Higgsless Electroweak Theory following from the Spherical Geometry

物理专业英语词汇(H)h maser 氢微波激射器氢脉泽h parameter h参数h region h 区h theorem h 定理haag araki theory 哈格荒木理论haag kastler theorem 哈格卡斯特勒定理hadamard transform spectrometer 阿达玛德变换光谱仪hadron 强子hadron electron storage ring 强子电子存储环hadron multiplet 强子多重态hadronic atom 强子原子hafnium 铪hagen poiseuille's law 哈根泊肃叶定律hair hygrometer 毛发湿度计halation 晕光half integral spin 半整数自旋half life 半衰期half life period 半周期half shadow apparatus 半影装置half shadow polarimeter 半影偏光计half tone 半音half value layer 半值层half value period 半衰期half wave dipole 半波偶极子half wave line 半波长线half wave rectification 半波整流half wavelength plate 半波片halftime 半周期halfwidth 半值宽度hall coefficient 霍耳系数hall constant 霍耳常数hall effect 霍耳效应hall generator 霍耳发生器hall mobility 霍耳迁移率halley's comet 哈雷彗星halo 晕halogen 卤halogen counter 卤计数管halogen leak detector 卤探漏器hamilton jacobi's equation 哈密顿雅可比方程hamilton's principle 哈密顿原理hamiltonian 哈密顿算符hamiltonian dynamics 哈密顿动力学hamiltonian formalism 哈密顿形式论hamiltonian function 哈密顿函数hamiltonian operator 哈密顿算符hard component 硬性成分hard landing 硬着陆hard magnetic material 硬磁材料hard superconductor 硬超导体hard x rays 硬x 射线hardening 硬化hardness 硬性hardware 硬件harmonic 谐音harmonic analysis 低解析harmonic analyzer 低解析器低分析器harmonic component 谐波分量harmonic function 低函数harmonic motion 谐运动harmonic oscillation 谐振荡harmonic oscillator 谐振子harmonic vibration 谐振荡harmonic wave 谐波harmonics 低函数hartley oscillator 哈脱莱振荡器hartmann diaphragm 哈特曼光栏hartmann flow 哈特曼流hartmann number 哈特曼数hartmann's dispersion formula 哈特曼色散公式hartree approximation 哈特里近似hartree fock approximation 哈特里福克近似hausdorff dimension 豪斯多夫维数hawking effect 霍金效应hawking penrose theorem 霍金彭罗塞定理hayashi phase 林相位he cd laser 氦镉激光器he counter 氦计数器he ne laser 氦氖激光器head 磁头head on collision 对头碰撞health physics 保健物理学hearing 听觉heat 热heat accumulator 回热器heat balance 热平衡heat budget 热平衡heat capacity 热容heat capacity at constant pressure 恒压热容heat conduction 热传导heat conductivity 热导率heat conductor 热导体heat content 焓heat convection 热对流heat effect 热效应heat emission 热发射heat energy 热能heat engine 热机heat equilibrium 热平衡heat exchange 热交换heat exchanger 换热器热交换器heat flux 热通量heat index 热指数heat insulation 热绝缘heat loss 热损失heat of adsorption 吸附热heat of atomization 原子化热heat of combustion 燃烧热heat of condensation 凝结热heat of crystallization 结晶热heat of dissociation 离解热heat of evaporation 蒸发热heat of fusion 融解热heat of hydration 水合热heat of ionization 电离热heat of mixing 混合热heat of phase transition 相转移热heat of reaction 反应热heat of solidification 凝固热heat of solution 溶解热heat of vaporization 汽化热heat output 热功率heat pattern 温度记录图heat pipe 热管heat quantity 热量heat radiation 热辐射heat rays 热射线heat release 放热heat reservoir 热库heat resistant 耐热性的heat source 热源heat test 加热试验heat tight 不透热的heat transfer 传热heat transmission 传热heat treatment 热处理heat wave 热浪heating 加热heating curve 加热曲线heating element 加热体heating surface 加热面heating unit 加热体heavenly body 天体heavenly twins 双子座heaviside layer 亥维赛层heaviside lorentz's system of units 亥维赛洛伦兹单位制heavy atom method 重原子法heavy current 强电流heavy electron 重电子heavy fermion 重费密子heavy hydrogen 氘heavy ion 重离子heavy ion accelerator 重离子加速器heavy ion beam 重离子束heavy ion nuclear reaction 重离子核反应heavy ion reaction 重离子反应heavy lepton 重轻子heavy metal 重金属heavy nucleus 重核heavy particle 重粒子heavy particle collision 重粒子碰撞heavy water 重水heavy water homogeneous reactor 重水型均匀堆heavy water reactor 重水堆hecto 百heisenberg force 海森伯力heisenberg model 海森伯模型heisenberg pauli method 海森伯泡利法heisenberg picture 海森伯绘景heisenberg uncertainty principle 海森伯测不准原理heisenberg's equation of motion 海森伯方程heisenberg's representation 海森伯表示heitler london theory 海特勒伦敦理论helical antenna 螺旋天线helical dislocation 螺形位错helical magnetic structure 螺旋形磁结构helical motion 螺旋运动helical spin structure 螺纹自旋结构helical spring 螺旋弹簧helical structure 螺旋形结构helicity 螺旋性helicoid 螺旋面helicon wave 螺旋形波heliocentric coordinates 日心坐标heliocentric system 日心系heliocentric theory 日心说heliograph 日照计heliographic coordinates 日面坐标heliostat 定日镜helium 氦helium cadmium laser 氦镉激光器helium fusion process 氦聚变反应helium leak detector 氦探漏器helium liquefaction 氦液化helium liquefier 氦液化器helium neon laser 氦氖激光器helium star 氦星helix accelerator 螺旋波导直线加速器helmholtz resonator 亥姆霍兹共振器helmholtz's vortex theorem 亥姆霍兹涡旋定理hemihedral form 半面晶形hemihedry 半面象hemimorphy 异极象henry 亨henry draper catalog 亨利德雷伯分光星表hercules 武仙座hermann mauguin notation 赫曼莫金记号hermitian form 厄密形式hermitian matrix 厄密矩阵hermitian operator 厄密算符herschel type reflector 赫谢耳望远镜hertz 赫hertz oscillator 赫兹振荡器hertzian vector 赫兹矢量hertzian wave 赫兹波hertzsprung russel diagram 赫罗图heterochromatic photometer 异色光度计heterochromatic photometry 多色光度学heterodyne 外差heterodyne reception 外差接收法heterodyne spectroscopy 外差光谱学heteroepitaxial growth 异质外延生长heteroepitaxy 异质外延法heterogeneity 非均匀性heterogeneous 非均匀的heterogeneous equilibrium 多相平衡heterogeneous radiation 非单色辐射heterogeneous reactor 非均匀堆heterogeneous system 非均匀系heterojunction laser 异质结激光器heterolaser 异质结激光器heteronuclear molecule 异核分子heterophase structure 非均匀相结构heteropolar bond 异极键heteropolar compound 异极化合物heteropolar crystal 异极晶体heterotope 异位素heusler alloy 赫斯勒合金hexadecapole deformation 十六极形变hexagonal close packed structure 六角密积结构hexagonal lattice 六方晶格hexagonal system 六角系hexahedron 六方体hexode 六极管hf laser 氟化氢激光器hf 激光器hidden parameter 隐参量higgs boson 希格斯玻色子higgs mechanism 希格斯机制higgs particle 希格斯粒子high altitude rocket 高空火箭high atmosphere 上层大气high definition television 高清嘶度电视high density exciton 高密度激子high density nuclear matter 高密度核物质high elasticity 高弹性high energy electron diffraction 高能电子衍射high energy nuclear physics 高能核物理学high energy radiation 高能辐射high energy region 高能区域high flux neutron beam reactor 高通量中子束堆high frequecy choke 高频扼力high frequency 高频high frequency ammeter 高频安培计high frequency amplifier 高频放大器high frequency furnace 高频炉high frequency heating 高频加热high frequency oscillator 高频振荡器high frequency resistor 高频电阻器high frequency transformer 高频变换器high frequency wattmeter 高频瓦特计high magnetic fields 强磁场high molecular compound 高分子化合物high polymer 高分子聚合物high polymer physics 高聚合体物理学high power laser 高功率激光器high pressure 高压high pressure arc discharge 高压电弧放电high pressure area 反气旋区域high pressure electronic phase transition 高压电子相变high pressure gage 高压计high pressure gas 高压气体high pressure physics 高压物理学high reflectance film 高反射膜high resolution nuclear magnetic resonance 高分辨率核磁共振high speed camera 高速照相机high speed flow 快速怜high speed scanning spectroscopy 高速扫描光谱学high tc superconductor 高tc 超导体high technology 高技术high temperature expansion 高温展开high temperature gas cooled reactor 高温气冷堆high temperature superconductor 高温超导体high tension 高压high vacuum 高真空high vacuum technique 高真空技术high velocity stars 高速星high voltage accelerator 高压加速器high voltage electron microscope 高压电子显微镜higher harmonic 高次谐波highly excited atom 高度受激原子highly excited level 高激发态highly ionized ion 高度电离离子highly sensitive 高灵敏度的hilbert space 希耳伯特空间hilbert transform 希耳伯特变换hildebrand rule 希尔得布兰德定则hill's equation 希耳方程histogram 直方图hodograph 速度图hodograph method 速度面法hodoscope 描迹器hohlraum 腔holding pump 保持泵hole 空腔hole burning 烧孔hole conduction 空穴传导hole diffusion 空穴扩散hole hole interaction 空穴空穴相互酌hole mobility 空穴迁移率hole theory 空穴理论hollow cathode discharge 空心阴极放电hollow space radiation 空腔辐射hologram 全息照相holographic diffraction grating 全息衍射光栅holographic interferometry 全息干涉度量学holographic microscope 全息显微镜holography 全息学holohedral form 全面形holohedry 全面象holomorphic function 全纯函数holon 霍伦holonomic system 完整力系holonomy group 完整群homocentric pencil 共心光束homogeneity 均匀性homogeneous broadening 均匀增宽homogeneous distribution 均匀分布homogeneous field 均匀场homogeneous function 齐次函数homogeneous medium 均匀介质homogeneous reactor 均匀堆homogeneous turbulence 同的流homogeneous universe 均匀宇宙homology 同调homometric structure 同x 光谱结构homomorphism 同晶形homonuclear molecule 同核分子homopolar bond 同极键homotopy 同伦hook on ammeter 钳式安培表hooke's law 胡克定律hopf bifurcation 霍普夫分岐hopping conductivity 跳动传导horizon 地平horizontal coordinates 地平坐标horizontal intensity 水平磁力强度horizontal parallax 地平视差horizontal resolution 水平分辨率horn antenna 喇叭天线horologium 时钟座horse power 马力horse shoe magnet 蹄形磁铁host crystal atom 基质晶体原子hot atom 热原子hot band 热带hot cathode 热阴极hot cathode ionization gage 热阴极电离真空计hot cathode magnetron gage 热阴极磁控管真空计hot cathode mercury vapour rectifier 热阴极汞汽整淋hot cathode x ray tube 热阴极x 射线管hot cave 高放射性物质工琢蔽室hot cell 高放射性物质工琢蔽室hot electron 热电子hot junction 热结hot laboratory 强放射性物质实验室hot universe 热宇宙hot wave 热浪hot wire ammeter 热线安培计hot wire galvanometer 热线检疗hot working 热加工hour 小时hour angle 时角hubbard model 哈费模型hubble constant 哈勃常数hubble space telescope 哈勃空间望远镜hubble's classification of galaxies 哈勃分类法hubble's law 速距关系hubble's time 哈勃年龄hue 色彩hum 哼鸣human counter 全身计数器human engineering 人类工程学humidity 湿度hund rule 洪德定则hunting 摆动huygens eyepiece 惠更斯目镜huygens fresnel principle 惠更斯菲涅耳原理huygens' principle 惠更斯原理hybrid bubble chamber 混合气泡室hybrid orbital 杂化轨道hybrid reactor 混合反应堆hybrider 混合反应堆hybridization of atomic orbits 原子轨道的杂化hydra 长蛇座hydrated electron 水化电子hydration 水化hydraulic radius 水力半径hydraulics 水力学hydroacoustics 水声学hydrodynamic drag 铃动力学阻力hydrodynamic instability 铃动力学不稳定性hydrodynamical model 铃动力学模型hydrodynamics 铃动力学hydroelasticity 水弹性hydrogen 氢hydrogen atom 氢原子hydrogen bomb 氢弹hydrogen bond 氢键hydrogen bubble chamber 氢气泡室hydrogen chloride laser 氯化氢激光器hydrogen electrode 氢电极hydrogen embrittlement 氢脆化hydrogen fluoride laser 氟化氢激光器hf 激光器hydrogen helium cycle 氢氦循环hydrogen laser 氢激光器hydrogen like atom 类氢原子hydrogen maser 氢微波激射器氢脉泽hydrogen scale 氢温标hydrogen spectrum 氢光谱hydrogen star 氢星hydrogenated amorphous semiconductor 氢化非晶态半导体hydrolysis 水解hydromagnetic wave 磁铃波hydromagnetics 磁铃动力学hydromechanics 铃力学hydrometer 比重计hydrophily 亲水性hydrophobic bond 疏水键hydrophoby 疏水性hydrophone 水听器hydrosphere 水圈hydrostatic balance 比重天平hydrostatic pressure 铃静压力hydrostatics 铃静力学hydrothermal synthesis method 水热合成法hydrus 水蛇座hygrograph 湿度记录仪hygrometer 湿度表hyper abrupt junction 超突变结hyper raman scattering 超喇曼散射hypercharge 超荷hyperconjugation 超共轭hyperfine interaction 超精细相互酌hyperfine structure 超精细结构hyperfragment 超裂片hyperfunction 超函数hypergeometric function 超几何函数hypermetropia 远视hypermicroscope 超倍显微镜hypermultiplet 超多重谱线hyperon 超子hyperopia 远视hyperquantization 超量子化hypersonic 特超声的hypersonic flow 特超声速流hypersonic velocity 特超声速hypersonic wave 特超声波hypocenter 震源hypochromatic shift 蓝移hypochromism 减色性hypothesis 假设hypothetical accident 假设事故hypsochromic effect 浅色效应hypsometer 沸点测定器沸点测高器hysteresis 滞后hysteresis constant 滞后常数hysteresis curve 滞后曲线hysteresis loop 滞后回线hysteresis loss 滞后损耗。

威尔逊-波尔金斯基方程（Wilson-Polchinski equation）是量子场论中描述量子场与费米子相互作用的基本方程之一。

该方程是量子场论中的一种高阶微分方程，由美国物理学家威尔逊（Kenneth Wilson）和波尔金斯基（Steven Polchinski）提出。

威尔逊-波尔金斯基方程的基本形式为：
(d/dt)ρ(x,t) = i[H,ρ(x,t)] + ∫ d^3y dt' C(x-y,t-t') [ρ(y,t'),[H,ρ(y,t')]]
其中，ρ(x,t)是场与费米子相互作用密度，H是哈密顿量，C是关联函数，表示场与费米子之间的相互作用。

威尔逊-波尔金斯基方程是量子场论中描述场与费米子相互作用的基本方程之一，在重整化群理论、量子电动力学、量子色动力学等领域有广泛的应用。

湘豫名校联考11月份高三一轮复习诊断考试语文试题阅读下面的文字，完成1～5题。

有一个深奥的问题——宇宙从何而来、如何产生？这个问题催生出宇宙大爆炸理论。

20世纪20年代，俄国科学家亚历山大·弗里德曼和比利时宇宙学家乔治·勒梅特通过求解爱因斯坦引力场方程，发现宇宙是膨胀的，但是当时这样的观念没有被科学界所接受，就连引力场方程的创造者爱因斯坦也极力反对。

这样的僵局直到1929年天才科学家埃德温·哈勃通过天文观测发现确实如此，人们才开始接受宇宙一直在膨胀的事实。

既然如此，回溯到很久以前，宇宙被限制在一个极其狭小的空间内。

换句话说，宇宙起源于一次极其猛烈的大爆炸，也就是说，宇宙是“炸”出来的。

尽管弗里德曼和勒梅特一直都孕育着这一思想，但是正式撰文提出宇宙大爆炸理论的是弗里德曼的学生乔治·伽莫夫。

1948年他和同事们提出了标准的热大爆炸模型。

但即便人们接受宇宙膨胀的事实，伽莫夫的热大爆炸模型在当时也不吃香，强有力的反对者便是大名鼎鼎的英国天文学家弗雷德·霍伊尔，“大爆炸”正是他的嘲讽之词。

伽莫夫提出的热大爆炸模型认为，宇宙开始于高温高密的原初物质，温度超过几十亿度，整个宇宙是各向同性的，物质分布是均匀的。

随着宇宙膨胀，温度和密度逐渐下降，慢慢演化形成了现在的星系等天体。

他们预言大爆炸之后38万年的时候，宇宙已经冷却到电子和原子核结合形成中性原子，这时光子失去碰撞对象电子，成为背景光子（即微波背景辐射），至今依然弥漫在宇宙当中，当前整个世界浸泡在背景光子海洋当中，且背景光子的温度在今天约为几开尔文。

可以说宇宙微波背景辐射是宇宙大爆炸理论的直接证据，能否找到它，对这一理论能否立足至关重要。

幸运的是，1964年美国贝尔实验室的无线电工程师阿诺·彭齐亚斯和罗伯特·威尔逊偶然间发现了宇宙微波背景辐射，这强有力地支持了大爆炸理论。

随后，美国航天局和欧洲宇航局对宇宙微波背景辐射进行了更加精细的探测，如1989年美国发射的微波背景探测者卫星COBE探测到的背景辐射谱是完美的黑体辐射谱，这给宇宙大爆炸理论提供了更有力的证明。

织构的测定方法1 织构定义单晶体在不同的晶体学方向上，其力学、电磁、光学、耐腐蚀、磁学甚至核物理等方面的性能会表现出显著差异，这种现象称为各向异性。

多晶体是许多单晶体的集合，如果晶粒数目大且各晶粒的排列是完全无规则的统计均匀分布，即在不同方向上取向几率相同，则这多晶集合体在不同方向上就会宏观地表现出各种性能相同的现象，这叫各向同性。

然而多晶体在其形成过程中，由于受到外界的力、热、电、磁等各种不同条件的影响，或在形成后受到不同的加工工艺的影响，多晶集合体中的各晶粒就会沿着某些方向排列，呈现出或多或少的统计不均匀分布，即出现在某些方向上聚集排列，因而在这些方向上取向几率增大的现象，这种现象叫做择优取向。

这种组织结构及规则聚集排列状态类似于天然纤维或织物的结构和纹理，故称之为织构。

织构测定在材料研究中有重要作用。

2 织构类型为了具体描述织构 (即多晶体的取向分布规律)，常把择优取向的晶体学方向 (晶向) 和晶体学平面 (晶面) 跟多晶体宏观参考系相关连起来。

这种宏观参考系一般与多晶体外观相关连，譬如丝状材料一般采用轴向；板状材料多采用轧面及轧向。

多晶体在不同受力情况下，会出现不同类型的织构。

轴向拉拔或压缩的金属或多晶体中，往往以一个或几个结晶学方向平行或近似平行于轴向，这种织构称为丝织构或纤维织构。

理想的丝织构往往沿材料流变方向对称排列。

其织构常用与其平行的晶向指数<UVW>表示。

某些锻压、压缩多晶材料中，晶体往往以某一晶面法线平行于压缩力轴向，此类择优取向称为面织构，常以{HKL}表示。

轧制板材的晶体，既受拉力又受压力，因此除以某些晶体学方向平行轧向外，还以某些晶面平行于轧面，此类织构称为板织构，常以{HKL}<UVW>表示。

3 织构的表示方法择优取向是多晶体在空间中集聚的现象，肉眼难于准确判定其取向，为了直观地表示，必须把这种微观的空间集聚取向的位置、角度、密度分布与材料的宏观外观坐标系 (拉丝及纤维的轴向，轧板的轧向、横向、板面法向) 联系起来。

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。

在对标准模型的突破中我们该如何选择?(SB1)作者苟文俭【摘要】：标准模型并非最后理论，在对粒子内部空间存在的描述中需要突破，对此我们应当向创建现代物理理论的先驱们学习，对描述粒子内部空间存在的物理理论起点另起炉灶，并使用不同于量子场的描述语言，才有可能与粒子存在的实际完全保度一致，从而使对标准模型的突破取得成功。

◎◎标准模型是粒子物理学标准模型的简称，下面都用它的英文缩写“SM”表示。

标题的符号“SB1”中的字母B取自英文短语Breakthrough dissertation（突破专题论文）的第一个字母，表示该文是突破标准模型专题论文的第一篇文章。

SM源自上世纪30年代创建的表述带电粒子参与电磁作用的QED(量子电动力学)，第－性原理是对粒子作用体系能量的拉格朗日量做规范对称变换，具有以QED为模板的统一的规范对称观念，包括了用SU(2)×U(1)群表述电、弱破缺对称的电弱统一理论、用SU(3)群表述强作用色对称的QCD(量子色动力学)、以及用幺模幺正群SU(3)×SU(2)×U(1)直积等方式表述强、弱、电作用统一的大统一理论。

粒子实验的测量事实是：任何自在的粒子均占有半径约为10-17m的空间位置。

对力程不大于10-17m的粒子动力学存在，就称是粒子内部空间的存在，力程大于了10-17m的粒子动力学存在，也称是粒子外部空间的存在。

量子力学(QM)、狭义相对论(SR)、QED的描述对象都属于粒子外部空间，而SM中的QCD、电弱统一理论的描述对象则属于粒子内部空间。

SM有很好的实验支持，但对粒子内部空间存在的描述面临了诸多难以克服的困难，也不能包揽最常见的引力作用。

当代几乎所有理论物理工作者都有这样的共识：SM并非最后理论，在对粒子内部空间存在的描述中，它需要有突破。

对SM的这种突破，我们该做如何选择呢？对此本文就关键性问题做简要论证。

(一)由于SM不能包揽最常见的引力作用，这证明它的规范对称观念并不具有普适性，也即是表征作用体系能量的拉格朗日量并不具有普适性。