which have the same technology but differentfactor endowments and tastes, (2) two commodities (X and Y) produced under increasing costs conditions, and (3) no transportation costs, tariffs, or other obstructions to trade. Prove geometrically that mutually advantageous trade between the two nations is possible.Note: Your answer should show the autarky (no-trade) and free-trade points of production and consumption for each nation, the gains from trade of each nation, and express the equilibrium condition that should prevail when trade stopsexpanding.)Ans.: See Figure 1 on page 74.Nations 1 and 2 have different production possibilities curves and differentcommunity indifference maps. With these, they will usually end up with differentrelative commodity prices in autarky, thus making mutually beneficial tradepossible.In the figure, Nation 1 produces and consumes at point A and Px/Py=PA in autarky,while Nation 2 produces and consumes at point A' and Px/Py=PA'. Since P A < P A', Nation 1 has a comparative advantage in X and Nation 2 in Y. Specialization inproduction proceeds u ntil point B in Nation 1 and point B' in Nation 2, at whichP B=P B' and the quantity supplied for export of each commodity exactly equals thequantity demanded f or import. Thus, Nation 1 starts at point A in production andconsumptionin autarky, moves to point B in production, and by exchanging BC ofX for CE of Y reaches point E in consumption. E > A since it involves more of bothX and Y and lieson a higher community indifference curve. Nation 2 starts at A' inproduction andconsumption in autarky, moves to point B' in production, and byexchanging B'C' of Y for C'E' of X reaches point E'in consumption (which exceedsA').At Px/Py=P B=P B', Nation 1 wants to export BC of X for CE of Y, while Nation 2wants to export B'C' (=CE) of Y for C'E' (=BC) of X. Thus, P B=P B'is theequilibrium relative commodity price because it clears both (the X and Y) markets. 3.Draw a figure showing: (1) in Panel A a nation's demand and supply curve for Atraded commodity and the nation's excess supply of the commodity, (2) in Panel Cthe trade partner's demand and supply curve for the same traded commodity and its excess demand for the commodity, and (3) in Panel B the supply and demand for the quantity traded of the commodity, its equilibrium price, and why a price above orbelow the equilibrium price will not persist. At any other price, QD QS, and P willchange to P2.Ans. See Figure 2 on page 74.The equilibrium relative commodity price for commodity X (the traded commodityexported by Nation 1 and imported by Nation 2) is P2 and the equilibrium quantityof commodity X traded is Q2.4.a) Identify the conditions that may give rise to trade between two nations.b) What are some of the assumptions o n which the Heckscher-Ohlin theory isbased?c) What does this theory say about the pattern of trade and effect of trade on factorprices?Ans. a) Trade can be based on a difference in factor endowments, technology, or tastes between two nations. A difference either in factor endowments or technology resultsin a different production possibilities frontier for each nation, which, unlessneutralized by a difference in tastes, leads to a difference in relative commodity price and mutually beneficial trade. If two nations face increasing costs and have identical production possibilities frontiers but different tastes, there will also be a difference inrelative commodity prices and the basis for mutually beneficial trade between thetwo nations. The difference in relative commodity prices is then translated i nto adifference in absolute commodity prices between the two nations, which is theimmediate cause of trade.– asb) The Heckscher-Ohlin theory (sometimes referred to as the modern theoryopposed to the classical theory - of international trade) assumes that nations have the same tastes, use the same technology, face constant returns to scale (i.e., a given percentage increase in all inputs increases output by the same percentage) but differ widely in factor endowments. It also says that in the face of identical tastes ordemand conditions, this difference in factor endowments will result in a difference inrelative factor prices between nations, which in turn leads to a difference in relativecommodity prices and trade. Thus, in the Heckscher-Ohlin theory, the internationaldifference in supply conditions alone determines the pattern of trade. To be noted isthat the two nations need not be identical in other respects in order for internationaltrade to be based primarily on the difference in their factor endowments.c) The Heckscher-Ohlin theorem postulates that each nation will export thecommodity intensive in its relatively abundant and cheap factor and import thecommodity intensive in its relatively scarce and expensive factor. As an importantcorollary, it adds that under highly restrictive assumptions, t rade will completelyeliminate the pretrade relative and absolute differences in the price of homogeneous factors among nations. Under less restrictive and more usual conditions, however,trade will reduce, but not eliminate, the pretrade differences in relative and absolutefactor prices among nations. In any event, the Heckscher-Ohlin theory does saysomething very useful on how trade affects factor prices and the distribution ofincome in each nation. Classical economists were practically silent on this point.5. consumers demand more of commodity X (the L-intensive commodity) and less ofcommodity Y (the K- intensive commodity). Suppose that Nation 1 is India,commodity X is textiles, and commodity Y is food. Starting from the no-tradeequilibrium position and using the Heckscher-Ohlin model, trace the effect ofthis change in tastes on India's(a) relative commodity prices and demand for food and textiles,(b) production of both commodities and factor prices, and(c) comparative advantage and volume of trade.(d) Do you expect international trade to lead to the complete equalization ofrelative commodity and factor prices between India and the United States?Why?Ans. a. The change in tastes can be visualized by a shift toward the textile axis in India's indifference map in such a way that an indifference curve is tangentto the steeper segment of India's production frontier (because of increasingopportunity costs) after the increase in demand for textiles. This will causethe pretrade relative commodity price of textiles to rise in India.b. The increase in the relative price of textiles will lead domesticproducers in India to shift labor and capital from the production of food tothe production of textiles. Since textiles are L-intensive in relation to food,the demand for labor and therefore the wage rate will rise in India. At thesame time, as the demand for food falls, the demand for and thus the priceof capital will fall. With labor becoming relative more expensive,producers in India will substitute capital for labor in the production of bothtextiles and food.Even with the rise in relative wages and in the relative price of textiles,India still remains the L-abundant and low-wage nation with respect to anation such as the United States. However, the pretrade difference in therelative price of textiles between India and the United States is nowsomewhat smaller than before the change in tastes in India. As a result thevolume of trade required to equalize relative commodity prices and hencefactor prices is smaller than before. That is, India need now export asmaller quantity of textiles and import less food than before for therelative price of textiles in India and the United States to be equalized.Similarly, the gap between real wages and between India and the UnitedStates is now smaller and can be more quickly and easily closed (i.e., witha smaller volume of trade).c. Since many of the assumptions required for the complete equalization ofrelative commodity and factor prices do not hold in the real world, greatdifferences can be expected and do in fact remain between real wages inIndia and the United States. Nevertheless, trade would tend to reduce thesedifferences, and the H-O model does identify the forces that must beconsidered to analyze the effect of trade on the differences in the relative andabsolute commodity and factor prices between India and the United States.5.(a) Explain why the Heckscher-Ohlin trade model needs to be extended.(b) Indicate in what important ways the Heckscher-Ohlin trade model can beextended.(c) Explain what is meant by differentiated products and intra-industry trade.Ans. (a) The Heckscher-Ohlin trade model needs to be extended because, while generally correct, it fails to explain a significant portion of international trade, particularly the trade in manufactured products among industrial nations.(b)The international trade left unexplained by the basic Heckscher-Ohlin trade modecan be explained by(1) economies of scale,(2) intra-industry trade, and(3) trade based on imitation gaps and product differentiation.(c)Differentiated products refer to similar, but not identical, products (such as cars,typewriters, cigarettes, soaps, and so on) produced by the same industry or broad product group. Intra-industry trade refers to the international trade in differentiated products.。
高二英语经济体系单选题50题
高二英语经济体系单选题50题1. In recent years, the price of housing in some big cities has been rising continuously. Which of the following factors mainly affects this phenomenon in terms of economic concepts?A. Supply and demandB. Production costC. Government subsidyD. Technological innovation答案：A。
解析：本题考查经济概念中的供求关系。
在大城市中，住房价格持续上涨，主要原因是供求关系。
随着人口流入大城市，对住房的需求增加，而土地等资源有限，住房的供应相对不足，从而推动房价上涨。
选项B生产成本虽然也可能影响房价，但在大城市房价持续上涨的主要因素还是供求关系。
选项C政府补贴通常会抑制房价上涨而不是导致房价持续上升。
选项D技术创新与房价持续上涨关系不大，不是主要影响因素。
从语法角度看，这是一个主从复合句，“in terms of economic concepts”为介词短语作状语。
2. When the supply of a certain product exceeds the demand, what will usually happen to its price?A. IncreaseB. Remain unchangedC. DecreaseD. Fluctuate randomly答案：C。
解析：本题考查供求关系对价格的影响这一经济概念。
当产品供过于求时，市场上产品数量多于需求数量，为了出售产品，商家往往会降低价格，所以价格通常会下降。
选项A价格增加是供不应求时的情况。
选项B价格保持不变不符合供求关系影响价格的规律。
选项D随机波动不是供过于求时价格的通常走向。
performance evaluation methods
performance evaluation methodsPerformance evaluation is one of the most critical aspects of any organization. It refers to the process of assessing an employee's work performance against predetermined standards of performance. The primary objective of performance evaluation is to identify the strengths and weaknesses of an employee and provide feedback to help them improve their work.There are several methods of performance evaluation used in organizations. This article will discuss some of these methods in detail.1. Self-EvaluationSelf-evaluation is a method of performance evaluation in which employees assess their performance against predetermined goals and standards. This method involves employees reflecting on their work, identifying their strengths and weaknesses, and documenting their accomplishments.Self-evaluation can be a valuable tool, as it allows employees to take ownership of their performance, encourages self-reflection, and can improve communication between employee and employer.2. Peer EvaluationPeer evaluation is a method of performance evaluation in which an employee's performance is assessed by their colleagues. This method involves colleagues providing feedback on the employee's work, interpersonal skills, and overall contribution to the team.Peer evaluation can be a useful tool, as it provides employees with valuable feedback from their colleagues, encourages teamwork and collaboration, and can help identify areas for improvement.3. Manager EvaluationManager evaluation is a method of performance evaluation in which an employee's performance is assessed by their manager. This method involves the manager providing feedback on the employee's work performance, as well as their contribution to the organization.Manager evaluation can be effective if the manager has a good understanding of the employee's work and can provide constructive feedback. However, this method can also be biased, as managers may be influenced by personal biases or factors outside of work.4. 360-Degree Feedback360-degree feedback is a method of performance evaluation in which an employee's performance is assessed by multiple sources, including colleagues, managers, and customers. This method involves gathering feedback from a variety of perspectives to provide a comprehensive view of theemployee's performance.360-degree feedback can be an effective tool, as it provides a more complete picture of an employee's performance, encourages collaboration and teamwork, and can help identify areas for improvement.In conclusion, there are several methods of performance evaluation used in organizations. Each method has itsstrengths and weaknesses, and the most effective method will depend on the objectives of the evaluation and the culture of the organization. Employers should consider using a varietyof methods to provide a comprehensive view of an employee's performance and encourage ongoing development and improvement.。
Simple Atoms, Quantum Electrodynamics and Fundamental Constants
a r Xi v:h ep-ph/3525v119May23Simple Atoms,Quantum Electrodynamics and Fundamental Constants Savely G.Karshenboim Max-Planck-Institut f¨u r Quantenoptik,85748Garching,Germany D.I.Mendeleev Institute for Metrology (VNIIM),St.Petersburg 198005,Russia Abstract.This review is devoted to precision physics of simple atoms.The atoms can essentially be described in the framework of quantum electrodynamics (QED),however,the energy levels are also affected by the effects of the strong interaction due to the nuclear structure.We pay special attention to QED tests based on studies of simple atoms and consider the influence of nuclear structure on energy levels.Each calculation requires some values of relevant fundamental constants.We discuss the ac-curate determination of the constants such as the Rydberg constant,the fine structure constant and masses of electron,proton and muon etc.1Introduction Simple atoms offer an opportunity for high accuracy calculations within the framework of quantum electrodynamics (QED)of bound states.Such atoms also possess a simple spectrum and some of their transitions can be measured with high precision.Twenty,thirty years ago most of the values which are of interest for the comparison of theory and experiment were known experimentally with a higher accuracy than from theoretical calculations.After a significant theoretical progress in the development of bound state QED,the situation has reversed.A review of the theory of light hydrogen-like atoms can be found in [1],while recent advances in experiment and theory have been summarized in the Proceedings of the International Conference on Precision Physics of Simple Atomic Systems (2000)[2].Presently,most limitations for a comparison come directly or indirectly fromthe experiment.Examples of a direct experimental limitation are the 1s −2s transition and the 1s hyperfine structure in positronium,whose values are known theoretically better than experimentally.An indirect experimental limitation is a limitation of the precision of a theoretical calculation when the uncertainty of such calculation is due to the inaccuracy of fundamental constants (e.g.of the muon-to-electron mass ratio needed to calculate the 1s hyperfine interval in muonium)or of the effects of strong interactions (like e.g.the proton structure for the Lamb shift and 1s hyperfine splitting in the hydrogen atom).The knowledge of fundamental constants and hadronic effects is limited by the experiment and that provides experimental limitations on theory.This is not our first brief review on simple atoms (see e.g.[3,4])and to avoid any essential overlap with previous papers,we mainly consider here the2Savely G.Karshenboimmost recent progress in the precision physics of hydrogen-like atoms since the publication of the Proceedings[2].In particular,we discuss•Lamb shift in the hydrogen atom;•hyperfine structure in hydrogen,deuterium and helium ion;•hyperfine structure in muonium and positronium;•g factor of a bound electron.We consider problems related to the accuracy of QED calculations,hadronic effects and fundamental constants.These atomic properties are of particular interest because of their appli-cations beyond atomic physics.Understanding of the Lamb shift in hydrogen is important for an accurate determination of the Rydberg constant Ry and the proton charge radius.The hyperfine structure in hydrogen,helium-ion and positronium allows,under some conditions,to perform an accurate test of bound state QED and in particular to study some higher-order corrections which are also important for calculating the muonium hyperfine interval.The latter is a source for the determination of thefine structure constantαand muon-to-electron mass ratio.The study of the g factor of a bound electron lead to the most accurate determination of the proton-to-electron mass ratio,which is also of interest because of a highly accurate determination of thefine structure con-stant.2Rydberg Constant and Lamb Shift in HydrogenAboutfifty years ago it was discovered that in contrast to the spectrum predicted by the Dirac equation,there are some effects in hydrogen atom which split the 2s1/2and2p1/2levels.Their splitting known as the Lamb shift(see Fig.1)was successfully explained by quantum electrodynamics.The QED effects lead to a tiny shift of energy levels and for thirty years this shift was studied by means of microwave spectroscopy(see e.g.[5,6])measuring either directly the splitting of the2s1/2and2p1/2levels or a bigger splitting of the2p3/2and2s1/2levels(fine structure)where the QED effects are responsible for approximately10%of the fine-structure interval.The recent success of two-photon Doppler-free spectroscopy[7]opens an-other way to study QED effects directed by high-resolution spectroscopy of gross-structure transitions.Such a transition between energy levels with dif-ferent values of the principal quantum number n is determined by the Coulomb-Schr¨o dinger formula(Zα)2mc2E(nl)=−,(2)2hSimple Atoms,QED and Fundamental Constants31s 2s 1/23/2Fig.1.Spectrum of the hydrogen atom (not to scale).The hyperfine structure is neglected.The label rf stands for radiofrequency intervals,while uv is for ultraviolet transitionswhere h is the Planck constant.Another problem in the interpretation of optical measurements of the hydrogen spectrum is the existence of a few levels which are significantly affected by the QED effects.In contrast to radiofrequency mea-surements,where the 2s −2p splitting was studied,optical measurements have been performed with several transitions involving 1s ,2s ,3s etc.It has to be noted that the theory of the Lamb shift for levels with l =0is relatively simple,while theoretical calculations for s states lead to several serious complifications.The problem of the involvement of few s levels has been solved by introducing an auxiliary difference [8]∆(n )=E L (1s )−n 3E L (ns ),(3)for which theory is significantly simpler and more clear than for each of the s states separately.Combining theoretical results for the difference [9]with measured frequencies of two or more transitions one can extract a value of the Rydberg constant and of the Lamb shift in the hydrogen atom.The most recent progress in determination of the Rydberg constant is presented in Fig.2(see [7,10]for references).Presently the optical determination [7,4]of the Lamb shift in the hydrogen atom dominates over the microwave measurements [5,6].The extracted value of the Lamb shift has an uncertainty of 3ppm.That ought to be compared with the uncertainty of QED calculations (2ppm)[11]and the uncertainty of the contributions of the nuclear effects.The latter has a simple form∆E charge radius (nl )=2(Zα)4mc 22δl 0.(4)To calculate this correction one has to know the proton rms charge radius R p with sufficient accuracy.Unfortunately,it is not known well enough [11,3]and leads to an uncertainty of 10ppm for the calculation of the Lamb shift.It is likely4Savely G.KarshenboimDate of publicationR y − 10 973 731.568 [m −1]Fig.2.Progress in the determination of the Rydberg constant by two-photon Doppler-free spectroscopy of hydrogen and deuterium.The label CODATA,1998stands for the recommended value of theRydberg constant (Ry =10973731.568549(83)m −1[10])Fig.3.Measurement of the Lamb shift in hydrogen atom.Theory is presented accord-ing to [11].The most accurate value comes from comparison of the 1s −2s transition at MPQ (Garching)and the 2s −ns/d at LKB (Paris),where n =8,10,12.Three re-sults are shown:for the average values extracted from direct Lamb shift measurements,measurements of the fine structure and a comparison of two optical transitions within a single experiment.The filled part is for the theorythat a result for R p from the electron-proton elastic scattering [12]cannot be improved much,but it seems to be possible to significantly improve the accuracy of the determination of the proton charge radius from the Lamb-shift experiment on muonic hydrogen,which is now in progress at PSI [13].Simple Atoms,QED and Fundamental Constants 53Hyperfine Structure and Nuclear EffectsA similar problem of interference of nuclear structure and QED effects exists for the 1s and 2s hyperfine structure in hydrogen,deuterium,tritium and helium-3ion.The magnitude of nuclear effects entering theoretical calculations is at the level from 30to 200ppm (depending on the atom)and their understanding is unfortunately very poor [11,14,15].We summarize the data in Tables 1and 2(see [15]1for detail).Hydrogen,1s 1420405.751768(1)[16,17]1420452-33Deuterium,1s 327384.352522(2)[18]327339138Tritium,1s 1516701.470773(8)[19]1516760-363He +ion,1s -8665649.867(10)[20]-8667494-213Table 1.Hyperfine structure in light hydrogen-like atoms:QED and nuclear contri-butions ∆E (Nucl).The numerical results are presented for the frequency E/hThe leading term (so-called Fermi energy E F )is a result of the nonrelativistic interaction of the Dirac magnetic moment of electron with the actual nuclear magnetic moment.The leading QED contribution is related to the anomalous magnetic moment and simply rescales the result (E F →E F ·(1+a e )).The result of the QED calculations presented in Table 1is of the formE HFS (QED)=EF ·(1+a e )+∆E (QED),(5)where the last term which arises from bound-state QED effects for the 1s state is given by∆E 1s (QED)=E F × 32+α(Zα)23ln 1(Zα)26Savely G.Karshenboim+4ln2−28115ln2+34π .(6)This term is in fact smaller than the nuclear corrections as it is shown in Table2 (see[15]for detail).A result for the2s state is of the same form with slightly different coeffitients[15].Hydrogen23-33Deuterium23138Tritium23-363He+ion108-213π (Zα)m R cSimple Atoms,QED and Fundamental Constants7 In the next section we consider the former option,comparison of the1s and2s hyperfine interval in hydrogen,deuterium and ion3He+.4Hyperfine Structure of the2s State in Hydrogen, Deuterium and Helium-3IonOur consideration of the2s hyperfine interval is based on a study of the specific differenceD21=8·E HFS(2s)−E HFS(1s),(9) where any contribution which has a form of(7)should vanish.D21(QED3)48.93711.3056-1189.252D21(QED4)0.018(3)0.0043(5)-1.137(53)D21(nucl)-0.0020.0026(2)0.317(36)Table 3.Theory of the specific difference D21=8E HFS(2s)−E HFS(1s)in light hydrogen-like atoms(see[15]for detail).The numerical results are presented for the frequency D21/hThe difference(9)has been studied theoretically in several papers long ago [28,29,30].A recent study[31]shown that some higher-order QED and nuclear corrections have to be taken into account for a proper comparison of theory and experiment.The theory has been substantially improved[15,32]and it is summarized in Table3.The new issues here are most of the fourth-order QED contributions(D21(QED4))of the orderα(Zα)3,α2(Zα)4,α(Zα)2m/M and (Zα)3m/M(all are in units of the1s hyperfine interval)and nuclear correc-tions(D21(nucl)).The QED corrections up to the third order(D21(QED3))and the fourth-order contribution of the order(Zα)4have been known for a while [28,29,30,33].For all the atoms in Table3the hyperfine splitting in the ground state was measured more accurately than for the2s state.All experimental results but one were obtained by direct measurements of microwave transitions for the1s and 2s hyperfine intervals.However,the most recent result for the hydrogen atom has been obtained by means of laser spectroscopy and measured transitions lie in the ultraviolet range[21,22].The hydrogen level scheme is depicted in Fig.4. The measured transitions were the singlet-singlet(F=0)and triplet-triplet (F=1)two-photon1s−2s ultraviolet transitions.The eventual uncertainty of the hyperfine structure is to6parts in1015of the measured1s−2s interval.8Savely G.Karshenboim1s2s F = 0 (singlet)Fig.4.Level scheme for an optical measurement of the hyperfine structure (hfs )in the hydrogen atom (notto scale)[22].The label rf stands here for radiofrequency intervals,while uv is for ultraviolet transitions21Fig.5.Present status of measurements of D 21in the hydrogen atom.The results are labeled with the date of the measurement of the 2s hyperfine structure.See Table 1for referencesThe optical result in Table 1is a preliminary one and the data analysis is still in progress.The comparison of theory and experiment for hydrogen and helium-3ion is summarized in Figs.5and 6.Simple Atoms,QED and Fundamental Constants9Fig.6.Present status of measurements of D21in the helium ion3He+.See Table1for references5Hyperfine Structure in Muonium and Positronium Another possibility to eliminate nuclear structure effects is based on studies of nucleon-free atoms.Such an atomic system is to be formed of two leptons.Two atoms of the sort have been produced and studied for a while with high accuracy, namely,muonium and positronium.•Muonium is a bound system of a positive muon and electron.It can be produced with the help of accelerators.The muon lifetime is2.2·10−6sec.The most accurately measured transition is the1s hyperfine structure.The two-photon1s−2s transition was also under study.A detailed review of muonium physics can be found in[34].•Positronium can be produced at accelerators or using radioactive positron sources.The lifetime of positronium depends on its state.The lifetime for the1s state of parapositronium(it annihilates mainly into two photons)is1.25·10−10sec,while orthopositronium in the1s state has a lifetime of1.4·10−7s because of three-photon decays.A list of accurately measuredquantities contains the1s hyperfine splitting,the1s−2s interval,2s−2pfine structure intervals for the triplet1s state and each of the four2p states,the lifetime of the1s state of para-and orthopositronium and several branchings of their decays.A detailed review of positronium physics can be found in[35].Here we discuss only the hyperfine structure of the ground state in muonium and positronium.The theoretical status is presented in Tables4and5.The theoretical uncertainty for the hyperfine interval in positronium is determined only by the inaccuracy of the estimation of the higher-order QED effects.The uncertainty budget in the case of muonium is more complicated.The biggest10Savely G.KarshenboimE F 1.000000000 4.459031.83(50)(3)a e0.0011596525170.926(1)QED2-0.000195815-873.147QED3-0.000005923-26.410QED4-0.000000123(49)-0.551(218)Hadronic0.000000054(1)0.240(4)Weak-0.000000015-0.065Table 4.Theory of the1s hyperfine splitting in muonium.The numerical results are presented for the frequency E/h.The calculations[36]have been performed for α−1=137.03599958(52)[37]andµµ/µp=3.18334517(36)which was obtained from the analysis of the data on Breit-Rabi levels in muonium[38,39](see Sect.6)and precession of the free muon[40].The numerical results are presented for the frequency E/hE F 1.0000000204386.6QED1-0.0049196-1005.5QED20.000057711.8QED3-0.0000061(22)-1.2(5)Table5.Theory of the1s hyperfine interval in positronium.The numerical results are presented for the frequency E/h.The calculation of the second order terms was completed in[41],the leading logarithmic contributions were found in[42],while next-to-leading logarithmic terms in[43].The uncertainty is presented following[44] source is the calculation of the Fermi energy,the accuracy of which is limited by the knowledge of the muon magnetic moment or muon mass.It is essentially the same because the g factor of the free muon is known well enough[45].The uncer-tainty related to QED is determined by the fourth-order corrections for muonium (∆E(QED4))and the third-order corrections for positronium(∆E(QED3)). These corrections are related to essentially the same diagrams(as well as the D21(QED4)contribution in the previous section).The muonium uncertainty is due to the calculation of the recoil corrections of the order ofα(Zα)2m/M [42,46]and(Zα)3m/M,which are related to the third-order contributions[42] for positronium since m=M.The muonium calculation is not completely free of hadronic contributions. They are discussed in detail in[36,47,48]and their calculation is summarizedSimple Atoms,QED and Fundamental Constants11∆ν(h a d r V P ) [k H z ]Fig.7.Hadronic contributions to HFS in muonium.The results are taken:a from [50],b from [51],c from [52]and d from [36,47]1s hyperfine interval in positronium [MHz]Fig.8.Positronium hyperfine structure.The Yale experiment was performed in 1984[53]and the Brandeis one in 1975[54]in Fig.7.They are small enough but their understanding is very important because of the intensive muon sources expected in future [49]which might allow to increase dramatically the accuracy of muonium experiments.A comparison of theory versus experiment for muonium is presented in the summary of this paper.Present experimental data for positronium together with the theoretical result are depicted in Fig.8.12Savely G.Karshenboim6g Factor of Bound Electron and Muon in MuoniumNot only the spectrum of simple atoms can be studied with high accuracy.Other quantities are accessible to high precision measurements as well among them the atomic magnetic moment.The interaction of an atom with a weak homoge-neous magneticfield can be expressed in terms of an effective Hamiltonian.For muonium such a Hamiltonian has the formH=e2m Ng′µ sµ·B +∆E HFS s e·sµ ,(10)where s e(µ)stands for spin of electron(muon),and g′e(µ)for the g factor ofa bound electron(muon)in the muonium atom.The bound g factors are now known up to the fourth-order corrections[55]including the term of the orderα4,α3m e/mµandα2m e/mµand thus the relative uncertainty is essentially better than10−8.In particular,the result for the bound muon g factor reads[55]2g′µ=g(0)µ· 1−α(Zα)2m e2 m e12πm e108α(Zα)3 ,(11)where g(0)µ=2·(1+aµ)is the g factor of a free muon.Equation(10)has been applied[38,39]to determine the muon magnetic moment and muon mass by measuring the splitting of sublevels in the hyperfine structure of the1s state in muonium in a homogeneous magneticfield.Their dependence on the mag-neticfield is given by the well known Breit-Rabi formula(see e.g.[56]).Since the magneticfield was calibrated via spin precession of the proton,the muon magnetic moment was measured in units of the proton magnetic moment,and muon-to-electron mass ratio was derived asmµµp µp1+aµ.(12)Results on the muon mass extracted from the Breit-Rabi formula are among the most accurate(see Fig.9).A more precise value can only be derived from the muonium hyperfine structure after comparison of the experimental result with theoretical calculations.However,the latter is of less interest,since the most important application of the precise value of the muon-to-electron mass is to use it as an input for calculations of the muonium hyperfine structure while testing QED or determining thefine structure constantsα.The adjusted CODATA result in Fig.9was extracted from the muonium hyperfine structure studies and in addition used some overoptimistic estimation of the theoretical uncertainty (see[36]for detail).Simple Atoms,QED and Fundamental Constants13Value of muon-to-electron mass ratio mµ/m eFig.9.The muon-to-electron mass ratio.The most accurate result obtained from com-parison of the measured hyperfine interval in muonium[38]to the theoretical calcu-lation[36]performed withα−1g−2=137.03599958(52)[37].The results derived from the Breit-Rabi sublevels are related to two experiments performed at LAMPF in1982 [39]and1999[38].The others are taken from the measurement of the1s−2s interval in muonium[57],precession of a free muon in bromine[40]and from the CODATA adjustment[10]7g Factor of a Bound Electron in a Hydrogen-Like Ion with Spinless NucleusIn the case of an atom with a conventional nucleus(hydrogen,deuterium etc.)an-other notation is used and the expression for the Hamiltonian similar to eq.(10) can be applied.It can be used to test QED theory as well as to determine the electron-to-proton mass ratio.We underline that in contrast to most other tests it is possible to do both simultaneously because of a possibility to perform experiments with different ions.The theoretical expression for the g factor of a bound electron can be pre-sented in the form[3,58,59]g′e=2· 1+a e+b ,(13) where the anomalous magnetic moment of a free electron a e=0.0011596522 [60,10]is known with good enough accuracy and b is the bound correction.The summary of the calculation of the bound corrections is presented in Table6. The uncertainty of unknown two-loop contributions is taken from[61].The cal-culation of the one-loop self-energy is different for different atoms.For lighter elements(helium,beryllium),it is obtained from[55]based onfitting data of [62],while for heavier ions we use the results of[63].The other results are taken from[61](for the one-loop vacuum polarization),[59](for the nuclear correction14Savely G.Karshenboimand the electric part of the light-by-light scattering(Wichmann-Kroll)contri-bution),[64](for the magnetic part of the light-by-light scattering contribution) and[65](for the recoil effects).4He+ 2.0021774067(1)10Be3+2.0017515745(4)12C5+ 2.0010415901(4)16O7+ 2.0000470201(8)18O7+ 2.0000470213(8)M iB(14)and the Larmor spin precession frequency for a hydrogen-like ion with spinless nucleusωL=g be2= Z−1 m eωc(16) or an electron-to-ion mass ratiom eZ−1g bωL.(17)Today the most accurate value of m e/M i(without using experiments on the bound g factor)is based on a measurement of m e/m p realized in Penning trap [66]with a fractional uncertainty of2ppm.The accuracy of measurements ofωc andωL as well as the calculation of g b(as shown in[58])are essentially better. That means that it is preferable to apply(17)to determine the electron-to-ion mass ratio[67].Applying the theoretical value for the g factor of the bound electron and using experimental results forωc andωL in hydrogen-like carbonSimple Atoms,QED and Fundamental Constants15Value of ptoron-to-electron mass ratio m p/m eFig.10.The proton-to-electron mass ratio.The theory of the bound g factor is taken from Table6,while the experimental data on the g factor in carbon and oxygen are from[68,69].The Penning trap result from University of Washington is from[66] [68]and some auxiliary data related to the proton and ion masses,from[10],we arrive at the following valuesm p16Savely G.Karshenboim8The Fine Structure ConstantThefine structure constant plays a basic role in QED tests.In atomic and particle physics there are several ways to determine its value.The results are summarized in Fig.11.One method based on the muonium hyperfine interval was briefly discussed in Sect.5.A value of thefine structure constant can also be extracted from the neutral-heliumfine structure[70,71]and from the comparison of theory [37]and experiment[60]for the anomalous magnetic moment of electron(αg−2). The latter value has been the most accurate one for a while and there was a long search for another competitive value.The second value(αCs)on the list of the most precise results for thefine structure constant is a result from recoil spectroscopy[72].Value of the Inverse fine structure constant α-1Fig.11.Thefine structure constant from atomic physics and QED We would like to briefly consider the use and the importance of the recoil result for the determination of thefine structure constant.Absorbing and emit-ting a photon,an atom can gain some kinetic energy which can be determined as a shift of the emitted frequency in respect to the absorbed one(δf).A mea-surement of the frequency with high accuracy is the goal of the photon recoil experiment[72].Combining the absorbed frequency and the shifted one,it is possible to determine a value of atomic mass(in[72]that was caesium)in fre-quency units,i.e.a value of M a c2/h.That may be compared to the Rydberg constant Ry=α2m e c/2h.The atomic mass is known very well in atomic units (or in units of the proton mass)[73],while the determination of electron mass in proper units is more complicated because of a different order of magnitude of the mass.The biggest uncertainty of the recoil photon value ofαCs comes now from the experiment[72],while the electron mass is the second source.Simple Atoms,QED and Fundamental Constants17 The success ofαCs determination was ascribed to the fact thatαg−2is a QED value being derived with the help of QED theory of the anomalous mag-netic moment of electron,while the photon recoil result is free of QED.We would like to emphasize that the situation is not so simple and involvement of QED is not so important.It is more important that the uncertainty ofαg−2originates from understanding of the electron behaviour in the Penning trap and it dom-inates any QED uncertainty.For this reason,the value ofαCs from m p/m e in the Penning trap[66]obtained by the same group as the one that determined the value of the anomalous magnetic moment of electron[60],can actually be correlated withαg−2.The resultα−1=137.03600028(10)(22)Cspresented in Fig.11is obtained using m p/m e from(18).The value of the proton-to-electron mass ratio found this way is free of the problems with an electron in the Penning trap,but some QED is involved.However,it is easy to real-ize that the QED uncertainty for the g factor of a bound electron and for the anomalous magnetic moment of a free electron are very different.The bound theory deals with simple Feynman diagrams but in Coulombfield and in partic-ular to improve theory of the bound g factor,we need a better understanding of Coulomb effects for“simple”two-loop QED diagrams.In contrast,for the free electron no Coulombfield is involved,but a problem arises because of the four-loop diagrams.There is no correlation between these two calculations.9SummaryTo summarize QED tests related to hyperfine structure,we present in Table7the data related to hyperfine structure of the1s state in positronium and muonium and to the D21value in hydrogen,deuterium and helium-3ion.The theory agrees with the experiment very well.The precision physics of light simple atoms provides us with an opportunity to check higher-order effects of the perturbation theory.The highest-order terms important for comparison of theory and experiment are collected in Table8.The uncertainty of the g factor of the bound electron in carbon and oxygen is related toα2(Zα)4m corrections in energy units,while for calcium the crucial order is α2(Zα)6m.Some of the corrections presented in Table8are completely known,some not.Many of them and in particularα(Zα)6m2/M3and(Zα)7m2/M3for the hyperfine structure in muonium and helium ion,α2(Zα)6m for the Lamb shift in hydrogen and helium ion,α7m for positronium have been known in a so-called logarithmic approximation.In other words,only the terms with the highest power of“big”logarithms(e.g.ln(1/Zα)∼ln(M/m)∼5in muonium)have been calculated.This program started for non-relativistic systems in[42]and was developed in[46,8,74,31,15].By now even some non-leading logarithmic terms have been evaluated by several groups[43,75].It seems that we have reached some numerical limit related to the logarithmic contribution and the calculation18Savely G.KarshenboimHydrogen,D2149.13(15),[21,22]48.953(3) 1.20.10Hydrogen,D2148.53(23),[23]-1.80.16Hydrogen,D2149.13(40),[24]0.40.28Deuterium,D2111.16(16),[25]11.3125(5)-1.00.493He+ion,D21-1189.979(71),[26]-1190.072(63) 1.00.013He+,D21-1190.1(16),[27]0.00.18parison of experiment and theory of hyperfine structure in hydrogen-like atoms.The numerical results are presented for the frequency E/h.In the D21case the reference is given only for the2s hyperfine intervalof the non-logarithmic terms will be much more complicated than anything else done before.Hydrogen,deuterium(gross structure)α(Zα)7m,α2(Zα)6mHydrogen,deuterium(fine structure)α(Zα)7m,α2(Zα)6mHydrogen,deuterium(Lamb shift)α(Zα)7m,α2(Zα)6m3He+ion(2s HFS)α(Zα)7m2/M,α(Zα)6m3/M2,α2(Zα)6m2/M,(Zα)7m3/M2 4He+ion(Lamb shift)α(Zα)7m,α2(Zα)6mN6+ion(fine structure)α(Zα)7m,α2(Zα)6mMuonium(1s HFS)(Zα)7m3/M2,α(Zα)6m3/M2,α(Zα)7m2/MPositronium(1s HFS)α7mPositronium(gross structure)α7mPositronium(fine structure)α7mPara-positronium(decay rate)α7mOrtho-positronium(decay rate)α8mPara-positronium(4γbranching)α8mOrtho-positronium(5γbranching)α8m。
The Running Coupling from SU(3) Lattice Gauge Theory
The Infrared Behavior of QCD Propagators in Landau Gauge
a r X i v :h e p -p h /0004141v 1 17 A p r 2000UNITU–THEP–2/2000,FAU–TP3–00/5hep-ph/0004141The Infrared Behavior of QCD Propagators in Landau Gauge ∗Reinhard Alkofer a and Lorenz von Smekalb a Institut f¨u r Theoretische Physik,Universit¨a t T¨u bingen,Auf der Morgenstelle 14,D-72076T¨u bingen,Germany.b Institut f¨u r Theoretische Physik III,Universit¨a t Erlangen–N¨u rnberg,Staudtstr.7,D-91058Erlangen,Germany.Some features of the solutions to the truncated Dyson-Schwinger equations(DSEs)for the propagators of QCD in Landau gauge are summarized.In particular,the Kugo-Ojima confinement criterion is realized,and positivity of transverse gluons is manifestly violated in these solutions.In Landau gauge,the gluon-ghost vertex function offers a convenient possibility to define a nonperturbative running coupling.The infrared fixed point ob-tained from this coupling which determines the 2-point interactions of color-octet quark currents implies the existence of unphysical massless states which are necessary to escape the cluster decomposition of colored clusters.The gluon and ghost propagators,and the nonperturbative running coupling,are compared to recent lattice simulations.A signifi-cant deviation of the running coupling from the infrared behavior extracted in simulations of 3-point functions is attributed to an inconsistency of asymmetric subtraction schemes due to a consequence of the Kugo-Ojima criterion:infrared enhanced ghosts.1.Confinement in Landau Gauge QCDCovariant quantum theories of gauge fields require indefinite metric spaces.Modifica-tions to the standard (axiomatic)framework of quantum field theory are also necessary to accommodate confinement in QCD.These seem to be given by the choice of either relaxing the principle of locality or abandoning the positivity of the representation space.Great emphasis has therefore been put on the idea of relating confinement to the violation of positivity in QCD.Just as in QED,where the Gupta-Bleuler prescription is to enforce the Lorentz condition on physical states,a semi-definite physical subspace can be defined as the kernel of an operator.The physical states then correspond to equivalence classes of states in this subspace differing by zero norm components.Besides transverse photons covariance implies the existence of longitudinal and scalar photons in QED.The latter two form metric partners in the indefinite space.The Lorentz condition eliminates half of these leaving unpaired states of zero norm which do not contribute to observables.Since the Lorentz condition commutes with the S -Matrix,physical states scatter into physical ones exclusively.Color confinement in QCD is ascribed to an analogous mechanism:No colored states should be present in the positive definite space of physical states defined by some suitable condition maintaining physical S -matrix unitarity.Within the framework of2BRS-algebra the completeness of the nilpotent BRS-charge Q B in a state space V of indef-=Ker Q B is defined inite metric is assumed.The(semi-definite)physical subspace Vphysby those states which are annihilated by the BRS charge Q B.Positivity is then proved for physical states[1]which are given by the cohomology H(Q B,V)=Ker Q B/Im Q B≃V s, the covariant space of equivalence classes of BRS-closed modulo exact states(in the image Im Q B of the BRS-charge).In perturbation theory the space H is formed by transverse gluon and quark states. Longitudinal and timelike gluons form(massless)quartet representations with ghosts and are thus unphysical.At the same time the global symmetry J aµ,νcorresponding to gauge transformations generated byθa(x)=a aµxµis spontaneously broken quite analogous to the displacement symmetry in QED.Nonperturbatively,Kugo and Ojima have shown that the identification of BRS-singlet states(in V s)with color singlets is generally possi-ble,in particular also for transverse gluons and quarks,if this global symmetry is restored dynamically[1–3].A sufficient condition for this restoration to happen is that the non-perturbative ghost propagator is more singular than a massless pole in the infrared,i.e.,−1G(p)=3the pure gauge theory can be solved in a one-dimensional approximation [8].Asymptotic expansions of the solutions in the infrared are obtained analytically.While the gluon propagator is found to vanish for small spacelike momenta in this way,an apparent con-tradiction with earlier studies that implied its infrared enhancement can be understood from the observation that the previously neglected ghost propagator now assumes just this:An infrared enhancement of ghosts as predicted by the Kugo-Ojima confinement criterion [3].This infrared behavior of the propagators in Landau gauge was later con-firmed qualitatively by studies of further truncated DSEs [12].Neither does it thus seem to depend on the particular 3-point vertices nor on the one-dimensional approximation employed in our original solutions.These solutions to the coupled gluon-ghost DSEs compare well with recent lattice results available for the gluon [13,14]and the ghost propagator [15](which implement various lattice versions of the Landau gauge condition).Indications towards an infrared vanishing gluon propagator are now seen on the lattice also [14].At least some suppression in the infrared is certainly excluded to be a finite size effect [13].Especially the ghost propagator,however,is in compelling agreement with the lattice data.This is an interesting result for yet another reason:In [15,14]the Landau gauge condition was supplemented by an algorithm to select gauge field configurations from the fundamental modular region which is to avoid Gribov copies.Thus,our results suggest that the existence of such gauge copies might have little effect on the solutions to the Landau gauge DSEs.The positivity violations of transverse gluons as seen in our results [8]combined with the evidence from roughly a decade of lattice simulations with considerably increasing statistics [16,9]leave little doubt on the significance of this result.3.Nonperturbative Running CouplingsLattice Landau gauge results have also become available for nonperturbative running couplings from simulations of the 3-gluon [17,18]and the quark-gluon vertex [19].These seem to have the common feature of a maximum value αmax S (µ0)at a finite momentum scale µ0>0.Below this scale decreasing values of the couplings are extracted towards smaller scales.Such qualitative forms lead to double-valued β-functions,however.Here,we would like to point out that this behavior seems likely to be an artifact of asymmetric subtraction schemes in theories with confinement realized by the Kugo-Ojima criterion.The reason is seen by relating results from asymmetric schemes αasymS to those of symmetric subtractionschemes αsymS which essentially results in a ratio of ghost renormalization functions [11],αasymS (µ)∝lim s →01+u (µ2)4support the infraredfixed point we obtained from the DSEs in[8](withαS(µ→0)≈9.5 and monotonically decreasing forµ>0).This is because such an infraredfixed point entails the existence of unphysical massless(bound)states in the color-octet channels of4-point functions(of gluon/ghost and quark/antiquark correlations).It might also be worthwhile to consider simulations of such4-point functions in lattice Landau gauge, and to assess possible indications for massless states in these correlations directly.The existence of massless unphysical states is a necessary condition for a failure of the cluster decomposition property for colored clusters,see Chap.4.3.4in Ref.[2].Recently we solved the coupled propagator DSEs with quarks included[20].Implica-tions on positivity violations and confinement for quarks are currently being investigated. AcknowledgementsR.A.thanks the organizers of Quark Nuclear Physics2000for making this stimulating conference possible.He is grateful to S.Furui,A.Schreiber,A.Thomas and A.Williams for many helpful discussions.Furthermore,he thanks all members of the CSSM for the extraordinary hospitality extended to him at his stay after the conference. REFERENCES1.T.Kugo and I.Ojima,Prog.Theor.Phys.Supl.66(1979)1.2.M.Nakanishi and I.Ojima,“Covariant Operator Formalism of Gauge Theories andGravity”,World Scientific Lecture Notes in Physics,Vol.27,Singapore1990.3.T.Kugo,Int.Symp.on BRS symmetry,Kyoto,Sept.18–22,1995,hep-th/9511033.4.K.Nishijima,Czech.J.Phys.46(1996)1;M.Chaichian and K.Nishijima,hep-th/9909158,and references therein.5.R.Oehme and W.Zimmermann,Phys.Rev.21(1980)471,1661.6. F.Strocchi,Phys.Lett.B62(1976)60,see also,Phys.Rev.D17(1978)2010.7.I.Ojima,Z.Phys.C5(1980)227.8.L.v.Smekal,A.Hauck and R.Alkofer,Phys.Rev.Lett.79(1997),3591;L.v.Smekal,A.Hauck and R.Alkofer,Ann.Phys.267(1998),1.9.J.E.Mandula,Phys.Rep.315(1999)273.10.S.Furui,these proceedings;H.Nakaijima and S.Furui,hep-lat/9909008.11.R.Alkofer,S.Ahlig and L.von Smekal,Fizika B8(1999)277[hep-ph/9901322];L.v.Smekal,habilitation thesis,Erlangen Univ.,1998,av.on request from the author.12.D.Atkinson and J.Bloch,Phys.Rev.D58(1998)094036;D.Atkinson and J.Bloch,Mod.Phys.Lett.A13(1998),1055.13.A.G.Williams,these proceedings;F.D.R.Bonnet et al.,hep-lat/0002020and references therein.14.A.Cucchieri,hep-lat/9908050and references therein.15.H.Suman and K.Schilling,Phys.Lett.B373,314(1996).16.H.Aiso et al.,Nucl.Phys.B(Proc.Suppl.)53(1997),570.17.B.All´e s et al.,Nucl.Phys.B502(1997)325.18.Ph.Boucaud et al.,JHEP10(1998)017;JHEP12(1998)004.19.J.I.Skullerud,Nucl.Phys.Proc.Suppl.63(1998)242.20.S.Ahlig,R.Alkofer,C.Lerche,and L.von Smekal,in preparation.。
The improved 10th order QED expression for a_{mu} new results and related estimates
a r X i v :h e p -p h /0507174v 1 14 J u l 2005The improved 10th order QED expresion for a µ:new results and related estimatesA.L.Kataev a∗aInstitute for Nuclear Research of the Russian Academy of Sciences,117312Moscow,RussiaNew estimates of the 10th order QED corrections to the muon anomalous magnetic moment are presented.The estimates include the information on definite improved 10th order QED contributions to a µ,calculated by Kinoshita and Nio.The final estimates are in good agreement with the ones,given recently by Kinoshita.1.INTRODUCTIONIn the last years both theoretical and experi-mental results for the anomalous magnetic mo-ment a µattracted special interest (for the most recent review see Ref.[1]).Careful analysis of the values of different theo-retical corrections to a µstimulated the new fresh glance on the pure QED expression for this clas-sical quantity.The work was started after defi-nite bugs in the previous calculations of eighth-order light-by-light-type diagrams [2]were de-tected and corrected [3].The evaluations of all mass-dependent α4QED contributions to a µwere completed in Ref.[4]and their numerical values have been greatly improved with respect to pre-vious results of Ref.[2].Moreover,the crude estimate of the α5QED correction to a µ,which is based on the calcula-tions of the dominant contributions to the sets of 10th order light-by-light-type diagrams (see Ref.[2]and Ref.[5])and the renormalization group inspired studies of Refs.[2,6]was also improved [7].In view of this it is worthwhile to reconsider the 10th order scheme-invariant estimates of Ref.[8],which were in qualitative agreement with the estimate from Ref.[6].π+A (4)iαπ3+ (2)and i =1,2,3.The first three corrections to a e are known in the analytical form from the calcu-12lations of Refs.[10]-[12].The updated value of the8th order correction to a e was presented in Ref.[7].The dominant numerical values of the terms A(4)2and A(6)2are known and read[1,7]:A(4)2(mµ/m e)=1.0942582887(104),(3) A(6)2(mµ/m e)=22.86837936(22).(4) Other terms in Eq.(2)are rather small and are of order10−4-10−5[1,7].The re-evaluation of the 8th order contributions to aµgives the improved number[4],namely:A(8)2(mµ/m e)=132.6823(72)(5) Notice,that the coefficients of A2(mµ/me)are positive and their values are increasing.This happens due to the contributions of the pow-ers of the relatively large renormalization-group (RG)controllable terms with ln(mµ/m e)≈5.6.Moreover,beginning from the6th or-der the light-by-light-type diagrams with internal fermion loop are starting to manifest themselves [14].Their typical contribution are proportional toπ2ln(mµ/m e)–factors,which have non-RG ori-gin and are dominating in the expressions for the corresponding coefficients of the8th order cor-rection.Thus,one may expect,that they will continue to dominate in higher orders also.2.2.10th order QED corrections to aµThefirst estimate of the10th-order correc-tion to aµwas given in Ref.[2]on the basis of rather preliminary numerical evaluation of the 10th-order diagrams with electron light-by-light subgraph and two one-loop electron vacuum po-larization insertions into internal virtual photons, coupled to the muon line.This estimate reads[2]∆1(A(10)2)≈570(140).(6) However,there are at least two other sets of dia-grams which were not taken into account in the estimate of Eq.(6)and may give sizable contribu-tion.Among them is the light-by-light-type di-agram,where one of three photons contains two-loop electron vacuum polarization insertion.Its contribution was estimated in Ref.[6]and reads∆2(A(10)2)≈176(35).(7)In the same work the contribution to A(210)of thediagram with electron loop,coupled to muon linebyfive photons,was estimates as[6]:∆3(A(10)2)≈185(85).(8)Eq.(8)includes theoretical and numerical infor-mation,gained from Refs.[5].Summing up theestimates of Eq.(6)-Eq.(8)one can get[6]∆4(A(10))=∆1+∆2+∆3≈930(170).(9)Another,more theoretical estimate,was madein Ref.[8].It is based on application of thescheme-invariant methods,namely the principleof minimal sensitivity[15]or the effective chargesmethod[16].In the estimates of Ref.[8]the infor-mation on the values of lower-order contributionsto aµ(up to8th order)and on the four-loop ex-pression for the QEDβ-function in the on-shellscheme[18]were used.The developed approach,when applied separately to the sets of non-light-by-light terms and the sum of light-by-light-typecontributions,gave the following numbers[8]∆ECH1(A(10)2)≈50(10)∆ECH2(A(10)2)≈521.(11)Note,that Eq.(11)contains the estimates for thesum of several10th order contributions,includ-ing the ones,estimated separately within otherapproaches in Eq.(6)and Eq.(7).However,to obtain thefinal estimate within this scheme-invariant method it is also necessary to add thecontribution of Eq.(8).Thus the estimate ofthe10th order QED correction to aµ,obtained inRef.[8],was∆ECH3(A(10))=∆ECH1+∆ECH2+∆3≈750.(12)Within existing theoretical uncertainties thenumber of Eq.(12)do not contradict to the oneof Eq.(9).However,quite recently more detailed10th or-der results,based on the calculations of Kinoshitaand Nio[17],were announced[7].These resultsare:∆1(A(10)2)=629.1407(118)(13)∆2(A(10)2)=181.1285(51)(14)∆3(A(10)2)=86.69(15)3 Kinoshita and Nio also calculated several othersets of10th order diagrams diagrams,includingthe ones evaluated previously in Refs.[18]-[21].The new estimate,which is based on the calcu-lated part of9080diagrams,contributing to thethe10th order QED contribution,is[7]:∆new(A(10)2)=677(40).(16)Note,that the calculations of the terms estimatedin Eq.(8)are leading to the essential reduction oftheir contribution into the10th order correctionto aµ(compare Eq.(15)with Eq.(8).Takinginto account the effect of reduction of the con-tribution of∆3into Eq.(12)we obtain a newestimate∆ECHnew (A(10)2)≈658(17)which is in perfect agreement with the estimate of Eq.(16),based on explicit calculations of Ref.[17].We believe,that this good agreement is not the accident and is demonstrating that both theo-retical logic of scheme-invariant methods and the results of exact calculations are in good shape and are supporting each other.More detailed analysis of these results will be presented elsewhere.As to phenomenological consequence,the agreement of the preliminary partial results of 10th order calculations to aµwith the scheme-invariant result of Eq.(16)demonstrates,that the uncertainties of the10th order QED contri-butions to aµare really small.However,there is the possibilities of decreasing current theoretical uncertainties to aµ.It can be done as the re-sult of taking into account in the calculations of the hadronic vacuum polarization contributions (for their evaluation see e.g.the reviews of Refs.[1],[22])new data in the low energy region,which will be obtained soon at Novosibirsk e+e−col-lider,and to rely on possible reconstruction of DAPHNE(Frascati)machine with the aim to measure the region in e+e−-annihilation cross-section,complementary to the one,studied at Novosibisrk and Bejing colliders. ACKNOWLEDGEMENTS This talk was prepared during the visit to ICTP(Trieste).I am grateful to the staffof this Center for providing excellent conditions for work.I also thank orga-nizers of NuFact05Workshop and V.Palladino in particular for invitation and hospitality in Fras-cati.I am grateful to V.Starshenko for the in-terest in the current status of different studies, related to aµand to T.Kinoshita for useful cor-respondence.REFERENCES1.M.Passera,J.Phys.G31(2005)R75.2.T.Kinoshita,B.Nizic and Y.Okamoto,Phys.Rev.D41(1990)593.3.T.Kinoshita and M.Nio,Phys.Rev.Lett.90(2003)021803.4.T.Kinoshita and M.Nio,Phys.Rev.D70(2004)113001.5. stein and A.S.Ylkhovsky,Phys.Lett.B233(1989)116.S.G.Karshenboim,Phys.Atom.Nucl.56(1993)857[Yad.Fiz.56N6(1993)252].7.T.Kinoshita,Nucl.Phys.Proc.Suppl.144(2005)206.8. A.L.Kataev and V.V.Starshenko,Phys.Rev.D52(1995)402.9.R.P.Feynman,in“The Quantum The-ory Fields”,Intescience Publishing Inc.,NY, 1961.10.J.S.Schwinger,Phys.Rev.73(1948)416.11.C.Sommerfield,Phys.Rev.107(1957)328;A.Petermann,Helv.Phys.Acta3(1957)407;M.V.Terentiev,J.Exp.Theor.Phys.16(1963)444.porta and E.Remiddi,Phys.Lett.B379(1996)283.13.T.Kinoshita,Nuov.Cim.B51(1967)140.14.J.Aldins,S.J.Brodsky,A.J.Dufner and T.Kinoshita,Phys.Rev.D1(1970)2378. 15.P.M.Stevenson,Phys.Rev.D23(1981)2916.16.G.Grunberg,Phys.Rev.D29(1984)2315.17.T.Kinoshita and M.Nio,work in progress.18.D.J.Broadhurst, A.L.Kataev andO.V.Tarasov,Phys.Lett.B298(1993)445.19.A.L.Kataev,JETP Lett.54(1991)602[Pisma Zh.Eksp.Teor.Fiz.54(1991)600].20.A.L.Kataev,Phys.Lett.B284(1992)401.porta,Phys.Lett.B328(1994)522.22.F.Jegerlehner,Nucl.Phys.Proc.Suppl.126(2004)325.。
CFA考试二级模拟试题精选0401-55(附详解)
CFA考试二级模拟试题精选0401-55(附详解）1、Using the H-model, the information in Exhibits 1 and 2, and Jatin’s estimates for growth and required return on the stock, the intrinsic value of CRN’s stock as of 2013 is closest to:【单选题】A.$22.22.B.$17.55.C.$18.38.正确答案:C答案解析:C is correct. The H-model is2、In regard to the measures of economic activity, the comment by which one of the research team members is most accurate?【单选题】A.Bergman.B.Rajan.C.Medeva.正确答案:A答案解析:Medeva's comment is most accurate. The percentage change in stock market value equals the percentage change in GDP plus the percentage change in the share of earnings (profit) in GDP plus the percentage change in the price-to-earnings multiple. Over short to immediate horizons, all three of these factors contribute to appreciation or depreciation of the stock market. In the long run, however, the growth rate of GDP must dominate. As noted, the ratio of earnings to GDP cannot rise forever.3、Is Petsas' response to Moyle regarding futures and spot prices most likely correct?【单选题】A.Yes.B.No, the explanation of when the spot price is less than the futures price is incorrect.C.No, the explanation of when the spot price exceeds the futures price is incorrect.正确答案:A答案解析:Petsas' response to Moyle is correct. Futures and spot prices must converge at expiration. If they do not, then it is possible to earn an arbitrage profit. If the spot price is greater than the futures price, then one could earn an arbitrage profit by buying the futures contract and executing the contract to purchase the underlying at the lower futures price and to sell it at the higher spot price. If the futures price exceeds the spot price at expiration, then an investor could purchase the asset at the spot price and enter into a short futures contract to sell it at the higher price, thus locking in a profit.4、Is Chang’s Statement 2 correct?【单选题】A.Yes.B.No, because the model’s coefficient estimates will be unbiased.C.No, because the model’s coefficient estimates will be consistent.正确答案:A答案解析:A is correct. Chang is correct because a correlated omitted variable will result in biased and inconsistent parameter estimates and inconsistent standard errors.5、Based on Exhibits 2 and 3, and assuming annual compounding, the per share value of Troubadour’s short position in the TSI forward contract three months after contract initiation is closest to:【单选题】A.$1.6549.B.$5.1561.C.$6.6549.正确答案:C答案解析:C is correct. The no-arbitrage price of the forward contract, three months after contract initiation, is6、The current no-arbitrage futures price of the Nikkei 225 futures contract (Position 1) is closest to:【单选题】A.15,951.81.B.16,047.86.C.16,112.21.正确答案:B答案解析:B is correct. The no-arbitrage futures price is7、Based upon Exhibit 1, the value of Property C using the direct capitalization method is closest to:【单选题】A.￡3,778,900.B.￡4,786,700.C.￡6,527,300.正确答案:C答案解析:C is correct. Under the direct capitalization method, the value of the property = NOI/(r – g).8、Is Aims correct in describing how we could transform a justified P/E ratio into a P/S ratio or a P/B ratio?【单选题】A.Yes.B.C.正确答案:A答案解析:9、Based on Exhibit 1, the best action that an investor should take to profit from the arbitrage opportunity is to:【单选题】A.buy on Frankfurt, sell on Eurex.B.buy on NYSE Euronext, sell on Eurex.C.buy on Frankfurt, sell on NYSE Euronext.正确答案:A答案解析:A is correct. This is the same bond being sold at three different prices so an arbitrage opportunity exists by buying the bond from the exchange where it is priced lowest and immediately selling it on the exchange that has the highest price. Accordingly, an investor would maximize profit from the arbitrage opportunity by buying the bond on the Frankfurt exchange (which has the lowest price of €103.7565) and selling it on the Eurex exchange (which has the highest price of €103.7956) to generate a risk-free profit of €0.0391 (as mentioned, ignoring transaction costs) per €100 par.10、Which of MacPhail's observations about the new executive compensation plan is most accurate?【单选题】A.1B.2C.3正确答案:A。
New Results on the Odderon in QCD
arXiv:hep-th/9805135v1 21 May 1998
1
Introduction
An interesting problem of QCD is to understand the behaviour of the theory in the Regge limit of large energy, fixed momentum transfer. In the Leading Logarithmic Approximation the leading pole in the C = +1 channel is the famous BFKL pomeron 1 . Later this was generalized to the channel odd under charge conjugation (C = −1) — the odderon 2 . In contrast to the BFKL case, however, the value of the intercept remained unknown despite the discovery of conformal symmetry and integrals of motion 3 . Recently substantial progress 4,5 has been made with the reduction of the problem to solving the Baxter equation (λ + i)3 Q(λ + i) + (λ − i)3 Q(λ − i) = (2λ3 + q2 λ + q3 )Q(λ) (1)
Can the maturity concept be used to separate the autogenous shrinkage and
Can the maturity concept be used to separate the autogenous shrinkage andthermal deformation of a cement paste at early age?Philippe Turcry a ,Ahmed Loukili a,*,Laurent Barcelo b ,Jean Michel Casabonne baLaboratoire Ge´nie Civil de Nantes St-Nazaire,Ecole Centrale de Nantes,BP 92101,44321Nantes Cedex,France bLAF ARGE,Laboratoire Central de Recherche,95rue du Montmurier,38290St-Quentin Fallavier,FranceReceived 3January 2001;accepted 18March 2002AbstractThe influence of temperature on the autogenous shrinkage of cement paste has been studied using the maturity approach based on Arrhenius’law.Application of this law requires knowledge of the apparent activation energy,E a ,of cement.In this work,E a has been determined by the ‘‘setting time method.’’The external volume change of cement paste was measured by hydrostatic weighing.In order to separate the thermal and autogenous deformations,the thermal dilation coefficient (TDC)was determined at both 20and 30°C.Investigations have shown that maturity can be used to predict autogenous shrinkage under isothermal and realistic conditions as long as temperatures remain between 10and 40°C.Outside of this temperature range,the calculated autogenous deformation and measured isothermal shrinkage are quite different and,as a result,autogenous shrinkage appears to be dependent on more than hydration advancement alone.D 2002Elsevier Science Ltd.All rights reserved.Keywords:Autogenous shrinkage;Temperature;Cement paste;Early age;Maturity concept1.IntroductionAt early age,thermal deformations and autogenous shrinkage occur simultaneously and may,if restrained,lead to the cracking of cementitious materials.These thermal deformations,e th ,result from the temperature rise caused by hydration reactions and are proportional to the thermal dilation coefficient (TDC)of the cement paste:e TH =TDC ÂD T .Autogenous shrinkage,on the other hand,is a consequence of chemical shrinkage:hydration products are denser than the unhydrated compounds.In the plastic state,this contraction is converted into settlement.Once the solid skeleton has been formed and in the absence of an external source of water,hydration reactions continue through the consumption of capillary water.This phenomenon is called ‘‘self-desiccation.’’According to the Kelvin equation,this self-desiccation gradually increases the tensile stress in pore water,which then leads to a global compressive stress on thesolid skeleton.A deformation,called autogenous shrinkage,e as ,thereby occurs.For the calculation of stresses at early age,autogenous shrinkage is assumed to be dependent solely on the degree of hydration,a ,with e as =e as (a ),and total deformation is taken as equal to the sum of thermal and autogenous deformations,i.e.,e total =e as +e th [1].However,recent studies [2,3]have shown that the autogenous shrinkage amplitude of concrete is influenced by the temperature history.It seems that for a given degree of hydration,concretes with different temperature histories do not develop the same autogenous shrinkage.These results question the applicabil-ity of the maturity concept.This paper focuses on the influence of temperature on the autogenous shrinkage of cement paste by use of the maturity concept [4].The rate of chemical reactions is affected by temperature,since cement hydration is thermally activated.Moreover,the microstructure itself will undergo change when formed at different temperatures.The maturity con-cept serves to predict the effect of temperature on certain material properties with respect to the degree of hydration (e.g.,compressive strength).This concept is based on *Corresponding author.Tel.:+33-2-40-37-16-67;fax:+33-2-40-37-25-35.Cement and Concrete Research 32(2002)1443–1450sensitivity of hydration reactions,called the apparent activa-tion energy,E a.This study deals first with the determination of apparent activation energy by using the setting time method[5,6]. Deformations of the cement paste at early age were meas-ured for different thermal conditions,both isothermal and ‘‘realistic.’’The method chosen to assess volume change was the measurement of buoyancy variations for a sample in a flexible latex mold through hydrostatic weighing,as presented in detail elsewhere in the literature[3].With this method,we also measured the TDC,which has allowed calculating thermal deformations in the realistic cases. Lastly,using the maturity approach,we have attempted to separate thermal deformation from autogenous shrinkage.2.Materials and experimental methods2.1.MaterialsAn ordinary type I Portland cement(CPA CEM I52.5 CP2),containing60%C3S,12%C2S,9%C3A,and8% C4AF,was used.The Blaine specific surface was332m2/kg. The water-to-cement(W/C)ratio was0.25.Cement and water were mixed for3min in order to ensure a homogen-eous mix.2.2.Experimental methods2.2.1.Determination of E a by means of the setting times methodThe maturity concept determines the time required at a reference temperature for the cement paste to achieve the same level of development as that under the influence of the actual time–temperature history.This time is called the ‘‘equivalent age’’and can be calculated by a function based on Arrhenius’law(Eq.(1)):t equ¼Z t0expE aR1273þq refÀ1273þqðtÞd tð1Þwhere t equ is the equivalent age at the reference temper-ature,q ref(h),t is the paste age(h),q(t)is the paste temperature at time t(°C),q ref is the reference temperature (°C),E a is the apparent activation energy(J/mol),and R is the universal gas constant(J/mol/K).The following proposed relation has been demonstrated theoretically[5]:lnD aD t¼ÀE aR1T0þconstantð2Þwhere T0is the temperature of the paste(K)under isothermal conditions and D t is the time required to increase the degree of hydration by an increment D a at T0.By deduce E a.Nevertheless,a way must be found to character-ize the degree of hydration a.The setting time method presumes that both the initial set time,t is,and final set time, t fs,are reached for definite levels of hydration(at a given W/ C ratio).This method therefore consists of measuring these specific times(t is and t fs)for several isothermal conditions and,in the subsequent step,calculating an activation energy for each period,initial setting and setting(t fsÀt is).Initial set time and setting time of cement pastes were measured using the Vicat needle apparatus,which operates in accordance with European Standard EN196-3.The samples were placed in a water bath at various temperatures (10,20,30,and40°C).The temperature inside the samples was measured through embedded thermocouples.2.2.2.External volume changeMeasurements of the external volume change of cement paste were conducted through hydrostatic weighing.Imme-diately after casting,a prophylactic without lubricant was filled with cement paste in order to form a spherical sample. The latex mold was closed using a thin stainless steel wire. The excess latex was then cut and the sample container was cleaned and weighed.The sample was hung under a balance and immediately immersed in the water bath at the chosen temperature.The sample mass was approximately90g.The bath temperature was controlled by a‘‘cryo-thermostat’’(Fig.1)with an accuracy of0.1°C.The external volume change results from a change in the buoyancy force and serves to alter the weight reading on the balance.Both the bath temperature and measured mass were continuously logged on the computer at5-min intervals for a period exceeding24h.In realistic tests,the bath temperature is imposed by a cement paste sample placed in a quasi-adiabatic enclosure after casting.The temperature is measured by a ther-mocouple introduced into the cement paste.The weighed sample therefore undergoes the same temperature history.A detailed description of this system is provided in Ref.[3].In order to obtain different temperature histories(Fig.2),the mass of the sample placed in the enclosure ischanged.P.Turcry et al./Cement and Concrete Research32(2002)1443–1450 14442.3.Calculation of the deformationsThe external shrinkage,expressed in cubic millimeters per gram cement,was obtained from Eq.(3)as a result of the calculation already discussed in detail [3]:D VM c¼r iw r w ðT ÞÀ1ÀM r V i r w ðT ÞV iM cð3Þwhere T is the bath temperature (°C),r iw is the initial density of water (g/cm 3),r w (T )is the density of water as a function of temperature (g/cm 3),V i is the initial sample volume (cm 3),D V is the volume change (cm 3),M r is the mass reading on the balance (g),and M c the cement mass in the sample (g).3.Results and discussion3.1.Determination of E a by the setting times method The results related to the initial set and setting times determined by the Vicat needle device have been listed in Table 1.Both the initial set and setting time increase with decreasing temperature.This finding has been previ-ously reported.Figs.3and 4were drawn by assuming isothermal con-ditions until the initial set;a linear curve was fitted to the data points.According to Eq.(2),the computed apparent activa-tion energies were 29kJ/mol for the time periods until theinitial set and 39kJ/mol between the initial and final sets.This procedure yields two activation energies,which is not unrealistic since E a reflects more of a mathematical than a chemical tool,thereby making it possible to estimate the global thermal sensitivity of all reactions taking place in the hydrating cement paste.3.2.Isothermal tests at 10,20,30,and 40°CExposed to each temperature,the external shrinkage was determined as the mean value of three measurementsandFig.2.Different realistic temperature histories.Table 1Initial set and setting time at different temperatures Averagetemperature (°C)Initial set time,t is (min)Setting time,t fs Àt is (min)121501382011090347050Fig.3.Arrhenius plot for initial set times.P .Turcry et al./Cement and Concrete Research 32(2002)1443–14501445expressed in cubic millimeters per gram of cement,with a variation of less than 8%.The external shrinkage at different temperatures versus real time has been plotted in Fig.5.It can be observed that temperature has an unsystematic effect on the autogenous deformation of cement paste.This result,which has also been reported by Bjøntegaard [2],is not surprising since the comparison was conducted in an inconsistent manner by virtue of not incorporating the temperature effect on the rate of cement hydration,which is responsible for auto-genous paring autogenous shrinkage curves versus real age is similar to comparing different materials;in this case,we need to apply the maturity concept.Fig.6shows deformation curves versus equivalent age,which has been calculated for each temperature using Eq.(1).E a is taken as equal to 29kJ/mol before the initial setand 39kJ/mol thereafter.The reference temperature is 20°C (as results obtained at 20°C do not change with time transformation).It is important to note that deformations must be initialized at the same equivalent age,i.e.,for the same theoretical degree of hydration.The selected equival-ent time origin was 3.25h,in correspondence with the final set time (Fig.6).It can be seen that the four curves follow similar trends with just little scatter,which is caused by measurement accuracy levels.The maturity concept there-fore leads to predicting with reasonable accuracy the auto-genous shrinkage of cement paste under isothermal conditions over the 10–40°C range.3.3.External volume change in realistic casesBy considering the behavior of material to be isotropic,linear deformation represents one-third of thevolumetricparison of deformation for different temperatures versus pasteage.P .Turcry et al./Cement and Concrete Research 32(2002)1443–14501446deformation calculated in Eq.(3).In this part,deformations are expressed in micrometers per meter.3.3.1.Deformation kineticsThree realistic temperature tests with initial temperatures of 10and 20°C were performed.A typical curve of a realistic temperature history (20–60°C)is illustrated in Fig.7.The realistic deformation curve can be divided into four phases:AB,BC,CD,and DE.In the first phase,it is observed that the isothermal and realistic deformations display the same shape since the temperature is constant in both tests.When temperature increases in the realistic test (B),the curves diverge;during BC,no ‘‘realistic’’deforma-tion is recorded.It seems that thermal deformations com-pensate for autogenous shrinkage.In the case of the ‘‘realistic’’test,thermal expansion occurs until the temper-ature peak (CD),while the rate of autogenous shrinkage at 20°C is decreasing.During the cooling period (DE),a large deformation caused by both thermal contraction and auto-genous shrinkage can be observed.Moreover,when the temperature returned to 20°C,the magnitude of the ‘‘real-istic’’deformation corresponds to the autogenous shrinkage recorded under isothermal conditions.It can thereby bestated that the total measured deformation under realistic conditions is equal to the sum of the measured deformation in the isothermal test and a thermal component related to temperature history.In order to separate thermal and auto-genous deformations,we have determined the evolution of the TDC with respect to time.3.4.TDC measurementsThe TDC was measured with the method of spontaneous heating by using hydrostatic weighing [3].Tests were carried out under two isothermal conditions:20and 30°C.Every hour,the bath temperature was increased by 4°C within a period of about 7min and then immediately decreased to the isothermal temperature.Fig.8presents the evolution in weight given by the balance without any water density correction.Note that the 4°C peak effect is different at very early age and after 2h,which reveals an evolution in the TDC.By using this method for the TDC calculation,it was assumed that the temperature rise was sufficiently fast for the deformation measured during heating to beconsid-parison of the isothermal test at 20°C and the 20–60°C realistictest.P .Turcry et al./Cement and Concrete Research 32(2002)1443–14501447ered only from a thermal origin.In spite of the disper-sion of experimental points (Fig.9),TDC seems to depend solely on equivalent age (with q ref =20°C).A TDC curve may be interpolated from our results in accordance with Eq.(4)below:TDC ðt equ Þ¼137*exp ð1:44Àt equ Þþ28:ð4ÞIt is observed in Fig.9that the TDC decreases sharply during the first few hours after casting and then remains constant from 8h onwards.Its value is high (28m m/m °C),yet in agreement with other cement paste TDC reported by other researchers [7].Miao et al.[8]reported a TDC of about 24m m/m °C at 7h after casting for a concrete with a W/C ratio of 0.28.It should be noted that the TDC value is very sensitive to the experimental measurement procedure used.3.5.Separation of thermal and autogenous deformations Interpolated TDC allows determining the thermal de-formation for any temperature history.We can also deduce autogenous deformation from total deformation by assum-ing that total deformation is the sum of the two other components.Moreover,deformation separation has to be performed by application of the maturity concept.Fig.10presents an example of separation in the case of the 10–40°C realistic test.3.6.Maturity concept approach results and discussion Figs.11and 12compare isothermal shrinkage at 10and 20°C,respectively,and calculate autogenous deformation.It can be observed that although the determined TDC is rather inaccurate,both the calculated and measureddefor-Fig.10.Separation of thermal and autogenous deformations for the 10–40°C temperaturehistory.P .Turcry et al./Cement and Concrete Research 32(2002)1443–14501448mations are nearly identical.The maturity approach pro-vides a good estimate of the autogenous shrinkage of cement paste.However,the method used to separate thermal and autogenous deformations yields a different result for the 20–60°C test (Fig.13).In this instance,the final amplitude of the calculated autogenous deformation is about 700m m/m higher than that measured in the isothermal test at 20°C.Moreover,the calculated deformation displays a significant dilation peak.In other words,the usually expected kinetics of autogenous shrinkage is not present herein.In Fig.13,it is observed that the final amplitude of the calculated autogenous deformation is nearly equal to the amplitude of isothermal shrinkage plus the final amplitude of thermal deformation.In fact,thermal deformation is not reversible because of TDC evolution:during the heating period,TDC is higher than the cooling phase and,con-sequently,temperature variations induce dilation.In the 10–40°C test (Fig.11),no dilation can be detected;paste heating and cooling must therefore occur at a time when TDC is constant.At this juncture,two assumptions can be made.Firstly,the maturity concept cannot predict autogenous deformation evolution and amplitude when the thermal history lies beyond a temperature field between 10and 40°C.The maturity concept is a mathematical tool that may be too simplistic for describing microstructural changes.For example,the hydration product form,and therefore chem-ical shrinkage,may be different at 20°C than at 60°C.The validity of the determined TDC can also be ques-tioned.Indeed,this TDC does not allow entirely separating thermal and autogenous deformations in the 20–60°C test.For example,dilation observed in the calculated autogenous deformation may be from a thermal origin.Afterwards,we determined a theoretical TDC that allows obtaining the same autogenous shrinkage by means of calculation as by iso-thermal measurement.This method has been developed by Laplante [1].Thermal deformation is presumed to be obtained by subtracting the measured isothermal deforma-tion from the measured total deformation.TDC is equal to the ratio of this deformation to the temperature difference between isothermal and realistictests.parison of the measured autogenous shrinkage at 20°C and the calculated autogenous deformation for the 20–30°Ctest.parison of Laplante method TDC and experimentalTDC.P .Turcry et al./Cement and Concrete Research 32(2002)1443–14501449Fig.14compares experimental TDC from isothermal tests and TDC calculated using the Laplante method.It is shown that the calculated coefficient does not present a typical evolution.TDC may be dependent on thermal history when the temperature of realistic history exceeds a certain limit.This result reveals the need for further work in TDC measurement,for example,in the realistic case.4.Conclusions and subsequent workBased on the assumption that the maturity concept is applicable throughout the hydration process,the following conclusions can be drawn:ÁBetween10and40°C,the maturity concept allowspredicting the isothermal autogenous shrinkage of cement paste measured using the volumetric method:autogenous shrinkage thus seems to be solely dependent on the degree of hydration.ÁIn realistic tests,total deformation is shown in aninitial analysis to be the sum of autogenous and thermal components.Separation of thermal and autogenous defor-mations is therefore made possible by use of a valuable TDC.ÁThe TDC is linked to the degree of hydration onlybetween20and30°C.ÁThe maturity concept allows estimating the autogen-ous deformation amplitude for thermal conditions between 10and40°C by measuring the isothermal shrinkage.ÁFor the20–60°C realistic test,both the calculated autogenous deformation and isothermal measured shrinkage differ.Autogenous deformation therefore seems to be affec-ted by thermal history above40°C.Nonetheless,a process must be developed in the future to accurately measure TDC under different thermal conditions:both isothermal and realistic.These results also need to be verified by means of linear tests.References[1]plante,Proprie´te´s Me´caniques des be´tons durcissants:AnalyseCompare´e des Be´tons Classiques et a`Tre`s Hautes Performances,PhD thesis,Ecole Nationale des Ponts et Chausse´es,Paris,1993(in French).[2]Ø.Bjøntegaard,Thermal dilation and autogenous deformation as driv-ing forces to self-induced stresses in high performance concrete,PhD thesis,The Norwegian University of Science and Technology,N-7491 Trondheim,1999.[3]A.Loukili,D.Chopin,A.Khelidj,J.Y.Le Touzo,A new approach todetermine autogenous shrinkage of mortar at early age considering temperature history,Cem.Concr.Res.30(6)(2000)915–922. [4]plante,S.Roussel,S.Lecrux,Technique maturome´trique:la loid’Arrhe´nius au service des chantiers,Proceedings of the Internation-al RILEM Conference,RILEM Publications,Arles,France,1998, pp.323–342(in French).[5]L.D’Aloia,De´termination de l’e´nergie d’activation apparente du be´tondans le cadre de l’application de la me´thode du temps e´quivalent a`la pre´vision au jeune aˆge:approches expe´rimentales me´caniques et calo-rime´trique,simulations nume´riques,PhD thesis,Institut National des Sciences Applique´es de Lyon,1998(in French).[6]R.C.A.Pinto,K.C.Hover,Application of maturity approach to settingtimes,ACI Mater.J.96(6)(1999)686–691.[7]N.Bouzoubaa,Thermal dilation coefficient of concrete,University ofSherbrooke,Canada,1992(in French).[8]B.Miao,P.C.Aı¨tcin,W.D.CooK,D.Mitchell,Influence of concretestrength on in situ properties of large columns,ACI Mater.J.90(3) (1993)214–219.P.Turcry et al./Cement and Concrete Research32(2002)1443–1450 1450。
理性看待优惠券的英语作文
理性看待优惠券的英语作文Here is an English essay on the topic of "Rational Perspective on Coupons" with a word count of more than 1000 words:Coupons have become a ubiquitous part of the modern consumer experience. They offer the promise of savings and discounts, enticing shoppers to take advantage of these promotional offers. While coupons can indeed provide tangible financial benefits, it is essential to adopt a rational and critical perspective when utilizing them. This essay will explore the nuances and considerations surrounding the use of coupons, highlighting both the advantages and potential drawbacks.One of the primary appeals of coupons is the opportunity to save money on purchases. Consumers can leverage these discounts to stretch their budgets and obtain products or services at a lower cost. This can be particularly beneficial for individuals or families on a tight financial footing, allowing them to access goods and services they might otherwise find unaffordable. Moreover, the sense of accomplishment and pride associated with "scoring a deal" can be a significant motivator for coupon usage.However, it is crucial to recognize that the allure of coupons can also lead to impulse purchases and overspending. Individuals may be tempted to buy items they do not genuinely need or would not have considered purchasing without the presence of a coupon. This can result in a net financial loss, as the perceived savings may be outweighed by the unnecessary expenditure. Additionally, the psychological impact of coupons can influence consumer behavior, leading individuals to make purchases they would not have otherwise made.Another factor to consider is the potential impact of coupons on the environment. Many coupons are distributed in physical form, often requiring the use of paper and ink resources. While some companies have embraced digital coupons, the overall environmental footprint of the coupon industry remains a concern. Consumers should be mindful of the sustainability implications of their coupon usage and seek out eco-friendly alternatives when possible.Furthermore, the redemption of coupons can sometimes be a time-consuming and frustrating process. Navigating the fine print, ensuring eligibility, and successfully redeeming the coupon can be a challenging task, particularly for those with limited time or technological proficiency. This can diminish the perceived value of the coupon and lead to a sense of dissatisfaction with the overall experience.It is also important to consider the potential impact of coupon usage on the businesses that offer them. While coupons can be an effective marketing tool to attract new customers and promote product awareness, they can also lead to a reduction in profit margins for the businesses. This can have broader implications, potentially affecting the prices of goods and services or the sustainability of certain businesses in the long run.Moreover, the proliferation of counterfeit or fraudulent coupons can undermine the integrity of the coupon system and create challenges for both consumers and businesses. Consumers may unknowingly attempt to redeem invalid coupons, leading to frustration and potential legal consequences, while businesses must invest resources in detecting and preventing coupon fraud.In conclusion, while coupons can offer tangible financial benefits, it is essential to approach their use with a rational and critical mindset. Consumers should carefully evaluate their purchasing habits, consider the environmental and ethical implications of coupon usage, and weigh the potential drawbacks against the perceived savings. By doing so, individuals can make informed decisions that align with their personal financial goals and values, maximizing the positive impact of coupons while minimizing the potential downsides. Ultimately, a balanced and thoughtful approach to coupon usagecan enable consumers to navigate the complex landscape of modern marketing and promotional strategies.。
set_operating_conditions -analysis -回复
set_operating_conditions -analysis -回复[set_operating_conditions analysis]Introduction:When it comes to running a successful business, setting the right operating conditions is crucial. These conditions define the parameters within which a business operates, ensuring efficiency, productivity, and profitability. In this article, we will explore the process of conducting a set_operating_conditions analysis, step by step.Step 1: Identify the PurposeBefore undertaking any analysis, it is essential to identify the purpose of conducting a set_operating_conditions analysis. This purpose could be to improve efficiency, reduce costs, enhance productivity, meet regulatory requirements, or respond to changing market conditions. Having a clear purpose helps focus the analysis and ensures that it aligns with the overall business strategy.Step 2: Identify Key Operating ConditionsThe next step involves identifying the key operating conditions that significantly impact business operations. These conditions may vary depending on the nature of the business. Examples of key operating conditions include temperature, pressure, humidity, time, resource availability, quality standards, safety regulations, and customer demands. It is important to involve relevant stakeholders throughout this process to ensure all perspectives are considered.Step 3: Gather DataOnce the key operating conditions are identified, it is necessary to gather data to understand the current state of these conditions. This could involve analyzing historical data, conducting surveys, observing work processes, collecting feedback from employees and customers, and studying industry standards and best practices. The data collected should provide a comprehensive understanding of the current operating conditions and any gaps or areas for improvement.Step 4: Analyze DataWith the data gathered, the next step is to analyze it to identify patterns, trends, and potential areas of improvement. This analysis can involve statistical techniques, like regression analysis or correlation analysis, to determine relationships between different variables. It is also crucial to consider the business context and any external factors that may influence the operating conditions.Step 5: Identify Opportunities for ImprovementBased on the data analysis, opportunities for improvement can be identified. These opportunities could range from optimizing processes, adjusting resource allocation, implementing technological solutions, enhancing employee training, or revising policies and procedures. Prioritizing these opportunities is essential to ensure that efforts and resources are allocated effectively.Step 6: Develop Action PlanOnce the opportunities for improvement are identified and prioritized, it is important to develop an action plan. This plan should outline the specific actions required, establish timelines,allocate responsibilities, and define key performance indicators to measure progress. It is crucial to involve relevant stakeholders and ensure their buy-in to maximize the chances of successful implementation.Step 7: Implement and MonitorWith the action plan in place, it is time to implement the necessary changes and monitor their effectiveness. This could involve testing and piloting new processes, training employees, acquiring new equipment or technology, or revising policies and procedures. Regular monitoring and feedback loops are essential to assess the impact of the changes and make any necessary adjustments.Step 8: Continuous ImprovementSetting operating conditions is not a one-time process but an ongoing effort. It is essential to foster a culture of continuous improvement within the organization. This could involve conducting regular reviews and audits, seeking feedback from employees and customers, monitoring industry trends and best practices, and staying updated with regulatory requirements. Thedata gathered during these processes can feed into futureset_operating_conditions analyses, ensuring that the business remains adaptable and responsive to changes.Conclusion:Conducting a set_operating_conditions analysis is a critical aspect of running a successful business. By identifying key operating conditions, gathering and analyzing data, identifying opportunities for improvement, and implementing changes, businesses can ensure efficiency, productivity, and profitability. Embracing a culture of continuous improvement is key to staying competitive in an ever-evolving business landscape.。
gre改革后样题解析
gre改革后样题解析GRE考试自2011年以来进行了改革，考试形式和内容都有所调整，新GRE样题的解析和备考策略对于考生来说非常重要。
下面，我们来分析一道新GRE改革后的样题。
样题：In the following passage, a single-level metaphor (a metaphor that goes inone direction only) connects the vehicle of the metaphor (a taxi driver) with the tenor of the metaphor (a good researcher). Choose the correct answer."One quality of a good researcher is the ability to be patient and persistent in the face of obstacles. This is something a taxi driver must possess as well. A taxi driver must navigate through unpredictable traffic, road closures, and demanding passengers. Similarly, a good researcher must navigate through the uncertainties and challenges of their research, persistently looking for solutions, even when faced with setbacks."解析：这道样题考察学生对隐喻的理解。
文章中把好的研究者与出租车司机进行比较，运用了单向隐喻，即出租车司机作为隐喻的载体，好的研究者作为隐喻的对象。
Improved $alpha^4$ Term of the Muon Anomalous Magnetic Moment
This result provides the most stringent test of the Standard Model. Unfortunately, such a test must wait for further improvement in the uncertainty of the hadronic corrections to aµ [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. The lowest-order hadronic vacuum-polarization effect has thus far been determined from two sources, (i) e+ e− annihilation cross section, and (ii) hadronic τ decays. Several recent evaluations are listed in Table I. Their differences (except for the one obtained from the τ decay data) are due to different interpretations and treatments of basically identical data. However, they all agree that the measurement of the e+ e− annihilation cross section, in particular in the region below ρ − ω resonances, must be improved substantially in order to reduce the experimental uncertainty significantly. Such efforts are underway at several laboratories. Particularly interesting and promising is new radiative-return measurements [17]. On the other hand, it is not clear at present whether the value from the τ -decay data can be improved much further because of the difficulty in evaluating more precisely the effect of isospin breaking [6, 7]. A new theoretical development is an attempt to calculate the hadronic vacuumpolarization effect on muon g − 2 in lattice QCD [18]. The NLO hadronic contribution has been evaluated by two groups [8, 19]: aµ (had.NLO ) = −10.1 (0.6) × 10−10 , aµ (had.NLO ) = −9.8 (0.1)exp (0.0)rad × 10−10 . (3)
The Relevant Scale Parameter in the High Temperature Phase of QCD
a rXiv:h ep-ph/9411293v114Nov1994CTP#2360INFNCA-TH-94-24The Relevant Scale Parameter in the High Temperature Phase of QCD Suzhou Huang (1,2)∗and Marcello Lissia (1,3)∗(1)Center for Theoretical Physics,Laboratory for Nuclear Science and Department of Physics,Massachusetts Institute of Technology,Cambridge,Massachusetts 02139(2)Department of Physics,FM-15,University of Washington,Seattle,Washington 98195†(3)Istituto Nazionale di Fisica Nucleare,via Negri 18,I-09127Cagliari,Italy †and Dipartimento di Fisica dell’Universit`a di Cagliari,I-09124Cagliari,Italy (October 1994)Abstract We introduce the running coupling constant of QCD in the high temper-ature phase,˜g 2(T ),through a renormalization scheme where the dimen-sional reduction is optimal at the one-loop level.We then calculate the rel-evant scale parameter,ΛT ,which characterizes the running of ˜g 2(T )with T ,using the background field method in the static sector.It is found that ΛT /ΛI.INTRODUCTIONAt high temperatures QCD is expected to undergo a partial dimensional reduction[1,2], namely static correlations at distances larger than the thermal wavelength(1/T)can be reproduced by a three dimensional Lagrangian,where only the static modes of the original theory are present.This reduced Lagrangian can be computed perturbatively up to a specific order in the QCD running coupling constant.In fact,non-perturbative infrared phenomena (e.g.thermo-mass generation)prevent the complete reduction,i.e.reduction to all orders in the QCD running coupling,from taking place[2].Consequently,observables can be reproduced only up to corrections of a specific order,before non-perturbative physics begins to dominate.Even though a complete dimensional reduction is not possible,the partial dimensional reduction of QCD still provides a simplified physical picture.However,phenomenological applications of this picture depends crucially on how high is the temperature above which this picture begins to take place.Since we expect corrections to vanish with some power of the QCD coupling,and since at zero temperature the asymptotic freedom starts dominating QCD physics at typical scales of about10to20timesΛMS .Contrary to this expectation,there are strong evidences[3–5]that the dimensional re-duction picture is already valid at temperatures as low as two or three times the critical temperature T c(the deconfining transition in the pure Yang-Mills case or the chiral restora-tion in full QCD).Since T c is numerically not very different fromΛMS .In fact,the definition of a scale parameter thatcharacterizes the approach to the dimensional reduction regime implies the definition of a suitable coupling constant,˜g2(T),that yields a sensible perturbative expansion at high temperature,i.e.an expansion whose coefficients contain minimal contribution from non-static modes.In this paper,we use the backgroundfield approach to define and compute the relevant coupling constant,and hence the scale parameterΛT.More specifically,we calculate the one-loop effective action for the backgroundfield in the static sector,and define the renormal-ization scheme by requiring that dimensional reduction be optimal for this gauge-invariant quantity.Furthermore,we verify by an explicit computation that this same renormaliza-tion scheme is also optimal for lattice perturbative calculations at high T,and therefore it provides a natural scale also for lattice simulations.In section II we introduce the renormalization scheme that defines the scale parame-terΛT within the backgroundfield approach.In section III,we apply this definition and calculateΛT/Λthe conclusions.Several technical points pertinent to the lattice perturbative calculation at high T are discussed in the Appendix.II.DIMENSIONAL REDUCTION AND OPTIMAL RENORMALIZATIONSCHEMEThe standard SU(N)Yang-Mills gauge theory reduces at the tree level to the three dimensional Yang-Mills theory with adjoint Higgs(φa≡Q a0)L RD=−12(D iφ)a(D iφ)a,(1) where F a ij=∂i Q a j−∂j Q a i−g3f abc Q b i Q c j and(D iφ)a=∂iφa−g3f abc Q b iφc.The couplingg3is related to the four dimensional coupling through g23=g2T.Since L RD is a super-renormalizable theory in three dimensions and there is no other dimensionful scale around, all the dynamical scales must be set by the coupling constant g23=g2T.Of course,once loop corrections are included the reduced theory in Eq.(1)would acquire new vertices and the coupling constant g23would depend on the original coupling g2in a more complicated way.For example,g23would receive corrections,such as g4T and so on.However,due to the asymptotic freedom of QCD(g2∼1/ln T)we still expect that dynamical scales are set by g23≈g2T,provided the scale parameter is chosen in a suitable way.Therefore,we believe that the concept of dimensional reduction involves two equally important aspects.On one hand,there is the possibility of a simplified description by using a theory L RD with less degrees of freedom in lower dimensions.On the other hand,the evolution of the parameters of L RD as a function of temperature should be dictated by the original theory.The main concern of our present work is to determine this evolution,which in turn determines the temperature dependence of the relevant physical observables.A.Background Field Method in the Static SectorIt is well known that the effective action calculated using the backgroundfield method[6] is gauge invariant for the background gaugefield at T=0.This gauge invariance guarantees that the coupling constant renormalization is related to the wavefunction renormalizationof the backgroundfield through Z g=Z−1/2A .Hence,the calculation of the quadratic partof the effective action,i.e.the two-point function for the backgroundfield,is sufficient to renormalize the coupling[6].Moreover,to the leading order,there is no magnetic mass generation atfinite T.There-fore,the one-loop effective action for the magnetic sector is invariant under time-independentgauge transformations also atfinite T,insuring that the relation Z g=Z−1/2A still holds forthe static backgroundfieldA a0(τ,x)=0,A a i(τ,x)=A a i(x).(2) The same conclusion can also be reached more formally by applying,for instance,the meth-ods of Ref.[6]to the backgroundfield of Eq.(2).The residual gauge invariance in the staticsector implies that,in order to compute the coupling constant renormalization atfinite T, we only need to compute the two-point function of the backgroundfield A a i in the static sector.We can still use the zero temperature Feynman rules,as given for instance by Abbott[6]. The only difference in the calculation is that time-components of all momenta become dis-crete Matsubara frequencies(2πnT),and the corresponding integrals become discrete sums.B.Subtraction ScaleAs exhaustively discussed by Landsman[2],the decoupling of the non-zero modes at high-T is maximal only in some specific renormalization schemes,such as the BPHZ scheme.In the backgroundfield method we only need tofix one renormalization condition:we demand that the two-point function for the backgroundfield in the low external momentum(relative to T)limit coincides with the contribution solely from zero modes.Landsman[2]uses afinite temperature renormalization group approach,since he dis-cusses thermal reduction in a more general context where several couplings are present. Thanks also to the backgroundfield approach,we deal with a simpler situation where only one coupling needs renormalization.Therefore,we can directly implement the renormalization condition by using the freedom in the choice of the subtraction scale,µ,which becomes a function of T.Intuitively,we expect µto be of order of T.The purpose of our paper is tofind out what is the proportionality constant.Then the reduced theory,Eq.(1),with the T-dependent coupling g23=g2(µ(T))T, reproduces the full two-point function up to corrections of order of p2/T2at the one-loop level.Due to the gauge invariance,the two-point function for the static backgroundfield A a i must have the form(δij p2−p i p j)δabΠM(p2,T,µ).(3) Specifically,we chooseµby requiring the following renormalization condition for the non-static contribution toΠM(p2,T,µ):ΠNS M(p2=0,T,µ(T))=0.(4) The procedure is best explained by directly going through the calculation in the next section.III.CALCULATION OF THE SCALE PARAMETERA.In the ContinuumIn the continuum calculation we use dimensional regularization in the spatial dimensions, that isd4k,(5)(2π)3−2ǫand theg2(µ)− 2132α+1√11+O(p2/T2),(6)where g2(µ)is the running coupling defined in theβ0ln(T2/Λ2T)=g2(µ) µ=4πT e−(γE+c),(8) which defines the scale parameterΛT=e(γE+c)MS.(9)This results has a clear physical interpretation.The non-static modes decouple in the high-T limit,but their presence is nevertheless revealed by the appearance of the new scale ΛT in the reduced theory(without any reference to the original theory,the only scale would be T).While this new scale is obviously related to the scaleΛprocess,represented by a different set of Feynman graphs,yields a different c in Eq.(9). However,we believe that typically|c|<∼1,and a different choice should not modify the scale ratio in Eq.(9)in an essential way.For example,Landsman[2]calculated the temperature dependent coupling renormalization factor Z g by imposing maximal dimensional reduction on the two-and three-point functions in the conventional effective action(where the rela-tionship Z g=Z−1/2A no longer holds).He did not express his result explicitly in terms ofthe scale ratio.But if we do it,wefind that his result is quite close to ours,i.e.Eq.(9)with c=0.Another example that clearly shows the necessity of using an optimal dimensional re-duction scheme for defining the relevant scale at high-T can be found in the Gross-Neveu model[7].In that model a similar strategy makes the sub-leading correction to the screening mass of order of˜g6(T),rather than˜g4(T),demonstrating that˜g2(T)is a sensible expansion parameter.Of course,the optimal dimensional reduction criterion is not the only way to define a temperature dependent coupling constant.For example,the quark-antiquark potential at a distance of order of1/T is used to define g2(T)in Ref.[3].While it is certainly legitimate to make such a choice,it is also true that,because the reduced theory is meant to reproduce the full theory only at distances much larger than1/T(spatial momenta small compared to T),definitions of the couplings made by matching short distance properties of the full and reduced theories do not necessarily define a scale that correctly characterizes the approach to the asymptotic high-T regime.At last,let us consider the effect of quarks on our result.If N f light quarks are present in the theory,results of Eqs.(7),(8)and(9)still apply,but withβ0=(11N−2N f)/(48π2) and c=(N/2−2N f ln4)/(11N−2N f),where we have adopted the convention for the trace of the Dirac-matrix:Trγµγν=−4δµν.For the phenomenological relevant case of N=N f=3,we get the value c=−0.2525, which corresponds toΛT/Λa suitable expansion parameter for lattice perturbative calculation at high temperature,and the necessity of using expansion parameters different from the bare lattice coupling g20(a) for perturbative calculations at zero temperature[8].In the following we verify that optimal dimensional reduction for the lattice effective action computed in the backgroundfield method defines indeed the same scale parameter we have found in the continuum calculation.For the sake of concreteness,we perform the calculation for the pure SU(N)Wilson action,but the same result is expected to hold for other actions as well.In general,the coupling defined in the lattice backgroundfield method should have the following dependence on the bare lattice coupling up to one-loopg2L(T)≡g20(a)+g40(a)β0 −ln(a2T2)+c T L .(10)We want to show that c T L is such that g2L(T)=˜g2(T).Since we have expressed˜g2(T)in terms of g2(µ)in theMS scheme[9,10]g20(a)=g2(µ)−g4(µ)β0 −ln(a2µ2)+c0L ,(11) and express also g2L(T)in Eq.(10)in terms of g2(µ)g2L(T)=g2(µ)−g4(µ)β0 −ln(µ2/T2)−c T L+c0L +O(g6(µ)).(12)By comparing Eq.(8)and Eq.(12)we see that to show g2L(T)=˜g2(T)is equivalent to show thatc T L=c0L+2γE−2ln(4π)+111−11γE+2f11+3f00+6f10−1+24π2z10+6π2−6π2/N2 .(14) The constants f ij and z ij are defined asf ij≡(4π)2 ∞dx x e−8x I20(2x)I i(2x)I j(2x)−θ(x−1)expansion on the lattice.The lattice correspondent of the continuum result of Eq.(6)in the Feynman gauge(α=1)isΠL M(p2,T,a)=116NTp2−β0−ln(a2T2)+c T L +O p2/T2,a|p|,aT ,(17)with c T L given byc T L=1(4πx)3/2.(19)Since,as shown in the Appendix,f′ij=f ij−γE−3ln4,this complete the proof of Eq.(13) and,therefore,of the fact that g2L(T)=˜g2(T).In other words,if we use˜g2(T)as the expansion parameter,the lattice effective action in the high-T limit takes the following formΠL M(p2,T,a)=116NTp2+O p2/T2,a|p|,aT ,(20)which is the same as its continuum counterpart,if we use the same coupling˜g2(T)(see Eq.(6)withα=1andµgiven by Eq.(7)).In both cases we have been able to absorb in the coupling constant all leading local corrections due to non-static modes,while the non-local ones are reproduced by the reduced theory.PARISON TO LATTICE RESULTIn the preceding section,we have demonstrated thatΛT is the relevant scale parameter in the high-T limit.Our argument is yet only perturbative in nature.However,as we emphasized earlier,the determination of the scale parameter is largely one-loop effect.Now let us compare our result with the scale parameter determined from a non-perturbative method:lattice measurement of the spatial string tension at high T.The primary reason for choosing the spatial string tension[4]rather than the heavy quark potential at distances of order of1/T[3]is that the concept of dimensional reduction only makes sense for large distance(low momentum)quantities.Bali et al.[4]measured the spatial string tension in SU(2)gauge theory as a function of temperatureσs(T).Then theyfitted their result to the expected form of the string tension in the three-dimensional SU(2)Yang-Mills theory12π2ln(T/ΛT)+17Even though the simulation process knows nothing about the dimensional reduction,the fitting formula Eq.(21)in fact defines the optimal three-dimensional coupling g23=g2(T)T through the string tension,similar in spirit to what we have done for the backgroundfield effective action.As a result,theirfitted value ofΛσT=(0.076±0.013)T c is thefirst,to our knowledge,non-perturbative determination of the scale that characterizes the high-T regime for the SU(2)gauge theory.In the scaling regime we expect that the critical temperature behaves likeT c=ΛL24π2βc5111N2βc ,(23)whereβc=2N/g20(a).From their critical couplingβc=2.74at Nτ=16,and the knownratioΛMS :T c=1.62ΛMS,(24) which is remarkably close to our resultΛT=eγE+1/22MS≈0.148Λlattice perturbative calculation at high T.Our results areΛT=0.148ΛMS for N=N f=3.We have argued that this scale is typical in the high-T regime,even if its precise value depends on the specific definition.The consequence of our result is that the high-T regime ofQCD,where the dimensional reduction picture appears to take place,sets in at temperatures as low as a few times of the critical temperature.Our calculation is in very good agreement with the non-perturbative determination ofthe scale parameter in the lattice simulations[4]in the SU(2)Yang-Mills theory,therefore reinforcing the advantage of the renormalization scheme based on the optimal dimensional reduction criterion.It would be of great interest to have other lattice measurements of the scale parameter using other observables,such as the ones related to the gluonic Debye-screening mass andthe deviations of the mesonic and baryonic screening masses from their free values.This work was supported in part by funds provided by the U.S.Department of Energy (DOE)under contract number DE-FG06-88ER40427and cooperative agreement DE-FC02-94ER40818.APPENDIX:In this appendix we discuss several points of the high temperature expansion in per-turbative lattice calculations.First we use the ghost bubble-graph to illustrate the general method,then we prove that f′ij−f ij=−γE−3ln4,andfinally discuss the convergence of the frequency sums to the corresponding zero temperature integrals.From the lattice action,see for instance Ref.[10],we derive the following expression for the ghost bubble-graphBµν(p)≡Nλ(1−cos kλa) ρ(1−cos(kρ−pρ)a),(A1)whereΩis the space-time volume and p=(0,p).Exponentiating the denominator and converting the spatial momentum sums into integrals(we work in the infinite spatial volume limit),we obtainBµν(p)=N(2π)3∞dαdβe−(α+β)(4−cos2πnα2+β2+2αβcos pλa cos(kλ−φλ)×e−i(kµ+kν−pνa)+e i(kµ+kν−pµa)−e i(kµ−kν−pµa+pνa)−e−i(kµ−kν) ,(A2)whereφλis implicitly defined by tanφλ=βsin(pλa)/[α+βcos(pλa)].Now we perform the spatial momentum integrals,yielding the modified Bessel functions.For the sake of concreteness,let us consider the componentµ=1andν=2B′12(p)=NNτ) 2 λ=1I1(α2+β2+2αβcos p3a) e−i(φ1+φ2−p2a)+e i(φ1+φ2−p1a)−e i(φ1−φ2−p1a+p2a)−e−i(φ1−φ2) .In Eq.(A3)B′is just B without the n=0term in the frequency sum.This static term is in fact the one that is directly reproduced by the reduced theory,and should be excluded from the contribution due to non-static modes.In the limit of|p|a≪1and|p|≪T(we are interested in the small lattice spacing and high-T limit),Eq.(A3)further simplifiesB′12(p)=−N p1p2NτNτ−1n=1e−x(1−cos2πn12∞dx x 1Nτ) e−3x I21(x)I0(x)−112∞dx x 1Nτ) 1NτNτ−1n=11π2a2T2+O(aT),(A6)and obtainB′12(p)=−Np1p2x−√√any power dependence on T trivially,and take the continuum limit of the frequency sums. Mathematically,this is guaranteed by the fact that the convergence of the limitlim Nτ→∞1Nτ= 1dx f(cos2πx)(A10)is exponential,at least when f(z)can be expanded as a power series in z,which includes the cases we are concerned with.Note that the terms with n=0should be included in these tadpole-like graphs,since they are not reproducible by the reduced theory.REFERENCES∗E-mail:shuang@ and lissia@†Present address.[1]T.Appelquist and R.D.Pisarski,Phys.Rev.D23(1981)2305;S.Nadkarni,Phys.Rev.D27(1983)917;A.N.Jourjine,Ann.Phys.155(1984)305;Alvarez-Estrada,Phys.Rev.D36(1987)2411;Ann.Phys.174(1987)442.[2]ndsman,Nucl.Phys.B322(1989)498;[3]A.Irback,cock,ler,B.Petersson and T.Reisz,Nucl.Phys.B363(1991)34;T.Reisz,Z.Phys.C53(1992)169;cock,ler and T.Reisz,Nucl.Phys.B369(1992)501;[4]G.S.Bali,et al.,Phys.Rev.Lett.71(1993)3059.[5]V.Koch,E.V.Shuryak,G.E.Brown and A.D.Jackson,Phys.Rev.D46(1992)3169;T.H.Hansson and I.Zahed,Nucl.Phys.B374(1992)227;S.Schramm and M.-C.Chu,Phys.Rev.D48(1993)2279;V.Koch,Phys.Rev.D49(1994)6063;M.Ishii and T.Hatsuda,UTHEP-282,July1994.[6]B.S.DeWitt,Phys.Rev.162(1967)1195,1239;J.Honerkamp,Nucl.Phys.B48(1972)269;G.’t Hooft,Nucl.Phys.B62(1973)444;L.F.Abbott,Nucl.Phys.B185(1981)189;D.G.Boulware,Phys.Rev.D23(1981)389.[7]S.Huang and M.Lissia,MIT preprint,CTP#2359(1994).[8]G.P.Lepage and P.B.Mackenzie,Phys.Rev.D48(1993)2250.[9]A.Hasenfratz and P.Hasenfratz,Phys.Lett.93B(1980)165;A.Hasenfratz and P.Hasenfratz,Nucl.Phys.B192(1981)210;R.Dashen and D.J.Gross,Phys.Rev.D23(1981)2340;P.Weisz,Phys.Lett.100B(1981)331;H.Kawai,R.Nakayawa and K.Seo,Nucl.Phys.B189(1981)40;[10]A.Gonzalez-Arroyo and C.P.Korthals Altes,Nucl.Phys.B205(1982)46.[11]M.Gao,Phys.Rev.D41,(1990)626.。
全新版第二版综合B1U4-A
全新版第二版综合B1U4-A"Some say that our <u>economy</u> would crumble almost immediately if all the <u>illegal</u> aliens, an estimated 20-million people left our nation tomorrow. One cannot <u>deny</u> that at the current 5.5%<u>unemployment</u> figure we need <u>additional</u> labor for our economy and our standard of living to continue. However, we must also <u>point out</u>: that does not mean we should not find a way to control our <u>borders</u>. We need some way to <u>keep track of</u> all those entering our nation. Not only due to the crime — 33% illegal aliens fill our prisons. But also because we need to guard against diseases, which we <u>were supposed to</u> have eradicated. Small Pox, Polio, etc.And what about Hepatitis C and TB, STDs and the pending Bird Flu? You see we do not live with our chickens here like others in the world that do. We do not need those issues here either. For those who have studied the illegal immigration issue since the Jordan Commission Era, they know that this is a serious issue and one we must <u>address</u> and not one we can go any longer without doing something about it. We need the problem fixed and if we do not, we will surely pay the price in the future.Recently the Department of Planning of New York issued a report which laid bare a full scale of the city. In 1970, 18% of the city's population was foreign-born. By 1995, the figure had risen to 33%, and another 20% were the US-born offsprings of immigrants. So immigrants and their children now form a majority of the city's population. Who are these New Yorkers? Why do they come here? Where are they from? (OK, time to drop the "they." I'm one of them.) The last question at least is easy to answer: we come from everywhere. In the list of the top 20 source nations of those sending immigrants to New York between 1990 and 1994 are six countries in Asia, five in the Caribbean, four in Latin America, three in Europe, plus Israel and former Soviet Union. And when we immigrants get here we roll up our sleeves. "If you're not ready to work when you get to New York," says a friend of mine, "you'd better hit the road." The mayor of New York once said, "Immigration continues to shape the unique character and drive the economic engine of New York City." He believes that immigrants are at the heart of what makes New York great. In Europe, by contrast, it is much more common to hear politicians worry about the loss of "unity" that immigration brings to their societies. In the quarter century since 1970, the United States admitted about 125 million legal immigrants, and has absorbed them into its social structures with an ease beyond the imagination of other nations. Since these immigrants are purposeful and hard-working, they will help America to make a fresh start in the next century. Following the lead of Canada, Australia, New Zealand and Britain, America would adopt a points system that will give priority to the sort ofyoung, employable immigrants who are most likely to contribute to the economy.The report issued by the Department of Planning of New York ________.put forward ways to control New York's population</option>2">concerned itself with the growth of New York's population</option><option id="3">studied the structure of New York's population</option><option id="4">suggested ways to increase New York's population</option><prompt>According to the second paragraph, which of the following is true of the immigrants in New York?</prompt>-<choice><option id="1">One can not find his place in New York unless he is ready to work.</option><option id="2">They found life in New York harder than in their own countries.</option><option id="3">Most of them have difficulty finding jobs.</option><option id="4">One can live on welfare if he does not want to work.</option><prompt>The mayor of New York considers immigration to be_________.</prompt>-<choice><option id="1">a big problem in the management of the city</option><option id="2">a push needed to develop the city</option><option id="3">a cause of disintegration of the city's social structure</option> <option id="4">an obstacle to the development of the city</option><prompt>Where are the new New Yorkers from?</prompt>-<choice><option id="1">Asia.</option><option id="2">Europe.</option><option id="3">All over the world.</option><option id="4">Latin America.</option><prompt>What is the author's attitude towards immigration to New York?</prompt>-<choice><option id="1">Negative.</option><option id="2">Worried.</option><option id="3">Indifferent</option><option id="4">Positive.</option><text>Large companies need a way to reach the savings of the public at large.The same problem, on a smaller scale, faces practically every company trying to develop new products and create new jobs. There can be little prospect of raising the sort of sums needed from friends and people we know, and while banks may agree to provide short-term finance, they are generally unwilling to provide money on a permanent basis for long-term projects. So companies turn to public, inviting people to lend them money, or take a share in the business in exchange for a share in future profits.This they do by issuing stocks and shares in the business through TheStock Exchange. By doing so they can put into circulation the savings of individuals and institution, both at home and overseas. When the saver needs his money back, he does not have to go to the company with whom he originally placed it. Instead, he sells his shares through a stockbroker to some other saver who is seeking to invest his money. Many of the services needed both by industry and by each of us are provided by the Government or by local authorities. Without hospitals, roads, electricity, telephones, railways, this country could not function. All these require continuousspending on new equipment and new development if they are to serve us properly, requiring more money than is raised through taxes alone. The government, local authorities, and nationalized industries thereforefrequently needed to borrow money to finance major capital spending, and they, too, come to The Stock Exchange. There is hardly a man or woman in this country whose job or whose standard of living does not depend on the ability of his or her employers to raise money to finance new development.In one way or another, this new money must come from the savings of the country. The Stock Exchange exists to provide a channel through which these savings can reach those who need finance.</text><prompt>Almost all companies involved in new production and development must ________.</prompt>-<choice><option id="1">rely on their own financial resources</option><option id="2">persuade the banks to provide long-term finance</option><option id="3">borrow large sums of money from friends and people we know</option><option id="4">depend on the population as a whole for finance</option><prompt>The money which enables these companies to go ahead with their projects is _______.</prompt>-<choice><option id="1">repaid to its original owners as soon as possible</option><option id="2">raised by the selling of shares in the companies</option><option id="3">exchanged for part ownership in The Stock Exchange</option> <option id="4">invested in different companies on The Stock<prompt>When the savers want their money back they _______.</prompt>-<choice><option id="1">ask another company to obtain their money for them</option> <option id="2">look for other people to borrow money from</option><option id="3">put their shares in the company back on the market</option> <option id="4">transfer their money to a more successful company</option><prompt>All the essential services on which we depend are________.</prompt>-<choice><option id="1">run by the Government or our local authorities</option><option id="2">in constant need of financial support</option><option id="3">financed wholly by rates and taxes</option><option id="4">unable to provide for the needs of the population</option><prompt>The Stock Exchange makes it possible for the Government, local authorities and nationalized industries ________.</prompt>-<choice><option id="1">to borrow as much money as they wish</option><option id="2">to make certain everybody saves money</option><option id="3">to raise money to finance new developments</option><option id="4">to make certain everybody lends money to them</option><prompt>The couple has moved most of their stuff; there are just a few ________ left.</prompt>-<choice><option id="1">odd and end</option><option id="2">odds and end</option><option id="3">odd and ends</option><option id="4">odds and ends</option><prompt>Leave my house now, or I will ________ the police.</prompt>-<choice><option id="1">send back</option><option id="2">sent out</option><option id="3">send in</option><option id="4">send for</option><prompt>I should like to rent a house, modern, cozy and ________ in a quiet environment.</prompt>-<choice><option id="1">after all</option><option id="2">before all</option><option id="3">above all</option><option id="4">first of all</option><prompt>The police found some stolen ________ hidden in the thief's apartment.</prompt>-<choice><option id="1">fortune</option><option id="2">wealth</option><option id="3">properties</option><option id="4">property</option><prompt>As we ________ the wood a rabbit ran out of the trees.</prompt>-<choice><option id="1">approaching</option><option id="2">approached</option><option id="3">approximated</option><option id="4">approximating</option><prompt>Tom will have to ________ the weak points in his French if he wants to pass the final exam.</prompt>-<choice><option id="1">work out</option><option id="2">work on</option><option id="3">work to</option><option id="4">work over</option><prompt>Some of the most important concepts in physics ________ their success to these mathematical systems.</prompt>-<choice><option id="1">oblige</option><option id="2">contribute</option><option id="3">owe</option><option id="4">attribute</option><prompt>Stand _______ when you're being spoken to.</prompt>-<choice><option id="1">highly</option><option id="2">upright</option><option id="3">primly</option><option id="4">right away</option><prompt>I took _______ of the opportunity to tell the president what I thought.</prompt>-<choice><option id="1">advantage</option><option id="2">care</option><option id="3">charge</option><option id="4">use</option><prompt>We'll have to think _______ a pretty good excuse for being late.</prompt>-<choice><option id="1">up</option><option id="2">about</option><option id="3">through</option><option id="4">over</option><prompt>I eventually found the letter I was looking for under a _______ of papers.</prompt>-<choice><option id="1">foundation</option><option id="2">stack</option><option id="3">bulk</option><option id="4">basis</option><prompt>The group _______ an interesting report on young people's responses to advertising.</prompt>-<choice><option id="1">turned up</option><option id="2">turned down</option><option id="3">turned in</option><option id="4">turned out</option><prompt>Her husband was not convinced by her _______ that they needed a bigger house.</prompt>-<choice><option id="1">attitude</option><option id="2">speech</option><option id="3">argument</option><option id="4">requirement</option><prompt>You must be _______ silent or the birds won't appear.</prompt>-<choice><option id="1">primly</option><option id="2">reluctantly</option><option id="3">mostly</option><option id="4">absolutely</option><prompt>She didn't _______ me for returning the wallet that I found.</prompt>-<choice><option id="1">so much as thank</option><option id="2">so much as to thank</option><option id="3">as much as thanking</option><option id="4">so much as thanking</option><prompt>__________ how to operate a switchboard, I had to ask the office supervisor to show me the correct procedures.</prompt>-<choice><option id="1">Not known</option><option id="2">Not to know</option><option id="3">Not knowing</option><option id="4">Having not known</option><prompt>His _______ change very quickly; one moment he is cheerful, and the next he's complaining about everything.</prompt>-<choice><option id="1">temper</option><option id="2">moods</option><option id="3">feeling</option><option id="4">sense</option><prompt>The _______ of human knowledge are being pushed further.</prompt>-<choice><option id="1">boundaries</option><option id="2">limits</option><option id="3">borders</option><option id="4">edges</option><prompt>The captive was ______ in a dungeon.</prompt>-<choice><option id="1">restricted</option><option id="2">confined</option><option id="3">controlled</option><option id="4">restrained</option><prompt>______________, the headmaster came into theclassroom.</prompt>-<choice><option id="1">By his hands in his pocket</option><option id="2">When his hands in his pocket</option><option id="3">With his hands in his pocket</option><option id="4">While his hands in his pocket</option>(没什么东西会削弱我们的决心) to modernize our country in the shortest possible time.(将需要相当一段时间) before scientists find any evidence of life in space.There'll certainly be some problems, but(没什么事你不能处理).(我们必须假定他是无罪的) until he is proved guilty.(我明白他说的话), but I failed to understand why he was so upset.。
英语作文 关于情商
EQ means emotional intelligence.The expression “emotional intelligence” is used to indicate a kind of intelligence thatinvolves the ability to perceive, assess and positively influenceone's own and other people's emotions.The basic significance of the emotinal intelligence that Time called "EQ" was suggested by management expert Karen Boylston:"Customers are telling businesses, ''I don''t care if every member of your staff graduated from Harvard. I will take my business and go where I am understood and treated with respect.''"If the evolutionary pressuresof the marketplace are making EQ, not IQ, the hot ticket for business success, it seems likely that individuals will want to know how to cultivate it.I have a modest proposal: Embrace a highly personal practice aimedat improving these four adaptive skills:Raising consciousness. I think of this as thinking differently on purpose. It''s about noticing what you are feeling and thinking and escaping the conditioned confines of your past.Raise your consciousness by catching yourself in the act of thinking as often as possible.Routinely take note of your emotions and ask if you''re facing factsor avoiding them.Using imagery. This is what you see Olympic ski racers doing before entering the starting gate. With their eyes closed and bodies swaying, they run the course in their minds first, which improves their performance. You can do the same by setting aside time each day to dream with passion about what you want to achieve. Considering and reconsidering events to choose the most creative response to them.When a Greek philosopher said 2,000 years ago that it isn''t events that matter but our opinion of them, this is what he was talking about. Every time sonething important happens, assign as many interpretations to it as possible, even crazy ones. Then go with the interpretation most supportive of your dreams. Integrating the perspectives of others. Brain research shows that our view of the world is limited by our genes and the experiences we''ve had.Learning to incorporate the useful perspctives of others is nothing less than a form of enlarging your senses. The next time someone interprets something differently from you --say, a controversial political event--pause to relect on the role of life experience and consider it a gift of perception. The force of habit--literally the established wiring of your brain -- will pull you away frompracticing these skills. Keep at it, however, because they are based on what we''re learning about the mechanisms of the mind.Within the first six months of life the human brain doubles in capacity; it doubles again by age four and then grows rapidly until we reach sexual maturity. The body has about a hundred billion nerve cells, and every experience triggers a brain response that literally shapes our senses. The mind, we now know, is not confined to the brain but is distributed throughout the body''s universe of cells. Yes, we do think with our hearts, brains, muscles, blood and bones. During a single crucial three-week period during our teenage years, chemical activity in the brain is cut in half. That done, we are "biologically wired" with what one of the nation''s leading brain researchers calls our own "world view". He says it is impossible for any two people to see the world exactly alike. So unique is the personal experience that people would understand the world differently. However, it is not only possible to change your world view, he says, it''s actually easier than overconing a drug habit. But you need a discipline for doing it. Hence, the method recommended here.No, it''s not a curriculum in the sense that an MBA is. But the latest research seems to imply that without the software of emotional maturity and self knowledge, the hardware of academic training alone is worth less and less.How to Cultivate EQWhat is the most valuable contribution employees make to their companies, knowledge or judgment? I say judgment. Knowledge, no matter how broad, is useless until it is applied. And application takes judgment, which involves something of a sixth sense—a high performance of the mind.This raises interesting questions about the best training for today’s business people. As Daniel Goleman suggests in his new book, Emotional Intelligence, the latest scientific findings seem to indicate that intelligent but infl exible people don’t have the right stuff in an age when the adaptiveability is the key to survival.In a recent cover story, Time magazine sorted through the current thinking on intelligence and reported,“New brain research suggests that emotions, not I Q, may be the true measure of human intelligence.” The basic significance of the emotional intelligence that Time called “EQ” was suggested by management expert Karen Boylston: “Customers are telling businesses,‘I don’t care if every member of your staffgraduated from Harvard. I will take my business and go where I am understood and treated with respect.’”If the evolutionary pressures of the marketplace are making EQ, not IQ, the hot ticket for business success, it seems likely that individuals will want to know how to cultivate it. I have a modest proposal: Embrace a highly personal practice aimed at improving these four adaptive skills.Raising consciousness. I think of this as thinking differently on purpose. It’s about noticing what you are feeling and thinking and escaping the conditioned confines of your past. Raise your consciousness by catching yourself in the act of thinking as often as possible. Routinely take note of your emotions and ask if you’re facing facts or avoiding them.Using imagery. This is what you see Olympic ski racers doing before entering the starting gate. With theireyes closed and bodies swaying, they run the course in their minds first, which improves their performance. You can do the same by setting aside time each day to dream with passion about what you want to achieve.Considering and reconsidering events to choose themost creative response to them. When a Greekphilosopher said 2,000 years ago that it isn’t events that matter but our opinion of them, this is what he was talking about. Every time something importanthappens, assign as many interpretations to it as possible, even crazy ones. Then go with the interpretation most supportive of your dreams.Integrating the perspectives of others. Brain research shows that our view of the world is limited by our genes and the experiences we’ve had. Learning to incorporate the useful perspectives of others is nothing less than a form of enlarging your senses. The next time someone interprets something differently from you—say, a controversial political event —pause to reflect on the role of life experience and consider it a gift of perception.The force of habit—literally the established wiringof your brain — will pull you away from practicing these skills. Keep at it, however, because they are based on what we’re learning about the mechanism of the mind.Within the first six months of life the human brain doubles in capacity. It doubles again by age four and then grows rapidly until we reach sexual maturity. The body has about a hundred billion nerve cells, and every experience triggers a brain response thatliterally shapes our senses. The mind, we now know, is not confined to the brain but is distributed throughout the body’s universe of cells. Yes, we do think with our hearts, brains, muscles, blood and bones.During a single crucial three-week period during our teenage years, chemical activity in the brain is cutin half. That done, we are “biologically wired” with what one of the nation’s leading brain researchers calls o ur own “world view”. He says it is impossiblefor any two people to see the world exactly alike. So unique is the personal experience that people would understand the world differently.However, it is not only possible to change your world view, he says, it’s actually easier than overcoming a drug habit. But you need a discipline for doing it. Hence, the method recommended here.No, it’s not a curriculum in the sense that an MBA is. But the latest research seems to imply that withoutthe software of emotional maturity and self-knowledge, the hardware of academic training alone is worth less and less.。
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ar Xi v :h e p -p h /0108065v 2 26 O c t 2001PM 01/xx February 1,2008New Evaluation of the QED Running Coupling and of the Muonium Hyperfine SplittingStephan NarisonLaboratoire de Physique Math´e matique,Universit´e de Montpellier 2,Place Eug`e ne Bataillon 34095-Montpellier Cedex 05,France and Center for Academic Excellence on Cosmology and Particle Astrophysics (CosPA),Depart-ment of Physics,National Taiwan University,Taipei,Taiwan,10617Republic of China.Email:narison@lpm.univ-montp2.frWe present a new independent evaluation of the hadronic and QCD contributions to the QED running coupling α(M Z )and to the muonium hyperfine splitting ν.We obtain:∆αhad =2770(17)×10−5and ∆νhad =232.5(2.5)bined with the QED and Electroweak Standard Model contributions,they lead to:α−1(M Z )=128.926(25)and to the Fermi energy splitting νF =4459031783(229)Hz ,where for the latter,we have used,in addition,the precise measurement of the muonium hyperfine splitting νexp .We use νF in order to predict the ratios of massesm µ/m e =206.768276(11)and of the magnetic moments µµ/µe B =4.84197047(25)×10−3,which are in excellent agreement with the ones quoted by the Particle Data Group.These remarkable agreements can provide strong constraints on some contributions beyond the Standard Model.1IntroductionA natural and important extension of our recent work [1](hereafter referred as SN)on the hadronic and QCD contributions to the anomalous magnetic moment of the muon and tau leptons a l ,is the evaluation of the hadronic and QCD contributions to the QED running coupling α(M Z )and to the muonium hyperfine splitting ν.The analysis is important as it will give a complete set of estimates of three independent observables within the same inputs used in SN.These self-contained results should pass tests from a comparison with high precision experiments and different existing predictions in the ing a dispersion relation,it is remarkable to notice that the different lowest order hadronic contributions for these three processes can be expressed in a closed form as a convolution of the e +e −→hadrons cross-section σH (t )with a QED kernel function K (t )which depends on each observable:O had =1x 2+(t/m 2l )(1−x ),(3)where m l is the lepton mass.It behaves for large t as:K a l (t ≫m 2l )≃m 2lαM 2Zwhere:ρν=2νF m e4m2µvµ= xµ,(7)and we take(for the moment)for a closed comparison with[4]1,the value of the Fermi energy splitting:νF=4459031920.(511)(34)Hz.(8) It behaves for large t as:Kν(t≫m2µ)≃ρν m2µ2ln t4 .(9)The different asymptotic behaviours of these kernel functions will influence on the relative weights of different regions contributions in the evaluation of the above integrals.2Input and Numerical StrategyThe different data input and QCD parametrizations of the cross-sectionσH(t)have been discussed in details in SN[1]and quoted in the last column of Table1,corresponding to the estimate in different regions.Table1is analogous to Table2of SN.We shall only sketched briefly the numerical strategy here:−Our result from the I=1isovector channel below3GeV2is the mean value of the one usingτ-decay and e+e−data.In both cases,we have used standard trapezo¨ıdal rules and/or least squarefits of the data in order to avoid theoretical model dependence parametrization of the pion form factor.In the region0.6−0.8GeV2around the ω-ρmixing,we use in both cases e+e−data in order to take properly the SU(2)F mixing.The SU(2)breaking in the remaining regions are taken into account by making the average of the two results fromτ-decay and e+e−and by adding into the errors the distance between this mean central value with the one from each data.−For the I=0isoscalar channel below3GeV2,we use the contributions of the resonancesω(782)andφ(1020) using narrow width approximation(NWA).We add to these contributions,the sum of the exclusive channels from 0.66to1.93GeV2.Above1.93GeV2,we include the contributions of theω(1.42),ω(1.65)andφ(1.68)using a Breit-Wigner form of the resonances.−For the heavy quarkonia,we include the contributions of known J/ψ(1S to4.415)andΥ(1S to11.02)families and use a NWA.We have added the effect of the¯t t bound state using the leptonic width of(12.5±1.5)keV given in[5].−Away from thresholds,we use perturbative QCD plus negligible quark and gluon condensate contributions, which is expected to give a good parametrization of the cross-section.These different expressions are given in SN. However,as the relative rˆo le of the QCD continuum is important in the estimate of∆αhad,we have added,to the usual Schwinger interpolating factor at orderαs for describing the heavy quark spectral function,the known α2s m2Q/t corrections given in SN.However,in the region we are working,these corrections are tiny.−On the Z-mass,the integral for∆αhad has a pole,such that this contribution has been separated in this case from the QCD continuum.Its value comes from the Cauchy principal value of the integral.3The QED Running Couplingα(M Z)The result given in Table1corresponds to the lowest order vacuum polarization.Radiative corrections to this result can be taken by adding the effects of the radiative modesπ0γ,ηγ,π+π−γ,....We estimate such effects to be:∆αhad=(6.4±2.7)×10−5(10) by taking the largest range spanned by the two estimates in[5]and[6].Adding this(relatively small)number to the result in Table1,gives the total hadronic contributions:∆αhad=2769.8(16.7)×10−5.(11) Using the QED contribution to three-loops[3]:∆αQED=3149.7687×10−5,(12) and the Renormalization Group Evolution of the QED coupling:α−1(M Z)=α−1(0) 1−∆αQED−∆αhad ,(13)Table1:Lowest order determinations of∆αhad×105and∆νhad[Hz]using combined e+e−and inclusiveτdecay data(2nd and4th columns)and averaged e+e−data(3rd and5th columns).τ+e+e−e+e−τ+e+e−e+e−Light Isovector4m2π→0.8314.5±2.3302.7±7.1152.9±1.8148.4±3.1[6,7,8]0.8→2.177.2±3.482.0±5.412.1±0.516.9±1.9[7,8]2.1→3.62.3±9.253.6±4.97.8±1.26.7±0.6[7,8]Total Light I=1454.0±10.6438.2±10.2172.8±2.2172.1±3.7Average446.1±10.4±7.9172.5±3.0±0.3Light IsoscalarBelow1.93ω31.5±1.112.7±0.4NWA[9]φ52.3±1.213.7±0.3NWA[9] 0.66→1.9311.6±3.02.7±0.7 exclusive[10] From1.93to3ω(1.42),ω(1.65)9.4±1.41.2±0.2BW[11,9]φ(1.68)14.6±4.61.7±.5BW[11,12,9]Total Light I=0119.0±5.932.1±1.0Heavy IsoscalarJ/ψ(1S→4.415)116.3±6.24.0±0.2NWA[9]Υ(1S→11.020)12.7±0.50.1±0.0NWA[9]T(349)−(0.1±0.0)≈0NWA[9,5]Total Heavy I=0128.9±6.24.1±.2QCD continuum3.→4.572330.1±1.017.5±.1(u,d,s)4.572→11.272503.0±1.05.0±.1(u,d,s,c)11.272→(M Z−3GeV)22025.7±2.01.3±0.0(u,d,s,c,b)(M Z+3GeV)2→4M2t−(794.6±0.6)≈0−Z-pole29.2±.5≈0principal value[5]4M2t→∞−(24.0±0.1)≈0(u,d,s,c,b,t)Total QCD Cont.2069.4±5.223.8±1.4one obtains thefinal estimate:α−1(M Z)=128.926(25),(14) which we show in Fig1for a comparison with recent existing determinations.One can notice an improved accuracy of the different recent determinations[3,6,5,13]2,which are in fair agreement with each others.Also a detailed comparison of each region of energy with the most recent work of[5]shows the same features(agreement and slight difference)like in the case of aµin SN,due to the slight difference in the parametrization of the data and spectral function.However,thefinal results are comparable.Finally,one can remark that due to the high-energy constant behaviour of the QED kernel function in this case,the low-energy region is no longer dominating.For aµ,the contribution of theρ-meson below1GeV is68%of the total contribution,while the sum of the QCD continuum is only7.4%(see e.g.SN).Here the situation is almost reversed:the contribution of theρ-meson below1GeV is only2%,while the sum of the QCD-continuum is73.6%.For this reason,improvement due to the new Novosibirsk e+e−data[15]in the low-energy region will not be very significant.At present,new BES data[16]in the J/ψregion are also available,which can be alternatively used.Below the J/ψresonances,the BES data are in excellent agreement with the QCD parametrization to orderα3s used here for3flavours,justifying the accuracy of your input.Above the J/ψresonances,the parametrization used here(sum of narrow resonances+QCD continuum away from thresholds)can also be compared with these data.On can notice that,in the resonance regions,the BES data are more accurate than previous ones,which may indicate that our quoted errors in Table1for the J/ψ270028002900ADH 98DH 98BP 01MOR 01J 01YT 01SN 01(this work)Figure 1:Recent determinations of ∆αhad and α−1(M Z ).The dashed vertical line is the mean central value.References to the authors are in [3,5,6,13].family contributions are overestimated.In addition,the threshold of the QCD continuum which we have taken above the J/ψresonances,matches quite well with the one indicated by the BES data.We expect that with this new improved estimate of α(M Z ),strong constraint on the Higgs mass can be derived.4The Muonium Hyperfine SplittingOur final result from Table 1:∆νhad =(232.5±3.2)Hz(15)is shown in Table 2in comparison with other determinations,where there is an excellent agreement with the most recent determination [4].Here,due to the (ln t )/t behaviour of the kernel function,the contribution of the low-Table 2:Recent determinations of ∆νhadFKM 99[17]240±7CEK 01[4]233±3SN 01(This work)232.5±3.2√4πανF ≃−65Hz ,|∆νweak(h.o)|≈0.7Hz,∆νhad(h.o)≃7(2)Hz,(16) one obtains the Standard Model(SM)prediction:νSM≡νF+∆νQED+∆νweak+∆νhad+∆νhad(h.o).(17) If one uses the relation:νF=ρF µµ(1+m e/mµ)3,(18)with:16ρF==1.00095783(5).(22)νFCombining this result with the previous experimental value ofν,one can deduce the SM prediction:νF=4459031783(226)Hz,(23) where the error is dominated here by the QED contribution at fourth order.However,this result is a factor two more precise than the determination in[4]given in Eq.(8),where the main error in Eq.(8)comes from the input values of the magnetic moment ing this result in Eq.(23)into the expression:νF=ρF m e(1+m e/mµ)3(1+aµ),(24)where:16ρF==206.768276(11),(26)m eto be compared with the PDG value206.768266(13)using the masses in MeV units,and with the one from[4]: 206.768276(24).After inserting the previous value of m e/mµinto the alternative(equivalent)relation:νF=ρF µµ(1+m e/mµ)3,(27) one can deduce the ratio of magnetic moments:µµ5ConclusionsWe have evaluated the hadronic and QCD contributions∆αhad and∆νhad respectively to the QED running coupling and to the Muonium hyperfine splitting.Our results shown in Eqs.(11)and(15),are in excellent agreement with existing determinations shown in Fig.1and Table2and are quite accurate.These results have been obtained within the same strategy and data input as the one of the anomalous magnetic moment obtained previously in SN [1].For this reason,they are self-contained outputs.One of the immediate consequences of these results is the prediction ofα(M Z)given in Eq.(14),while we have used the result for the muonium hyperfine splitting for a high precision measurement of the ratios of the muon over the electron mass given in Eq.(26)and of magnetic moments given in Eq.(28).These Standard Model predictions are in excellent agreement with the ones quoted by PDG[9].These agreements can be used for providing strong constraints on some model buildings beyond the Standard Model.AcknowledgementsIt is a pleasure to thank W-Y.Pauchy Hwang for the hospitality at CosPA-NTU(Taipei),where this work has been 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