Can the quark model be relativistic enough to include the parton model

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前进中的物理学及人类文明

•《前进中的物理学与人类文明》期末考试（20）一、单选题（题数：50，共 50.0 分）1在经典物理中什么能分别体现物质的分离性和连续性？（）（1.0分）1.0分正确答案：A 我的答案：A2量子力学中不涉及以下哪个概念？（）（1.0分）1.0分正确答案：C 我的答案：C3以下哪个不是人类现在主要研究高能物理的实验？（）（1.0分）1.0分正确答案：D 我的答案：D4根据量子力学可以推出坐标和以下哪个物理量不能同时精确测量？（）（1.0分）1.0分正确答案：C 我的答案：C5引力与距离的几次方成反比？（）（1.0分）1.0分正确答案：A 我的答案：A6宇宙学原理认为宇宙介质在大尺度下是（）。

（1.0分）1.0分正确答案：C 我的答案：C7布朗运动中的气体分子满足怎样的分布率？（）（1.0分）1.0分正确答案：B 我的答案：B8大爆炸理论预言中子数与（）数之比为1:7。

（1.0分）1.0分正确答案：A 我的答案：A9中子星内部聚集着大量（）。

（1.0分）1.0分正确答案：A 我的答案：A10量子力学中引入量子自旋这个概念不是为了说明（）。

（1.0分）0.0分正确答案：D 我的答案：C11《自然哲学的数学原理》是谁的著作？（）（1.0分）1.0分正确答案：D 我的答案：D12高斯定理反映了静电场的什么特性？（）（1.0分）0.0分正确答案：A 我的答案：B13由开普勒第二定律推导行星角速度ω与其到太阳的距离r的关系为（）。

（1.0分）1.0分正确答案：A 我的答案：A14CPT不包括（）。

（1.0分）1.0分正确答案：D 我的答案：D15开普勒定律中的面积定律本质上是一种（）。

（1.0分）1.0分正确答案：B 我的答案：B16以下哪个试验支持爱因斯坦的狭义相对论？（）（1.0分）1.0分正确答案：A 我的答案：A17在经典理论（非量子理论）中，电子围绕原子核轨道运动的模型会导致下列哪种现象的出现？（）（1.0分）1.0分正确答案：B 我的答案：B182005年被定为世界物理年是为了纪念（）。

Baryon-Number Nonconservation and the Stability of Strange Matter

UCRHEP-T160 August 1996
Baryon-Number Nonconservation and
arXiv:hep-ph/9609211v1 30 Aug 1996
the Stability of Strange Matter
E. Keith and Ernest Ma Department of Physics University of California Riverside, California 92521
1
Introduction
Matter containing a large number of strange quarks may have a lower energy per baryon than ordinary nuclei and be absolutely stable[1, 2]. This intriguing possibility has generated a great deal of interest across many subﬁelds of physics. A crucial implicit assumption for the stability of this new kind of matter, called strange matter, is that the baryon number B is exactly conserved. Of course, we know nuclei are stable against ∆B = 0 decays. The best mode-independent experimental lower limit to date is 1.6 × 1025 years[3]. However, there may be eﬀective ∆B = 0 interactions which are highly suppressed for nuclei but not for strange matter. We examine such a hypothesis here and show that whereas such exotic decays are possible, the relevant lifetime should be longer than 105 years. In Sec. 2 we review brieﬂy the present experimental constraints on ∆B = 0 interactions. These come mainly from the nonobservation of proton decay and of neutron-antineutron oscillation. We then point out the possible consequences of an eﬀective ∆B = 2, ∆Ns = 4 operator (where Ns denotes the number of s quarks) on the stability of strange matter. We proceed to discuss some possible theoretical origins of such an operator in Sec. 3 and Sec. 4. We deal ﬁrst with the supersymmetric standard model with R-parity nonconserving terms of

802_am_强子物理_乔从丰

迄今为止，共发现三代，六种味道的夸克
强子物理
轻子家族
第一个轻子—电子
1931年，泡利为了解释β衰变中的能量失踪现象，预言了一种未知的极其微小的中性粒子带走了β衰变中那一部分能量和动量，最终被费米命名为“中微子” （Neutrino）。
1933年，费米指出：β衰变就是核内一个中子通过弱相互作用衰变成一个电子、一个质子和一个反中微子。中微子只参与弱作用，具有最强的穿透力。由于中微子与物质间的相
夸克间相互作用
根据目前人类的认识，自然界有四种基本相互作用：强相互作用、电磁相互作用、弱相互作用、万有引力
量子色动力学（QCD）是目前人类认识到的，自然界中最基本的四种相互作用之一，是描述基本粒子之间强相互作用的量子理论。
强相互作用
1964年，Greenberg引入了夸克的一种自由度——“颜色”（color）夸克带颜色荷。每味夸克就有三种颜色分别是红、绿和蓝（RGB）。
原子核 = 质子 + 中子
问题1：带正电的质子为何被束缚在一起？问题2：质子和中子是否具有内部结构？
强子物理
原子核内的相互作用—发现介子
1935年，日本科学家汤川秀树（Yukawa Hideki，1907-1981）提出了“交换粒子”的概念，作为新相互作用理论的基本概念。
1936年，美国科学家安德森在宇宙线中发现一种比电子约重207倍的粒子，当时误认为就是介子，后来发现这种粒子其实并不参与强相互作用是一种轻子，所以改名为μ子。
1909年卢瑟福指导他的学生做了一个著名物理实验。他们用alpha粒子轰击金箔，发现绝大多数alpha粒子与金原子的散射角很小，但也有少数alpha粒子散射角很大，甚至大于90度
他们由此推断，金原子内大部分空间是空的，质量较大并带有正电荷的部分集中在很小的，称之为核的区域

ResearchObjectives

Research ObjectivesThe MILC Collaboration is engaged in a broad research program in Quantum Chromodynamics (QCD).This research addresses fundamental questions in high energy and nuclear physics,and is directly related to major experimental programs in theseﬁelds.It includes studies of the mass spectrum of strongly interacting particles,the weak interactions of these particles,and the behavior of strongly interacting matter under extreme conditions.The Standard Model of High Energy Physics encompasses our current knowledge of the funda-mental interactions of subatomic physics.It consists of two quantumﬁeld theories:the Weinberg-Salaam theory of electromagnetic and weak interactions,and QCD,the theory of the strong interac-tions.The Standard Model has been enormously successful in explaining a wealth of data produced in accelerator and cosmic ray experiments over the past thirty years;however,our knowledge of it is incomplete because it has been difﬁcult to extract many of the most interesting predictions of QCD,those that depend on the strong coupling regime of the theory,and therefore require non-perturbative calculations.At present,the only means of carrying out non-perturbative QCD calculations fromﬁrst principles and with controlled errors,is through large scale numerical sim-ulations within the framework of lattice gauge theory.These simulations are needed to obtain a quantitative understanding of the physical phenomena controlled by the strong interactions,to de-termine a number of the fundamental parameters of the Standard Model,and to make precise tests of the Standard Model’s range of validity.Despite the many successes of the Standard Model,it is believed by high energy physicists that to understand physics at the shortest distances,a more general theory,which uniﬁes all four of the fundamental forces of nature,will be required.The Standard Model is expected to be a limiting case of this more general theory,just as classical mechanics is a limiting case of the more general quantum mechanics.A central objective of the experimental program in high energy physics,and of lattice QCD simulations,is to determine the range of validity of the Standard Model,and to search for new physics beyond it.Thus,QCD simulations play an important role in efforts to obtain a deeper understanding of the fundamental laws of physics.QCD is formulated in the four-dimensional space-time continuum;however,in order to carry out numerical calculations one must reformulate it on a lattice or grid.It should be emphasized that the lattice formulation of QCD is not merely a numerical approximation to the continuum formu-lation.The lattice regularization of QCD is every bit as valid as continuum regularizations.The lattice spacing a establishes a momentum cutoffπ/a that removes ultraviolet divergences.Stan-dard renormalization methods apply,and in the perturbative regime they allow a straightforward conversion of lattice results to any of the standard continuum regularization schemes.Lattice QCD calculations proceed in two steps.In theﬁrst,one uses importance sampling tech-niques to generate gauge conﬁgurations,which are representative samples from the Feynman path integrals that deﬁne QCD.These conﬁgurations are saved,and in the second step they are used to calculate a wide variety of physical quantities.It is necessary to generate conﬁgurations with a range of lattice spacings,and then perform extrapolations to the zero lattice spacing limit.Fur-thermore,the computational cost of calculations rises as the masses of the quarks,the fundamental constituents of strongly interacting matter,decrease.Until recently,it has been too expensive to carry out calculations with the masses of the two lightest quarks,the up and the down,set to their physical values.Instead,one has performed calculations for a range of up and down quark masses, and extrapolated to their physical values guided by chiral perturbation theory,an effectiveﬁeld theory that determines how physical quantities depend on the masses of the lightest quarks.The extrapolations in lattice spacing(continuum extrapolation)and quark mass(chiral extrapolation) are the major sources of systematic errors in QCD calculations,and both must be under control in order to obtain trustworthy results.In our current simulations,we are,for theﬁrst time,working at or near the physical masses of the up and down quarks.The gauge conﬁgurations produced in these simulations greatly reduce,and will eventually eliminate,the systematic errors associatedwith the chiral extrapolation.A number of different formulations of QCD on the lattice are currently in use by lattice gauge theorists,all of which are expected to give the same results in the continuum limit.In recent years, major progress has been made in theﬁeld through the development of improved formulations(im-proved actions)which reduceﬁnite lattice spacing artifacts.Approximately twelve years ago,we developed one such improved action called asqtad[1],which signiﬁcantly increased the accuracy of our simulations for a given amount of computing resources.We have used the asqtad action to generate an extensive library of gauge conﬁgurations with small enough lattice spacings and light enough quark masses to perform controlled calculations of a number of physical quantities. Computational resources provided by the DOE and NSF have enabled us to complete our program of generating asqtad gauge conﬁgurations.These conﬁgurations are publicly available,and have been used by us and by other groups to study a wide range of physical phenomena of importance in high energy and nuclear physics.Ours was theﬁrst set of full QCD ensembles that enabled control over both the continuum and chiral extrapolations.We have published a review paper describing the asqtad ensembles and the many calculations that were performed with them up to2009[2]. Over the last decade,a major component of our work has been to use our asqtad gauge conﬁg-urations to calculate quantities of importance to experimental programs in high energy physics. Particular emphasis was placed on the study of the weak decays and mixings of strongly interact-ing particles in order to determine some of the least well known parameters of the standard model and to provide precise tests of the standard model.The asqtad ensembles have enabled the calcu-lation of a number of physical quantities to a precision of1%–5%,and will enable many more quantities to be determined to this precision in the coming years.These results are already having an impact on experiments in high energy physics;however,in some important calculations,partic-ularly those related to tests of the standard model,higher precision is needed than can be provided by the existing asqtad ensembles.In order to obtain the required precision,we are now working with the Highly Improved Staggered Quark(HISQ)action developed by the HPQCD Collabora-tion[3].We have performed tests of scaling in the lattice spacing using HISQ valence quarks with gauge conﬁgurations generated with HISQ sea quarks[4].We found that lattice artifacts for the HISQ action are reduced by approximately a factor of2.5from those of the asqtad action for the same lattice spacing,and taste splittings in the pion masses are reduced by approximately a factor of three,which is sufﬁcient to enable us to undertake simulations with the mass of the Goldstone pion at or near the physical pion mass.(“Taste”refers to the different ways one can construct the same physical particle in the staggered quark formalism.Although particles with different tastes become identical in the continuum limit,their masses can differ atﬁnite lattice spacing).More-over,the improvement in the quark dispersion relation enables us to include charm sea quarks in the simulations.The properties of the HISQ ensembles are described in detail in Ref.[5],and the ﬁrst physics calculations using the physical quark mass ensembles in Refs.[6,7,8].The current status of the HISQ ensemble generation project is described at the link HISQ Lattice Generation and some initial calculations with them at Recent Results.The HISQ action also has major advan-tages for the study of QCD at high temperatures,so we have started to use it in our studies of this subject.Projects using the HISQ action will be a major component of our research for the next several years.Our research is currently focused on three major areas:1)the properties of light pseudoscalar mesons,2)the decays and mixings of heavy-light mesons,3)the properties of strongly interacting matter at high temperatures.We brieﬂy discuss our research in each of these areas at the link Recent Results.References[1]The MILC Collaboration:C.Bernard et al.,Nucl.Phys.(Proc.Suppl.),60A,297(1998);Phys.Rev.D58,014503(1998);G.P.Lepage,Nucl.Phys.(Proc.Suppl.),60A,267(1998);Phys.Rev.D59,074501(1999);Kostas Orginos and Doug Toussaint(MILC),Nucl.Phys.(Proc.Suppl.),73,909(1999);Phys.Rev.D59,014501(1999);Kostas Orginos,Doug Tou-ssaint and R.L.Sugar(MILC),Phys.Rev.D60,054503(1999);The MILC Collaboration:C.Bernard et al.,Phys.Rev.D61,111502(2000).[2]The MILC Collaboration: A.Bazavov et al.,Rev.Mod.Phys.82,1349-1417(2010)[arXiv:0903.3598[hep-lat]].[3]The HPQCD/UKQCD Collaboration: E.Follana et al.,Phys.Rev.D73,054502(2007)[arXiv:hep-lat/0610092].[4]The MILC Collaboration: A.Bazavov al.,Phys.Rev.D82,074501(2010)[arXiv:1004.0342].[5]The MILC Collaboration: A.Bazavov al.,Phys.Rev.D87,054505(2013)[arXiv:1212.4768].[6]The MILC Collaboration: A.Bazavov et al.,Phys.Rev.Lett.110,172003(2013)[arXiv:1301.5855].[7]The Fermilab Lattice and MILC Collaborations:A.Bazavov,et al.,Phys.Rev.Lett.112,112001(2014)[arXiv:1312.1228].[8]The MILC Collaboration:A.Bazavov et al.,Proceedings of Science(Lattice2013)405(2013)[arXiv:1312.0149].。

Mach cone shock waves at RHIC

a rXiv:071.4124v1[he p-ph]22Oct27Mach cone shock waves at RHIC ∗J ¨o rg Ruppert †Department of Physics,McGill University,3600University Street,Montreal,QC,H3A 2T8Canada and Thorsten Renk Department of Physics,PO box 35FIN-40014,University of Jyv¨a skyl¨a ,Finland,and Helsinki Institute of Physics,PO Box 64,FIN-00014,University of Helsinki,Finland.Energy and momentum lost by hard jets propagating through hot and dense nuclear matter have to be redistributed in the medium.It has been conjectured that collective sound modes are excited.Those lead to Mach cone nuclear shock waves in the nuclear medium that are shown to account for three and four particle angular correlation structures of hadrons with a (semi-)hard trigger hadron in heavy-ion collisions at RHIC.1.Introduction The quenching of QCD jets created in relativistic nuclear collisions has been proposed as an important indicator of the creation of a quark-gluonplasma [1].It is extensively studied theoretically and experimentally at RHIC.The main emphasis in most theoretical studies (before 2005)has been solely on the description of the radiative energy loss which the lead-ing parton suﬀers while traversing the nuclear medium due to the emis-sion of partonic secondaries.In this paper we focus on another aspect of the in-medium jet physics,namely the question if the jets traversing the medium can transfer energy and momentum to collective modes in the nu-clear medium that might be able to account for the emergence of peculiar signals in the particle correlation measurements.Recently,measurements of two-and three-particle correlations involving one hard trigger particle2ISMD-ruppert-2printed on February2,2008have shown a surprising splitting of the away side peak for all centralities but peripheral collisions,qualitatively very diﬀerent from a broadened awayside peak observed in p-p or d-Au collisions[2].Interpretations in termsof colorless[3,4]and colored[5]sound modes have been suggested for anexplanation of this phenomenon.For an overview also discussing alternativemechanisms,see[6]and references therein.While the microscopic excita-tion mechanism of the colorless modes is under investigation[7],a detailedtheoretical study of the experimentally observable correlations is alreadynow possible if this mechanism is assumed to eﬀectively excite the mode.In the following,we discuss how such shockwaves lead to observable correlationsignals in the dynamical environment of a heavy-ion collision.2.The modelA Monte Carlo simulation of the hard back to back process in themedium is performed.There are four main stages in the modeling:1)the primary hard pQCD process,2)the description of the soft medium,3)the energy loss from hard to soft degrees of freedom,4)the simulation ofthe shockwave propagation and its modiﬁcation of the soft medium until de-coupling.For brevity we only present a sketch of the model here,a detaileddescription of the model can be found in[8].The soft medium is described by a parametrized evolution model[9]which gives a good description of thebulk matter transverse momentum spectra and HBT correlation radii.Theenergy loss for a given parton path inside this medium is described prob-abilistically by P(∆E,E)path,which is the probability for a hard partonof energy E to lose energy∆E while traversing the medium in the ASWformalism[10].Since we are interested in the energy deposition on aver-age in a given volume we focus on the distribution of the average energy <∆E>= ∞0P(∆(E))∆Ed∆E along the paths to infer dE/dx,see Fig.1 in[8].We assume that a fraction f of the energy lost to the medium excitesa shockwave characterized by a dispersion relation E=c s p where c s is thespeed of sound inferred from the equation of state by c2s=∂p/∂ǫ.Thedispersion relation determines the initial angle of propagation of the shockfront asφ=arccos c s.The time dependent energy transfer to the mode perunit time is given by fdE/dτ.Each piece of the front is propagated withthe local speed of sound through the medium.Once a wavefront has evolved until it satisﬁed freeze-out condition T=T F it cannot propagate further leading to an additional boost at freeze-out.The Cooper-Frye formalism is employed to calculate the hadronic distribution accordingly.On the near-side the trigger condition is realized.The important role of longitudinal and transverse expansion as well asﬂow eﬀects on the observed correlation signal are discussed in[8].ISMD-ruppert-2printed on February 2,200833.ResultsIn order to show how the excitation of a collective mode can account forthe observed correlation signal in a quantiative manner,we show in Fig.1the correlation signal and its sensitivity to diﬀerent descriptions of the soft background.We chose an energy independent f =0.75which accounts for the expansionFig.1.Correlation signal on the away side for diﬀerent soft background medium density distributions and evolutions (see text,not acceptance-averaged).patterns (Bjorken and non-Bjorken evolution)and two diﬀerent transverse densities (box and nuclear proﬁle T A ).Due to the position of the freeze-out hypersurface at large radii for the box density,the shockwave gets on average longer exposure to transverse ﬂow in this scenario which leads to a less pronounced maximum since transverse ﬂow can erase a peak if ﬂow and shockwave are not aligned.The angle is larger for longitudinal Bjorken expansion which is due to the fact that initial cooling is rapid and therefore the averag temperature quickly approaches the phase transition temperature T c where c s is small.In this speciﬁc calculation we suppressed a full rapidity averaging,leading to a somewhat larger angle than expected if averaging were performed.In Fig.2we show the resulting 3-particle correlation for non-Bjorken evolution with initial box density and nuclear density proﬁle,for details of the calculation see [8].The region close to the trigger is not studied.Our results ﬁt nicely with the fact that transverse ﬂow can erase in some conﬁgurations one or even both of the wings of the cone.In this case,only the diagonal region is populated whereas if both wings appear the oﬀdiagonal maxima are populated.In this sense 2-and especially 3-particle correlation measurements do not only reveal information about the smallness of c s in the evolution,indicating the existence of a (cross-over)phase transition to a quark gluon plasma,but also can eventually be used4ISMD-ruppert-2printed on February 2,2008Aφφ12。

核子中奇异夸克分布不对称性与轻味夸克碎裂效应

29 10 2005 10HIGH ENERGY PHYSICS AND NUCLEAR PHYSICSVol.29,No.10Oct.,2005*( 100871)– , . , .D ..1, –[1—3]. ,. ,, –(DIS) (global analysis)[4,5], ,(intrinsic sea theory) ,µ CCFR NuTeV,[6,7]. ,. ,[4,8—12]NuTeVWeinberg [13,14],.. ,Fν2 F¯ν2,:Fν2−F¯ν2=2x[s(x)−¯s(x)]. ,,. c.CCFR NuTeV µ [6,15,16].νµs→µ−c νµd→µ−c,Cabibbo ,c ;, ¯c.CCFR NuTeV µµ+(µ−) c(¯c) ,c→H(c¯q)→µ+X. µ,µ ,. ,CCFR νµ(¯νµ) ,c(¯c) µ+(µ−) ¯B c(¯B¯c):¯Bc−¯B¯c0.1147∼0−20%[6]., ,µ . ,CCFR NuTeV µ,.( c ¯c10 965dξd y =G2s2|V cd|2].(1)s=2MEν ,r2≡(1+Q2/M2W)2.ξ . , c ,ξ Bjorken:ξ≈x(1+m2c /Q2). (1)f c≡1−m2c/2MEνξ c, [18]., ¯cd2σ¯νµN→µ+¯c Xπr2f c•ξ[¯s(ξ)|V cs|2+¯d(ξ)+¯u(ξ)dξd y−d2σ¯νµN→µ+¯c Xπr2f c•ξ (s(ξ)−¯s(ξ))|V cs|2+d v(ξ)+u v(ξ)2ξ[d v(ξ)+u v(ξ)] ,|V cs|2≃0.95 |V cd|2≃0.05[19] .12S−|V cs|2+Q V|V cd|2,(4)S−≡ ξ[s(ξ)−¯s(ξ)]dξ,Q V≡ ξ[d v(ξ)+u v(ξ)]dξ., NuTeV.[9—12],NuTeV ., (4) ,c ¯c P SA( 1).1 NuTeV c ¯c P SADing-Ma[9]Q2030%—80%0.007—0.01812%—26% Alwall-Ingelman[10]20GeV230%0.00915% Ding-Xu-Ma[11]Q2060%—100%0.014—0.02221%—29% Wakamatsu[12]16GeV270%—110%0.022—0.03530%—40%966 (HEP&NP) 29 2S+|V cs|2+(Q V+2Q S)|V cd|2.(5)S+≡ ξ[s(ξ)+¯s(ξ)]dξ,Q S≡ ξ[¯u(ξ)+¯d(ξ)]dξ.CTEQ5 Q2=16GeV2 S+,Q V,Q S, |V cs|2=0.95,|V cd|2=0.05,1 2S−/Q V 0.007(0.022), R 20%(25%). ,c ¯c, c¯c.3 µ, , c,( µ) ( ) . cH+d3σνµN→µ−H+Xdξd y D H+q(z),(6)D H+q(z) q H+ ,z H+ q . H+ c D+(c¯d) D0(c¯u) ,H− D−(¯c d) ¯D0(¯c u).c H+ H+ . , Lund , q¯qexp(−bm2q)[20], s¯s λ∼0.3[21,22], c¯c 10−5., . µ [17]. . , e+e− . , , c ¯c , D , c , , , c(¯c) , µ . , c ¯c D(c¯q) ¯D(¯c q). , , , :u→cu),d→D−(dξd y d z=G2s2|V cd|2]+δ dσνN→µ−µ+Xdξd y d z LQF=G2s2|V ud|2(1−y)2,(8)D q(z)≡D Dq(z)+D D∗q(z), D Dq(z)≡D¯D0u(z)=D D0¯u(z)=D D−d(z)=D D+¯d(z),D D∗q(z)≡D¯D∗0u(z)=D D∗0¯u(z)=D D∗−d(z)=D D∗+¯d(z). , D q(z) q , . (8) ,¯BD(∗)+=1dξd y d z=G2s2|V cd|2]+δ dσ¯νN→µ+µ−Xdξd y d z LQF=G2s2•|V ud|2(1−y)2.(10)10 967(σνN→µ−µ+X−σ¯νN→µ+µ−X)total≈−1Q V|V cd|2+2S−|V cs|2•D q¯BD(∗)+¯f c ¯Bc.D q¯BD(∗)+d x d y d z=G2s2|V ud|2D q(z)B¯D0,(12),B¯D0 ¯D0 µ− , ¯D∗0¯D0 , B¯D0 .,µ+µ+d3σ¯νN→µ+µ+Xπr2x¯u(x)+¯d(x)σµ−µ+≈Q ud|V ud|2¯fc¯Bc,(14)Q ud≡1¯fc¯Bc,D qσµ−µ+.(15)CDHSW[26] ( )µ µ σµ−µ−/σµ−µ+(σµ+µ+/σµ+µ−). 2E vis 100—200GeV ,3 .2 , , σµ−µ−/σµ−µ+σµ−µ−/σµ− ,, σµ−µ−/σµ−µ+, ,.2CDHSW 100<E vis<200GeV µ [26]pµ>6GeV(3.5±1.6)%(1.6±0.74)×10−4(4.5±2.0)%(2.2±1.0)×10−4 pµ>9GeV(2.9±1.2)%(1.05±0.43)×10−4(4.4±1.8)%(1.7±0.7)×10−4 pµ>15GeV(2.3±1.0)%(0.52±0.22)×10−4(4.1±2.3)%(0.8±0.45)×10−4968 (HEP&NP) 29dξd y d z −d3σ¯νµN→µ+H−Xπr2f cξ[(s(ξ)−¯s(ξ))|V cs|2+ d v(ξ)+u v(ξ)πr2xd v(x)+u v(x)πr2xd v(x)+u v(x)10 969(References)1Brodsky S J,MA B-Q.Phys.Lett.,1996,B381:3172Signal A I,Thomas A W.Phys.Lett.,1987,B191:2053Burkardt M,Warr B J.Phys.Rev.,1992,D45:9584Olness F et al.hep-ph/03123235Barone V et al.Eur.Phys.J.,2000,C12:2436Bazarko A O et al(CCFR Collaboration).Z.Phys.,1995, C65:1897Mason D(NuTeV Collaboration).hep-ex/04050378Kretzer S et al.Phys.Rev.Lett.,2004,93:0418029DING Y,MA B-Q.Phys.Lett.,2004,B590:216;DING Yong,L¨U Zhun,MA Bo-Qiang.HEP&NP,2004,28(9): 947(in Chinese)( , , . ,2004,28(9):947) 10Alwall J,Ingelman G.Phys.Rev.,2004,D70:111505.11DING Y,XU R-G,MA B-Q.Phys.Lett.,2005,B607:101 12Wakamatsu M.hep-ph/041120313Zeller G P et al.Phys.Rev.Lett.,2002,88:09180214Zeller G P et al.Phys.Rev.,2002,D65:11110315Rabinowitz S A et al.Phys.Rev.Lett.,1993,70:13416Goncharov M et al.Phys.Rev.,2001,D64:11200617Godbole R M,Roy D P.Z.Phys.,1984,C22:39;Z.Phys., 1989,C42:21918Astier P et al(NOMAD Collaboration).Phys.Lett.,2000, B486:3519Eidelman S et al(Particle Data Group).Phys.Lett.,2004, B592:120Andersson B et al.Nucl.Phys.,1981,B178:24221Laﬀerty G D.Phys.Lett.,1995,B353:54122Abe K et al(SLD Collaboration).Phys.Rev.Lett.,1997, 78:334123Smith J,Valenzuela G.Phys.Rev.,1983,D28:107124Aitala E M et al(Fermilab E791Collaboration).Phys.Lett.,1996,B371:15725Dias de Deus J,Dur˜a es F.Eur.Phys.J.,2000,C13:647 26Burkhardt H et al.Z.Phys.,1986,C31:3927Sandler P H et al.Z.Phys.,1993,C57:1,and References Therein.28Jonker M et al.Phys.Lett.,1981,B107:24129de Lellis G et al.Phys.Rep.,2004,399:22730Kayis-Topaksu A et al(CHORUS Collaboration).Phys.Lett.,2002,B549:4831¨Oneng¨u t G et al(CHORUS Collaboration).Phys.Lett., 2004,B604:145Nucleon Strange Asymmetry and the Light QuarkFragmentation Eﬀect*GAO Pu-Ze MA Bo-Qiang(School of Physics,Peking University,Beijing100871,China)Abstract Nucleon strange asymmetry is an important non-perturbative eﬀect in the study of nucleon structure,but it has not been checked by experiments yet.For eﬀectively measuring the nucleon strange asymmetry,we investigate the light quark fragmentation eﬀect that may aﬀect the measurement of the strange asymmetry.We suggest an inclusive measurement of charged and neutral charmed hadrons by using an emulsion target in the neutrino and antineutrino in-duced charged current deep inelastic scattering,in which the strange asymmetry eﬀect and the light quark fragmentation eﬀect can be separated.Key words strange asymmetry,light quark fragmentation,charged current deep inelastic scattering。

feynman-stückelberg 公约

费曼-斯图克尔伯格公约feynman-stückelberg 公约feynman-stückelberg 公约是一种关于反物质的解释，它认为反物质是正物质的负能量解，沿着时间的反方向运动。

这种解释最早由瑞士物理学家恩斯特·斯图克尔伯格（Ernst Stueckelberg）在1938年提出，后来由美国物理学家理查德·费曼（Richard Feynman）在1949年独立地重新发现，并用于量子电动力学的计算中。

feynman-stückelberg 公约可以用数学上的变换来表达，即将时间t和能量E同时取相反数，这样就可以将一个正能量的正物质粒子转化为一个负能量的反物质粒子，反之亦然。

这种变换不改变粒子的动量和自旋，因此不违反任何守恒定律。

费曼-斯图克尔伯格公约的历史背景费曼-斯图克尔伯格公约的提出是为了解决狄拉克方程的一个困难，即狄拉克方程不仅有正能量的解，也有负能量的解。

狄拉克最初认为，负能量解对应于电子在原子核内部的状态，而正能量解对应于电子在原子核外部的状态。

但是，这种解释很快遇到了问题，例如：为什么负能量电子不会发射无穷多的光子？为什么负能量电子不会与正能量电子相互作用？为什么负能量电子不会被观测到？狄拉克后来提出了一个更加大胆的假设，即所有的负能量状态都已经被电子占据了，形成了一个无限密度的“狄拉克海”。

当一个负能量电子吸收一个足够大的光子后，它会跃迁到一个正能量状态，留下一个空穴。

这个空穴就相当于一个正电荷、正能量、与电子相反自旋的粒子，也就是我们所说的正电子。

当正电子和电子相遇时，它们会互相湮灭，释放出两个光子。

这样就可以解释正电子的存在和湮灭过程。

狄拉克海的假设虽然具有创造性，但也有很多问题。

例如：为什么只有电子有狄拉克海？为什么狄拉克海不会对其他粒子产生影响？为什么狄拉克海不会塌缩？为什么狄拉克海不会产生无限大的真空能？等等。

这些问题表明，狄拉克海并不是一个完美的理论。

The Standard Model of Particle Physics

a r X i v :h e p -p h /9812285v 1 8 D e c 1998The Standard Model of Particle PhysicsMary K.Gaillard 1,Paul D.Grannis 2,and Frank J.Sciulli 31University of California,Berkeley,2State University of New York,Stony Brook,3Columbia UniversityParticle physics has evolved a coherent model that characterizes forces and particles at the mostelementary level.This Standard Model,built from many theoretical and experimental studies,isin excellent accord with almost all current data.However,there are many hints that it is but anapproximation to a yet more fundamental theory.We trace the development of the Standard Modeland indicate the reasons for believing that it is incomplete.Nov.20,1998(To be published in Reviews of Modern Physics)I.INTRODUCTION:A BIRD’S EYE VIEW OF THE STANDARD MODEL Over the past three decades a compelling case has emerged for the now widely accepted Standard Model of elementary particles and forces.A ‘Standard Model’is a theoretical framework built from observation that predicts and correlates new data.The Mendeleev table of elements was an early example in chemistry;from the periodic table one could predict the properties of many hitherto unstudied elements and compounds.Nonrelativistic quantum theory is another Standard Model that has correlated the results of countless experiments.Like its precursors in other ﬁelds,the Standard Model (SM)of particle physics has been enormously successful in predicting a wide range of phenomena.And,just as ordinary quantum mechanics fails in the relativistic limit,we do not expect the SM to be valid at arbitrarily short distances.However its remarkable success strongly suggests that the SM will remain an excellent approximation to nature at distance scales as small as 10−18m.In the early 1960’s particle physicists described nature in terms of four distinct forces,characterized by widely diﬀerent ranges and strengths as measured at a typical energy scale of 1GeV.The strong nuclear force has a range of about a fermi or 10−15m.The weak force responsible for radioactive decay,with a range of 10−17m,is about 10−5times weaker at low energy.The electromagnetic force that governs much of macroscopic physics has inﬁnite range and strength determined by the ﬁnestructure constant,α≈10−2.The fourth force,gravity,also has inﬁnite range and a low energy coupling (about 10−38)too weak to be observable in laboratory experiments.The achievement of the SM was the elaboration of a uniﬁed description of the strong,weak and electromagnetic forces in the language of quantum gauge ﬁeld theories.Moreover,the SM combines the weak and electromagnetic forces in a single electroweak gauge theory,reminiscent of Maxwell’s uniﬁcation of the seemingly distinct forces of electricity and magnetism.By mid-century,the electromagnetic force was well understood as a renormalizable quantum ﬁeld theory (QFT)known as quantum electrodynamics or QED,described in the preceeding article.‘Renormalizable’means that once a few parameters are determined by a limited set of measurements,the quantitative features of interactions among charged particles and photons can be calculated to arbitrary accuracy as a perturbative expansion in the ﬁne structure constant.QED has been tested over an energy range from 10−16eV to tens of GeV,i.e.distances ranging from 108km to 10−2fm.In contrast,the nuclear force was characterized by a coupling strength that precluded a perturbativeexpansion.Moreover,couplings involving higher spin states(resonances),that appeared to be onthe same footing as nucleons and pions,could not be described by a renormalizable theory,nor couldthe weak interactions that were attributed to the direct coupling of four fermions to one another.In the ensuing years the search for renormalizable theories of strong and weak interactions,coupledwith experimental discoveries and attempts to interpret available data,led to the formulation ofthe SM,which has been experimentally veriﬁed to a high degree of accuracy over a broad range ofenergy and processes.The SM is characterized in part by the spectrum of elementaryﬁelds shown in Table I.The matterﬁelds are fermions and their anti-particles,with half a unit of intrinsic angular momentum,or spin.There are three families of fermionﬁelds that are identical in every attribute except their masses.Theﬁrst family includes the up(u)and down(d)quarks that are the constituents of nucleons aswell as pions and other mesons responsible for nuclear binding.It also contains the electron and theneutrino emitted with a positron in nuclearβ-decay.The quarks of the other families are constituentsof heavier short-lived particles;they and their companion charged leptons rapidly decay via the weakforce to the quarks and leptons of theﬁrst family.The spin-1gauge bosons mediate interactions among fermions.In QED,interactions among elec-trically charged particles are due to the exchange of quanta of the electromagneticﬁeld called photons(γ).The fact that theγis massless accounts for the long range of the electromagnetic force.Thestrong force,quantum chromodynamics or QCD,is mediated by the exchange of massless gluons(g)between quarks that carry a quantum number called color.In contrast to the electrically neutralphoton,gluons(the quanta of the‘chromo-magnetic’ﬁeld)possess color charge and hence couple toone another.As a consequence,the color force between two colored particles increases in strengthwith increasing distance.Thus quarks and gluons cannot appear as free particles,but exist onlyinside composite particles,called hadrons,with no net color charge.Nucleons are composed ofthree quarks of diﬀerent colors,resulting in‘white’color-neutral states.Mesons contain quark andanti-quark pairs whose color charges cancel.Since a gluon inside a nucleon cannot escape its bound-aries,the nuclear force is mediated by color-neutral bound states,accounting for its short range,characterized by the Compton wavelength of the lightest of these:theπ-meson.The even shorter range of the weak force is associated with the Compton wave-lengths of thecharged W and neutral Z bosons that mediate it.Their couplings to the‘weak charges’of quarksand leptons are comparable in strength to the electromagnetic coupling.When the weak interactionis measured over distances much larger than its range,its eﬀects are averaged over the measurementarea and hence suppressed in amplitude by a factor(E/M W,Z)2≈(E/100GeV)2,where E is the characteristic energy transfer in the measurement.Because the W particles carry electric charge theymust couple to theγ,implying a gauge theory that unites the weak and electromagnetic interactions,similar to QCD in that the gauge particles are self-coupled.In distinction toγ’s and gluons,W’scouple only to left-handed fermions(with spin oriented opposite to the direction of motion).The SM is further characterized by a high degree of symmetry.For example,one cannot performan experiment that would distinguish the color of the quarks involved.If the symmetries of theSM couplings were fully respected in nature,we would not distinguish an electron from a neutrinoor a proton from a neutron;their detectable diﬀerences are attributed to‘spontaneous’breakingof the symmetry.Just as the spherical symmetry of the earth is broken to a cylindrical symmetry by the earth’s magneticﬁeld,aﬁeld permeating all space,called the Higgsﬁeld,is invoked to explain the observation that the symmetries of the electroweak theory are broken to the residual gauge symmetry of QED.Particles that interact with the Higgsﬁeld cannot propagate at the speed of light,and acquire masses,in analogy to the index of refraction that slows a photon traversing matter.Particles that do not interact with the Higgsﬁeld—the photon,gluons and possibly neutrinos–remain massless.Fermion couplings to the Higgsﬁeld not only determine their masses; they induce a misalignment of quark mass eigenstates with respect to the eigenstates of the weak charges,thereby allowing all fermions of heavy families to decay to lighter ones.These couplings provide the only mechanism within the SM that can account for the observed violation of CP,that is,invariance of the laws of nature under mirror reﬂection(parity P)and the interchange of particles with their anti-particles(charge conjugation C).The origin of the Higgsﬁeld has not yet been determined.However our very understanding of the SM implies that physics associated with electroweak symmetry breaking(ESB)must become manifest at energies of present colliders or at the LHC under construction.There is strong reason, stemming from the quantum instability of scalar masses,to believe that this physics will point to modiﬁcations of the theory.One shortcoming of the SM is its failure to accommodate gravity,for which there is no renormalizable QFT because the quantum of the gravitationalﬁeld has two units of spin.Recent theoretical progress suggests that quantum gravity can be formulated only in terms of extended objects like strings and membranes,with dimensions of order of the Planck length10−35m. Experiments probing higher energies and shorter distances may reveal clues connecting SM physics to gravity,and may shed light on other questions that it leaves unanswered.In the following we trace the steps that led to the formulation of the SM,describe the experiments that have conﬁrmed it,and discuss some outstanding unresolved issues that suggest a more fundamental theory underlies the SM.II.THE PATH TO QCDThe invention of the bubble chamber permitted the observation of a rich spectroscopy of hadron states.Attempts at their classiﬁcation using group theory,analogous to the introduction of isotopic spin as a classiﬁcation scheme for nuclear states,culminated in the‘Eightfold Way’based on the group SU(3),in which particles are ordered by their‘ﬂavor’quantum numbers:isotopic spin and strangeness.This scheme was spectacularly conﬁrmed by the discovery at Brookhaven Laboratory (BNL)of theΩ−particle,with three units of strangeness,at the predicted mass.It was subsequently realized that the spectrum of the Eightfold Way could be understood if hadrons were composed of three types of quarks:u,d,and the strange quark s.However the quark model presented a dilemma: each quark was attributed one half unit of spin,but Fermi statistics precluded the existence of a state like theΩ−composed of three strange quarks with total spin3A combination of experimental observations and theoretical analyses in the1960’s led to anotherimportant conclusion:pions behave like the Goldstone bosons of a spontaneously broken symmetry,called chiral symmetry.Massless fermions have a conserved quantum number called chirality,equalto their helicity:+1(−1)for right(left)-handed fermions.The analysis of pion scattering lengths andweak decays into pions strongly suggested that chiral symmetry is explicitly broken only by quarkmasses,which in turn implied that the underlying theory describing strong interactions among quarksmust conserve quark helicity–just as QED conserves electron helicity.This further implied thatinteractions among quarks must be mediated by the exchange of spin-1particles.In the early1970’s,experimenters at the Stanford Linear Accelerator Center(SLAC)analyzed thedistributions in energy and angle of electrons scattered from nuclear targets in inelastic collisionswith momentum transfer Q2≈1GeV/c from the electron to the struck nucleon.The distributions they observed suggested that electrons interact via photon exchange with point-like objects calledpartons–electrically charged particles much smaller than nucleons.If the electrons were scatteredby an extended object,e.g.a strongly interacting nucleon with its electric charge spread out by acloud of pions,the cross section would drop rapidly for values of momentum transfer greater than theinverse radius of the charge distribution.Instead,the data showed a‘scale invariant’distribution:across section equal to the QED cross section up to a dimensionless function of kinematic variables,independent of the energy of the incident electron.Neutrino scattering experiments at CERN andFermilab(FNAL)yielded similar parison of electron and neutrino data allowed adetermination of the average squared electric charge of the partons in the nucleon,and the result wasconsistent with the interpretation that they are fractionally charged quarks.Subsequent experimentsat SLAC showed that,at center-of-mass energies above about two GeV,theﬁnal states in e+e−annihilation into hadrons have a two-jet conﬁguration.The angular distribution of the jets withrespect to the beam,which depends on the spin of theﬁnal state particles,is similar to that of themuons in anµ+µ−ﬁnal state,providing direct evidence for spin-1√where G F is the Fermi coupling constant,γµis a Dirac matrix and12fermions via the exchange of spinless particles.Both the chiral symmetry of thestrong interactions and the V−A nature of the weak interactions suggested that all forces except gravity are mediated by spin-1particles,like the photon.QED is renormalizable because gauge invariance,which gives conservation of electric charge,also ensures the cancellation of quantum corrections that would otherwise result in inﬁnitely large amplitudes.Gauge invariance implies a massless gauge particle and hence a long-range force.Moreover the mediator of weak interactions must carry electric charge and thus couple to the photon,requiring its description within a Yang-Mills theory that is characterized by self-coupled gauge bosons.The important theoretical breakthrough of the early1970’s was the proof that Yang-Mills theories are renormalizable,and that renormalizability remains intact if gauge symmetry is spontaneously broken,that is,if the Lagrangian is gauge invariant,but the vacuum state and spectrum of particles are not.An example is a ferromagnet for which the lowest energy conﬁguration has electron spins aligned;the direction of alignment spontaneously breaks the rotational invariance of the laws ofphysics.In QFT,the simplest way to induce spontaneous symmetry breaking is the Higgs mech-anism.A set of elementary scalarsφis introduced with a potential energy density function V(φ) that is minimized at a value<φ>=0and the vacuum energy is degenerate.For example,the gauge invariant potential for an electrically charged scalarﬁeldφ=|φ|e iθ,V(|φ|2)=−µ2|φ|2+λ|φ|4,(3)√λ=v,but is independent of the phaseθ.Nature’s choice forθhas its minimum atspontaneously breaks the gauge symmetry.Quantum excitations of|φ|about its vacuum value are massive Higgs scalars:m2H=2µ2=2λv2.Quantum excitations around the vacuum value ofθcost no energy and are massless,spinless particles called Goldstone bosons.They appear in the physical spectrum as the longitudinally polarized spin states of gauge bosons that acquire masses through their couplings to the Higgsﬁeld.A gauge boson mass m is determined by its coupling g to theHiggsﬁeld and the vacuum value v.Since gauge couplings are universal this also determines the√Fermi constant G for this toy model:m=gv/2,G/2|φ|=212F=246GeV,leaving three Goldstone bosons that are eaten by three massive vector bosons:W±and Z=cosθw W0−sinθw B0,while the photonγ=cosθw B0+sinθw W0remains massless.This theory predicted neutrino-induced neutral current(NC)interactions of the typeν+atom→ν+anything,mediated by Z exchange.The weak mixing angleθw governs the dependence of NC couplings on fermion helicity and electric charge, and their interaction rates are determined by the Fermi constant G Z F.The ratioρ=G Z F/G F= m2W/m2Z cos2θw,predicted to be1,is the only measured parameter of the SM that probes thesymmetry breaking mechanism.Once the value ofθw was determined in neutrino experiments,the√W and Z masses could be predicted:m2W=m2Z cos2θw=sin2θwπα/QUARKS:S=1LEPTONS:S=13m3m Q=0m quanta mu1u2u3(2–8)10−3e 5.11×10−4c1c2c3 1.0–1.6µ0.10566t1t2t3173.8±5.0τ 1.77705/3g′,where g1isﬁxed by requiring the same normalization for all fermion currents.Their measured values at low energy satisfy g3>g2>g1.Like g3,the coupling g2decreases with increasing energy,but more slowly because there are fewer gauge bosons contributing.As in QED,the U(1)coupling increases with energy.Vacuum polarization eﬀects calculated using the particle content of the SM show that the three coupling constants are very nearly equal at an energy scale around1016GeV,providing a tantalizing hint of a more highly symmetric theory,embedding the SM interactions into a single force.Particle masses also depend on energy;the b andτmasses become equal at a similar scale,suggesting a possibility of quark and lepton uniﬁcation as diﬀerent charge states of a singleﬁeld.V.BRIEF SUMMARY OF THE STANDARD MODEL ELEMENTSThe SM contains the set of elementary particles shown in Table I.The forces operative in the particle domain are the strong(QCD)interaction responsive to particles carrying color,and the two pieces of the electroweak interaction responsive to particles carrying weak isospin and hypercharge. The quarks come in three experimentally indistinguishable colors and there are eight colored gluons. All quarks and leptons,and theγ,W and Z bosons,carry weak isospin.In the strict view of the SM,there are no right-handed neutrinos or left-handed anti-neutrinos.As a consequence the simple Higgs mechanism described in section IV cannot generate neutrino masses,which are posited to be zero.In addition,the SM provides the quark mixing matrix which gives the transformation from the basis of the strong interaction charge−1Finding the constituents of the SM spanned theﬁrst century of the APS,starting with the discovery by Thomson of the electron in1897.Pauli in1930postulated the existence of the neutrino as the agent of missing energy and angular momentum inβ-decay;only in1953was the neutrino found in experiments at reactors.The muon was unexpectedly added from cosmic ray searches for the Yukawa particle in1936;in1962its companion neutrino was found in the decays of the pion.The Eightfold Way classiﬁcation of the hadrons in1961suggested the possible existence of the three lightest quarks(u,d and s),though their physical reality was then regarded as doubtful.The observation of substructure of the proton,and the1974observation of the J/ψmeson interpreted as a cp collider in1983was a dramatic conﬁrmation of this theory.The gluon which mediates the color force QCD wasﬁrst demonstrated in the e+e−collider at DESY in Hamburg.The minimal version of the SM,with no right-handed neutrinos and the simplest possible ESB mechanism,has19arbitrary parameters:9fermion masses;3angles and one phase that specify the quark mixing matrix;3gauge coupling constants;2parameters to specify the Higgs potential; and an additional phaseθthat characterizes the QCD vacuum state.The number of parameters is larger if the ESB mechanism is more complicated or if there are right-handed neutrinos.Aside from constraints imposed by renormalizability,the spectrum of elementary particles is also arbitrary.As discussed in Section VII,this high degree of arbitrariness suggests that a more fundamental theory underlies the SM.VI.EXPERIMENTAL ESTABLISHMENT OF THE STANDARD MODELThe current picture of particles and interactions has been shaped and tested by three decades of experimental studies at laboratories around the world.We brieﬂy summarize here some typical and landmark results.FIG.1.The proton structure function(F2)versus Q2atﬁxed x,measured with incident electrons or muons,showing scale invariance at larger x and substantial dependence on Q2as x becomes small.The data are taken from the HERA ep collider experiments H1and ZEUS,as well as the muon scattering experiments BCDMS and NMC at CERN and E665at FNAL.A.Establishing QCD1.Deep inelastic scatteringPioneering experiments at SLAC in the late1960’s directed high energy electrons on proton and nuclear targets.The deep inelastic scattering(DIS)process results in a deﬂected electron and a hadronic recoil system from the initial baryon.The scattering occurs through the exchange of a photon coupled to the electric charges of the participants.DIS experiments were the spiritual descendents of Rutherford’s scattering ofαparticles by gold atoms and,as with the earlier experi-ment,showed the existence of the target’s substructure.Lorentz and gauge invariance restrict the matrix element representing the hadronic part of the interaction to two terms,each multiplied by phenomenological form factors or structure functions.These in principle depend on the two inde-pendent kinematic variables;the momentum transfer carried by the photon(Q2)and energy loss by the electron(ν).The experiments showed that the structure functions were,to good approximation, independent of Q2forﬁxed values of x=Q2/2Mν.This‘scaling’result was interpreted as evi-dence that the proton contains sub-elements,originally called partons.The DIS scattering occurs as the elastic scatter of the beam electron with one of the partons.The original and subsequent experiments established that the struck partons carry the fractional electric charges and half-integer spins dictated by the quark model.Furthermore,the experiments demonstrated that three such partons(valence quarks)provide the nucleon with its quantum numbers.The variable x represents the fraction of the target nucleon’s momentum carried by the struck parton,viewed in a Lorentz frame where the proton is relativistic.The DIS experiments further showed that the charged partons (quarks)carry only about half of the proton momentum,giving indirect evidence for an electrically neutral partonic gluon.1011010101010FIG.2.The quark and gluon momentum densities in the proton versus x for Q 2=20GeV 2.The integrated values of each component density gives the fraction of the proton momentum carried by that component.The valence u and d quarks carry the quantum numbers of the proton.The large number of quarks at small x arise from a ‘sea’of quark-antiquark pairs.The quark densities are from a phenomenological ﬁt (the CTEQ collaboration)to data from many sources;the gluon density bands are the one standard deviation bounds to QCD ﬁts to ZEUS data (low x )and muon scattering data (higher x ).Further DIS investigations using electrons,muons,and neutrinos and a variety of targets reﬁned this picture and demonstrated small but systematic nonscaling behavior.The structure functions were shown to vary more rapidly with Q 2as x decreases,in accord with the nascent QCD prediction that the fundamental strong coupling constant αS varies with Q 2,and that at short distance scales (high Q 2)the number of observable partons increases due to increasingly resolved quantum ﬂuc-tuations.Figure 1shows sample modern results for the Q 2dependence of the dominant structure function,in excellent accord with QCD predictions.The structure function values at all x depend on the quark content;the increases at larger Q 2depend on both quark and gluon content.The data permit the mapping of the proton’s quark and gluon content exempliﬁed in Fig.2.2.Quark and gluon jetsThe gluon was ﬁrmly predicted as the carrier of the color force.Though its presence had been inferred because only about half the proton momentum was found in charged constituents,direct observation of the gluon was essential.This came from experiments at the DESY e +e −collider (PETRA)in 1979.The collision forms an intermediate virtual photon state,which may subsequently decay into a pair of leptons or pair of quarks.The colored quarks cannot emerge intact from the collision region;instead they create many quark-antiquark pairs from the vacuum that arrange themselves into a set of colorless hadrons moving approximately in the directions of the original quarks.These sprays of roughly collinear particles,called jets,reﬂect the directions of the progenitor quarks.However,the quarks may radiate quanta of QCD (a gluon)prior to formation of the jets,just as electrons radiate photons.If at suﬃciently large angle to be distinguished,the gluon radiation evolves into a separate jet.Evidence was found in the event energy-ﬂow patterns for the ‘three-pronged’jet topologies expected for events containing a gluon.Experiments at higher energy e +e −colliders illustrate this gluon radiation even better,as shown in Fig.3.Studies in e +e −and hadron collisions have veriﬁed the expected QCD structure of the quark-gluon couplings,and their interference patterns.FIG.3.A three jet event from the OPAL experiment at LEP.The curving tracks from the three jets may be associated with the energy deposits in the surrounding calorimeter,shown here as histograms on the middle two circles,whose bin heights are proportional to energy.Jets1and2contain muons as indicated,suggesting that these are both quark jets(likely from b quarks).The lowest energy jet3is attributed to a radiated gluon.3.Strong coupling constantThe fundamental characteristic of QCD is asymptotic freedom,dictating that the coupling constant for color interactions decreases logarithmically as Q2increases.The couplingαS can be measured in a variety of strong interaction reactions at diﬀerent Q2scales.At low Q2,processes like DIS,tau decays to hadrons,and the annihilation rate for e+e−into multi-hadronﬁnal states give accurate determinations ofαS.The decays of theΥinto three jets primarily involve gluons,and the rate for this decay givesαS(M2Υ).At higher Q2,studies of the W and Z bosons(for example,the decay width of the Z,or the fraction of W bosons associated with jets)measureαS at the100GeV scale. These and many other determinations have now solidiﬁed the experimental evidence thatαS does indeed‘run’with Q2as expected in QCD.Predictions forαS(Q2),relative to its value at some reference scale,can be made within perturbative QCD.The current information from many sources are compared with calculated values in Fig.4.4.Strong interaction scattering of partonsAt suﬃciently large Q2whereαS is small,the QCD perturbation series converges suﬃciently rapidly to permit accurate predictions.An important process probing the highest accessible Q2 scales is the scattering of two constituent partons(quarks or gluons)within colliding protons and antiprotons.Figure5shows the impressive data for the inclusive production of jets due to scattered partons in pp collisions reveals the structure of the scattering matrix element.These amplitudes are dominated by the exchange of the spin1gluon.If this scattering were identical to Rutherford scattering,the angular variable0.10.20.30.40.511010FIG.4.The dependence of the strong coupling constant,αS ,versus Q using data from DIS structure functions from e ,µ,and νbeam experiments as well as ep collider experiments,production rates of jets,heavy quark ﬂavors,photons,and weak vector bosons in ep ,e +e −,and pt ,is sensitive not only to to perturbative processes,but reﬂectsadditional eﬀects due to multiple gluon radiation from the scattering quarks.Within the limited statistics of current data samples,the top quark production cross section is also in good agreement with QCD.FIG.6.The dijet angular distribution from the DØexperiment plotted as a function ofχ(see text)for which Rutherford scattering would give dσ/dχ=constant.The predictions of NLO QCD(at scaleµ=E T/2)are shown by the curves.Λis the compositeness scale for quark/gluon substructure,withΛ=∞for no compositness(solid curve);the data rule out values of Λ<2TeV.5.Nonperturbative QCDMany physicists believe that QCD is a theory‘solved in principle’.The basic validity of QCD at large Q2where the coupling is small has been veriﬁed in many experimental studies,but the large coupling at low Q2makes calculation exceedingly diﬃcult.This low Q2region of QCD is relevant to the wealth of experimental data on the static properties of nucleons,most hadronic interactions, hadronic weak decays,nucleon and nucleus structure,proton and neutron spin structure,and systems of hadronic matter with very high temperature and energy densities.The ability of theory to predict such phenomena has yet to match the experimental progress.Several techniques for dealing with nonperturbative QCD have been developed.The most suc-cessful address processes in which some energy or mass in the problem is large.An example is the confrontation of data on the rates of mesons containing heavy quarks(c or b)decaying into lighter hadrons,where the heavy quark can be treated nonrelativistically and its contribution to the matrix element is taken from experiment.With this phenomenological input,the ratios of calculated par-tial decay rates agree well with experiment.Calculations based on evaluation at discrete space-time points on a lattice and extrapolated to zero spacing have also had some success.With computing advances and new calculational algorithms,the lattice calculations are now advanced to the stage of calculating hadronic masses,the strong coupling constant,and decay widths to within roughly10–20%of the experimental values.The quark and gluon content of protons are consequences of QCD,much as the wave functions of electrons in atoms are consequences of electromagnetism.Such calculations require nonperturbative techniques.Measurements of the small-x proton structure functions at the HERA ep collider show a much larger increase of parton density with decreasing x than were extrapolated from larger x measurements.It was also found that a large fraction(∼10%)of such events contained aﬁnal。

Quarkyonic Matter and the Phase Diagram of QCD

Quarkyonic Matter and the PhaseDiagram of QCDLarry McLerranAugust 7,2008Physics Department and Riken Brookhaven Research Center,Building 510ABrookhaven National Laboratory,Upton,NY-11973,USAAbstractQuarkyonic matter is a new phase of QCD at ﬁnite temperature and density which is distinct from the conﬁned and de-conﬁned phases.Its existence is unambiguously argued in the large numbers of colors limit,N c →∞,of QCD.Hints of its existence for QCD,N c =3,are shown in lattice Monte-Carlo data and in heavy ion experiments.1Quarkyonic Matter and the Large N c limit of QCDThe large N c limit of QCD has provided numerous insights into the structure of strongly interacting matter,both in vacuum,[1],and at ﬁnite temperature.[2]The large N c approximation allows a correct reproduction of both qualitative and semi-quantitative features of QCD.If the number of fermions is held ﬁnite as N c →∞,then QCD in this limit is conﬁning in vacuum.The spectrum of the conﬁned world consists of non-interacting conﬁned mesons and glueballs.At ﬁnite temperature,there is a ﬁrst order phase transition between a conﬁned world of glueballs and mesons and an unconﬁned world of gluons.The energy density,pressure and entropy are parametrically of order one in the conﬁned world since the conﬁned states are colorless,but in the de-conﬁned world are of order N 2c ,corresponding to the N 2c gluon degrees of freedom.The latent heatof the phase transition is of order N2c .As one approaches the phase transition from lower temperature,the tran-sition is hinted at by the existence of a Hagedorn spectrum of particles,whose density accumulates as one approaches the phase transition temperature.This accumulation resolves the paradoxical situation that at large N c ,hadrons do not interact,which seems to contradict the existence of a de-conﬁning phase transition.If there is an accumulation of states at the Hagedorn temperature,then the the high density of states very near to the transition temperature can1a r X i v :0808.1057v 1 [h e p -p h ] 7 A u g 2008compensate for weak interaction strength,resulting in a strongly interacting gas of hadrons.The results of lattice computations for QCD(N c=3)are in qualitative accord with the results at large N c.[3]There is a rapid change at at a well deﬁned temperature,although not a strict discontinuity when aﬁnite number of quarkﬂavors are included.The presence of quarks makes the order parameter for conﬁnement not so well deﬁned,since the order parameter is e−βF q where inverse temperature isβand the change in the free energy of the system,F q, is that due to the addition of a quark.In a theory with no light quarks,one can still probe the system with a heavy quark source,which corresponds to the order parameter.In such a theory,e−βF q=0in the conﬁned phase because the quarks have inﬁnite mass.In the de-conﬁned phase,the order parameter isﬁnite.When light quarks are included,these light quarks can form bound states with the heavy quark probes,and so the free energy need never be inﬁnite. The presence of light quarks therefore does not allow for an order parameter for conﬁnement,In QCD,since there is no order parameter associated with conﬁnement,there need be no strict phase transition,and there appears not to be for realistic quark masses.There is nevertheless a quite rapid transition at a temperature of about200MeV,where the energy density changes by of order N2c,in accord with large N c arguments.The popular wisdom for QCD atﬁnite temperature and density is that there is a line of cross overs,perhaps converting to aﬁrst order phase transition at high density and low temperature,that separates the conﬁned and de-conﬁned world.Typically plots are made as a function of temperature T and baryon chemical potential,µ.Such a hypothetical diagram is shown in Figure1.At very high temperature and density,there may be phase transitions associated with color superconductivity,which aﬀect transport properties of quark-gluon matter,but are not so important for bulk properties such as pressure and energy density.[4]Unfortunately,the conventional wisdom about the phase diagram has never been explicitly veriﬁed.It is quite diﬃcult to disentangle the assumptions built into various model computations from the hard predictions of QCD.[5]Lattice Monte-Carlo computations are extremely diﬃcult at high baryon density.[3] In this talk,I will review the recent results concerning the phase diagram atﬁnite T andµin the limit of a large number of colors.[6]In this limit,it is possible to extract model independent results.The surprise result of these considerations is that in addition to the conﬁned and de-conﬁned phases of QCD, there is a third phase.It turns out that the pressure and energy density of this phase behave like a gas of quarks at very high baryon density,but nevertheless is conﬁned.Conﬁnement is important for properties of the matter near the Fermi surface,where excitations are required to be bound into color singlets Rob Pisarski and I named this phase the quarkyonic phase,since it has properties of both high density baryonic matter and de-conﬁned quark matter.To understand how such a new phase of matter might come about,we need to understand that dynamical quarks do not modify the potential between heavy test quarks at large N c.We shallﬁrst consider the case that N c→∞but that2Figure 1:The conventional wisdom about the QCD phase transition at ﬁnite temperature and density.the number of quark ﬂavors is held ﬁxed.We will later turn to the case where N F /N c is held ﬁxed.This limit with ﬁnite number of ﬂavors is easiest to consider since there is a conﬁned and a de-conﬁned phase.For ﬁnite N F /N c ,there is no distinction between a conﬁned and de-conﬁned phase,although there might perhaps be a remnant of these phases associated with a cross over.In Figure 2,the gluon loop and quark loop modiﬁcations of the potential are shown.At ﬁnite temperature,the ﬁrst diagram Debye screens the potential at large distances.This can short out the linear potential when the temperaute is high enough.The second diagram corresponds to a quark loop and is suppressed by 1/N c at large N c .When expressed in terms of the t’Hooft coupling,the temperature T and the quark chemical pottential µQ ,it is of order αT 2F (µQ /T )/N c Note that the baryon chemical potential is µB =N c µQ .Typically,the baryon chemical potential is of order the baryon mass M B ∼N c ΛQCD .The high density limit is µQ >>ΛQCD .In order for the quark loops to be important,the quark chemical potential must be of order µQ ∼√N c ΛQCD which approaches inﬁnity in the large N c limitThis argument shows that the presence of baryons at ﬁnite density does not aﬀect the values of the conﬁnement-deconﬁnement transition temperature.How can there be any non-trivial physics due to ﬁnite baryon number density?It turns out that at large N c there is another order parameter,which is the baryon number density.Remember that the baryon number density isρB ∼e (µB −M B )/T(1)3Figure 2:Diagrams which modify the potential at high energy density .Since both µB and M B are of order N c ,ρB ∼e −κN c so long as µB ≤M B .Here κis a constant of order 1.Therefore there is a ﬁnite region in the µB −T plane where the baryon number density is zero.This is the conﬁned-baryonless world.At high temperature,in the de-conﬁned world,the quarks are the correct degrees of freedom in which to measure baryon number and the baryon number is ﬁnite.As one increases the baryon number density at temperatures below the conﬁnement temperature,there is a phase which is conﬁned,but the baryon number chemical potential is large enough that the baryon number density is ﬁnite.The bottom line of these arguments is that there are two order parameters corresponding to conﬁnement and to baryon number.This in principle allows four possible phases.The phase where there is de-cofninement and zero baryon number density is apparently not realized in nature,but the other three may be.We can compute the dependence of the pressure and energy density on N c for the quarkyonic phase.To do this,assume the quark chemical potential is large compared to ΛQCD .The pressure and energy density are computable in this limit and are of order N c .It is remarkable that the bulk properties of quarkyonic matter may be computed using perturbation theory at very high density.This is despite that such matter is conﬁned.This is not unprecedented,since computations of scattering processes at short distances may be done in perturbation theory,even though the processes take place in the conﬁned vac-uum.The perturbation expansion works for bulk thermodynamic quantities because the major contribution arises from quarks deep inside the Fermi sea,where short distance interactions dominate.Pairing processes near the Fermi surface are sensitive to long distance aﬀects,and presumably pairs which form near the Fermi surface must be conﬁned.The fact that the energy density and pressure are proportional to N c may also be seen in a Skyrmyonic description of baryons for two ﬂavors.Such a description follows from the large N c limit.[7]The action for Skyrmions is S = d 4x f 2πtr V µV †µ+κtr [V µ,V ν]2 (2)In this equation,V µis a derivative of a n SU (2)group element,and both f πand κare constants of order N c .We see that the action is therefore of order N c ,so that bulk quantities such as pressure and energy density computed in this theory should also be of order N cThese arguments show that the conﬁned-baryonless phase has bulk proper-ties of order 1in N c ,the de-coniined phase of order N 2c and the quarkyonic4phase is of order N c The phase diagram for QCD in the large N c limit is shownin Fig.3.Figure3:The phase diagram for large N c QCD.The change in the bulk properties of the system whenµB crosses the conﬁnement-quarkyonic transition is of order N c.We can also estimate the width of the transition region.Recall that in the large N c limit baryons are very strongly interacting.When the number density of baryons becomes of order1/Λ3QCDor when the Fermi momentum is k F∼ΛQCD,,one will no doubt have madea transition to quarkyonc matter.This density is controlled by the Fermi mo-mentum.For baryons with large masses of order N c,we see that the baryonchemical potential is of order,µB∼M B+k2F /2M B.This means that in a widthof order1/N c inµB or of order1/N2c inµQ,the transition is achieved.In the large N c limit,this width shrinks to zero.2Finite N F/N cTheﬁnite ratio of N F/N c in the large N c limit implies that there is no distinction between the conﬁned and de-conﬁned worlds atﬁnite temperature and density. The baryon number density remains a valid order parameter.The transition is driven because of the huge degeneracy of the lowest mass baryon states.There are of order e N c G(N F/N c)such states,where G is a function determined by Young-Tableau which counts such states.The baryon density isρB∼e N c G(N F/N c)e−M B/T+µB/T(3) This has a transition whenµB=M B−T N c G(N c/N F)In this case the world is divided into that of mesons without baryons,and a world withﬁnite baryon number density.53Phenomenology and SpeculationIt is tempting to speculate on the nature of the phase transition in QCD for N c =3and realistic numbers of ﬂavors.It is diﬃcult a priori to know whether phase transitions remain or whether they become cross overs.I have little to say about this.It is clear that the diagram drawn in Fig.3becomes smoothed due to ﬁnite N c and N F eﬀects.This means that the transition line at small µB and ﬁnite T has some small decrease as µB increases.When µB ∼√N c ΛQCD ,the line of ﬁnite temperature transitions will have either disappeared or have dipped near T =0.If it dips down,it probably is a weak transition because the eﬀect of de-conﬁnement is to liberate gluons and at low T and high µ,and there the ratio of gluons to quarks is very small.Most likely,the ﬁnite temperature line of transitions ends in a second order point,if it was ever a ﬁrst order transition.Presumably,there is still a tricritical region as in the large N c limit.If the transition becomes a cross over,then perhaps a critical point slides along the line of quarkyonic-conﬁned transition.The large N c considerations must be further developed in order to say any-thing about the chiral transition.Chiral symmetry breaking should be a Fermi surface eﬀect in the quarkyonic phase.[8]Whether or not it is restored in the quarkyonic phase,or only approximately restored is not resolved.A hypothetical phase diagram for QCD is shown in Fig.4.Figure 4:A hypothetical phase diagram for QCD.Perhaps the strongest hints for the existence of a quarkyonic phase come from the ratios of integrated yields of particles produced in heavy ion experiments.[9].This is supposed to give information about the decoupling temperature and chemical potential of matter produced in heavy ion collisions.Since the energy density jumps by of order N c N F Λ4QCD across the quarkyonic transition,and since in large N c ,particle cross sections do not change their N c dependence[10],one might expect that the freeze out occurs at the quarkyonic phase transition.In Figure 5,the supposed decoupling temperature and baryon chemical po-tential are computed for various energies of experiments.Note that the line goes to zero temperature at about the nucleon mass.This is easy to interpret6in terms of the quarkyonic phase transition,but diﬃcult to understand if the line corresponded to the conﬁnement transition.Figure5:The decoupling temperature and density of matter produced in heavy ion collisions.Also shown on the plot are results of computations from the bag model and from lattice gauge theory which show the weak dependence on baryon chemical potential of the conﬁnement transition line.There is some lattice data which argues in favor of the existence of the quarkyonic phase.In the computations of Fodor et.al.,micro-canonical tech-niques were used on lattices of very small size.[11]They found the phase diagram shown in Figure6.4ConclusionsQuarkyonic matter forces us to revise our conception of the phase diagram of QCD.There are of course many unanswered questions:How does the chiral transition interplay with the quarkyonic transition?How is quarkyonic mat-ter related to Skyrmionic crystals?[7]What is the nature of the Fermi surface of quarkyonic matter?How is the liquid gas phase transition related to the quarkyonic phase transitions?These are of course many more.7Figure6:The phase diagram found by Fodor and colleagues.5AcknowledgementsI thank Arkady Vainshtein and Misha Voloshin for inviting me to Continuous Advances in QCD,where this talk was presented.Their gracious hospitality is greatly appreciated.I thank Rob Pisarski and Yoshimasa Hidaka with whom many of these idea were developed.I thank my colleagues at Rob Pisarski and Yoshimasa Hidaka for their clever insights,and with whom these ideas were de-veloped.I also thank Kenji Fukushima for his intuitive insights concerning such matter,and Kzysztof Redlich for his many insights concerning the properties of matter atﬁnite baryon number density.My research is supported under DOE Contract No.DE-AC02-98CH10886.References[1]G.’t Hooft,Nucl.Phys.B72,461(1984);B75,461(1974)[2]C.B.Thorn,Phys.Lett.B99458(1981)[3]For a review see F.Karsch,Prog.Theor.Phys.Suppl.168,237(2007).[4]M.G.Alford,K.Rajagopal and F.Wilczek,Phys.Lett.B422247(1998);R.Rapp,T.Shafer,E.Shuryak and M.Velkovsky,Phys.Rev.Lett.81,53 (1998)[5]K.Fukushima,Phys.Rev.D77,114028(2008).[6]L.McLerran and R.Pisarski,Nucl.Phys.A796,83(2007);Y.Hidaka,L.McLerran and R.Pisarski,Nucl.Phys.A808117(2008).[7]M.Kutschera,C.J.Pethick and D.G.Ravenhall,Phys.Rev.Lett.53,10411984;I.R.Klebanov,Nucl.Phys.B262,1331985;A.S.Goldhaber8and N.S.Manton,Phys.Lett.B198,2311987;N.S.Manton,Comm.Math.Phys.111,4691987;A.D.Jackson,A.Wirzba and N.S.Manton, Nucl.Phys.B495,4991989;H.Forkel,A.D.Jackson,M.Rho,C.Weiss,A.Wirzba and H.Bang,Nucl.Phys.B504,8181989;M.Kugler andS.Shtrikman,Phys.Lett.B208,4911988;Phys.Rev.D40,34211989;R.A.Battye and P.M.Sutcliﬀe,Phys.Rev.Lett.79,3631997Rev.Mod.Phys.14,292002Nucl.Phys.B705,3842005Phys.Rev.C73,0552052006 [8]L.Ya.Glozman and R.F.Wagenbrunn,Phys.Rev.D77,054927(2008),arXiv:0709.3080arXiv0805.4799;L.Ya.Glozman,arXiv:0803.1636[9]A.Adronic,P.Braun-Munzinger,K.Redlich and J.Stachel,Phys.Lett.B571,36(2003);P.Braun-Munzinger,D,Magestro,K.Redlich and J.Stachel,Phys.Lett.B518,41(2001);J.Cleymans and K.Redlich,Phys.Rev.Lett.52,84(1998);J.Cleymans and K.Redlich,Phys.Rev.C60 054908(1999);F.Beccatini,J.Cleymans,A.Keranen,E.Suhonen and K.redlich,Phys.Rev.C64,024901(2001)[10]L.Csernai,J.Kapusta and L.McLerran,Phys.Rev.Lett.97,152303(2006).[11]Z.Fodor,S.Katz and C.Schmidt,JHEP0703,121(2007).9。

潘必才,量子力学

潘必才,量子力学1.引言1.1 概述潘必才是一位杰出的科学家，他对量子力学的贡献不可忽视。

量子力学作为现代物理学的基石，在解释微观世界中的奇异现象和发展科技领域中起到了至关重要的作用。

潘必才通过深入研究和探索，为量子力学的发展做出了巨大的贡献。

量子力学是关于微观粒子行为的科学，它描述了微观世界中粒子的运动和相互作用。

与经典力学不同，量子力学在描述粒子行为时引入了概率的概念。

这一概念在解释微观粒子行为中起到了关键的作用，并对科学和技术的发展产生了深远的影响。

潘必才在量子力学的起源和基本原理方面进行了深入的研究。

他对量子理论的形成和发展历程有着深刻的理解，并提出了许多重要的概念和理论。

他的研究成果不仅对量子力学的发展有着重要的贡献，而且为其他领域的科学研究提供了启示和借鉴。

潘必才的贡献为我们理解和探索微观世界带来了新的突破和进展。

在本文中，我们将主要关注潘必才在量子力学的研究中的贡献。

我们将深入探讨他对量子力学的起源和基本原理的理解，同时还将探讨潘必才对量子力学发展的影响以及对未来研究的展望。

通过对这些内容的分析和讨论，我们希望能更全面地了解和认识潘必才的研究成果对量子力学领域的重要性和启示意义。

1.2文章结构文章结构:本文主要从潘必才和量子力学两个方面展开讨论。

首先介绍潘必才这位杰出物理学家的背景和贡献，然后详细解析量子力学的起源及其基本原理。

最后，在结论部分对整篇文章进行总结，同时展望未来对量子力学的研究方向和可能的发展。

在潘必才的章节中，我们将介绍他的个人经历和成就。

潘必才是一位中国籍的物理学家，他对量子力学的研究做出了重要贡献。

我们将回顾他的教育背景、职业生涯以及他对量子力学领域的具体研究内容。

此外，还会探讨潘必才的研究对后续量子力学研究的影响和意义。

在量子力学的起源部分，我们将回顾量子力学的历史和发展。

我们会介绍早期物理学家的实验和理论贡献，以及他们对量子力学的奠基作用。

同时，我们将探讨量子力学的核心概念，如波粒二象性、不确定性原理等。

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College Park, Maryland 20742, U.S.A.
Marilyn E. Noz 2 Department of Radiology, New York University,
New York, New York 10016, U.S.A.
Abstract
Since quarks are regarded as the most fundamental particles which constitute hadrons that we observe in the real world, there are many theories about how many of them are needed and what quantum numbers they carry. Another important question is what keeps them inside the hadron, which is known to have space-time extension. Since they are relativistic objects, how would the hadron appear to observers in diﬀerent Lorentz frames? The hadron moving with speed close to that of light appears as a collection of Feynman’s partons. In other words, the same object looks diﬀerently to observers in two diﬀerent frames, as Einstein’s energy-momentum relation takes diﬀerent forms for those observers. In order to explain this, it is necessary to construct a quantum bound-state picture valid in all Lorentz frames. It is noted that Paul A. M. Dirac studied this problem of constructing relativistic quantum mechanics beginning in 1927. It is noted further that he published major papers in this ﬁeld in 1945, 1949, 1953, and in 1963. By combining these works by Dirac, it is possible to construct a Lorentz-covariant theory which can explain hadronic phenomena in the static and high-speed limits, as well as in between. It is shown also that this Lorentz-covariant bound-state picture can explain what we observe in high-energy laboratories, including the parton distribution function and the behavior of the proton form factor.
Thus, the symmetry of combining these quantum numbers has been and still is an important branch of physics. Unlike the proton and electron in the hydrogen atom, quarks have never been observed as free particles. They are always conﬁned inside the hadron. Thus the only way of determining their properties is through observing the symmetry properties of hadrons.
There are then three steps. First, we have to assemble the physical principles needed to construct this scheme. We shall need space-time transformation laws of special relativity and uncertainty principles of quantum mechanics applicable to position and momentum variables. Since we are interested in constructing a Lorentz-covariant theory, we need the time-energy uncertainty relation. However, this time-energy relation does not allow excited states, and has to be treated diﬀerently. This is the ﬁrst hurdle we have to overcome.
arXiv:0803.2633v1 [hep the quark model be relativistic enough to include the parton model?
Y. S. Kim 1 Center for Fundamental Physics, University of Maryland,
2
This covariant oscillator formalism will satisfy all physical laws of quantum mechanics and special relativity.
The third step is to see whether the theory tells the story of the real world. For this purpose, we discuss in detail the proton form factors and Feynman’s parton picture [2, 3]. Indeed, it has been the most outstanding issue in high energy physics whether the quark model and parton model are two diﬀerent limiting cases of one Lorentz-covariant entity. We examine this issue in detail.
Then there comes the question of the binding forces between them, and the dynamics governing those forces. If the hadrons are assumed to be quantum bound states, there are localized probability distributions whose boundary conditions generate discrete mass spectra. This aspect of quantum mechanics is well known. On the other hand, it is not yet completely clear how the localized probability distribution would look to observers in diﬀerent Lorentz frames. Protons coming from high-energy accelerators are quantum bound states seen in a Lorentz frame moving very fast with respect to their rest frame. This is the question on which we would like to concentrate in this review paper.
1email: yskim@ 2email: marilyne.noz@
1
1 Introduction
The hydrogen atom played the pivotal role in the development of quantum mechanics. Its discrete energy levels led to the concept of a localization condition for the probability distribution, and thus to the bound-state picture of quantum mechanics. Likewise, the quark model is still playing the central role in high-energy physics [1]. In this model, hadrons are bound states of more fundamental particles called“quarks” with their own internal quantum numbers, such as isospins, unitary spins, and then ﬂavors.