Composite model with neutrino large mixing

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。

西安交通大学——核反应堆物理分析(共470题)从反应堆物理的角度看，良好的慢化剂材料应具有什么样的性能？答案：慢化剂是快中子与它的核发生碰撞后能减速成热中子的材料，这与它的三种中子物理性能有关：δ－平均对数能量缩减；Σs－宏观散射截面；Σa－宏观吸收截面。

综合评价应是δ和Σs都比较大而Σa又较小的材料才是较好的慢化材料，定量地用慢化能力δΣs和慢化比δ和Σs/Σa来比较。

试列出常用慢化剂的慢化能力和慢化比。

核力所具有的特点是什么？答案：基本特点是：核力是短程力，作用范围大约是1～2×10-13cm；核力是吸引力，中子与中子，质子与中子，质子与质子之间均是强吸引力。

核力与电荷无关。

核力具有饱和性，每一核子只与其邻近的数目有限的几个核子发生相互作用。

4. 定性地说明：为什么燃料温度Tf越高逃脱共振吸收几率P越小？答案：逃脱共振吸收几率P是快中子慢化成热中子过程中逃脱238U共振吸收峰的几率，在燃料温度低的时候，ζa共振峰又高又窄，如图所示，当燃料温度升高后，238U的ζa的共振峰高度下降了，然而却变宽了，因而不仅原来共振峰处能量的中子被吸收，而且该能量左右的中子也会被吸收。

温度越高共振峰变得越宽，能被该共振峰吸收的中子越多，逃脱共振吸收几率P就越小，这种效应也称为多谱勒展宽。

试定性地解释燃料芯块的自屏效应。

答案：中子在燃料中穿行一定距离时的吸收几率，可表示为：P(a)=1-e-X/λ其中λ为吸收平均自由程，X为中子穿行距离。

一般认为X＝5λ时，中子几乎都被吸收了[P(a)→1]。

对于压水堆，燃料用富集度为3.0%的UO2，中子能量为6.7ev，穿行距离在5λa=0.0315cm内被吸收的几率为99.3%，所以很难有6.7ev的中子能进入到燃料芯块中心，这种现象称为自屏效应。

6. 什么是过渡周期？什么是渐近周期？答案：在零功率时，当阶跃输入－正反应性ρ0（ρ0<β）后，反应堆功率的上升速率（或周期）是随ρ0输入后的时间t而改变的（如图所示）。

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。

第二章夸克与轻子Quarks and leptons2.1 粒子园The particle zoo学习目标Learning objectives：我们怎样发现新粒子？能否预言新粒子？什么是奇异粒子？大纲参考：3.1.1￣太空入侵者宇宙射线是由包括太阳在内的恒星发射而在宇宙空间传播的高能粒子。

如果宇宙射线粒子进入地球大气层，就会产生寿命短暂的新粒子和反粒子以及光子。

所以，就有“太空入侵者”这种戏称。

发现宇宙射线之初，大多数物理学家都认为这种射线不是来自太空，而是来自地球本身的放射性物质。

当时物理学家兼业余气球旅行者维克托·赫斯（Victor Hess）就发现，在5000m高空处宇宙射线的离子效应要比地面显著得多，从而证明这种理论无法成立。

经过进一步研究，表明大多数宇宙射线都是高速运动的质子或较小原子核。

这类粒子与大气中气体原子发生碰撞，产生粒子和反粒子簇射，数量之大在地面都能探测到。

通过云室和其他探测仪，人类发现了寿命短暂的新粒子与其反粒子。

μ介子（muon）或“重电子”（符号μ）。

这是一种带负电的粒子，静止质量是电子的200多倍。

π介子（pion）。

这可以是一种带正电的粒子（π＋）、带负电的粒子（π－）或中性不带电粒子（π0），静止质量大于μ介子但小于质子。

K介子（kaon）。

这可以是一种带正电的粒子（K＋）、带负电的粒子（K－）或中性不带电粒子（K0），静止质量大于π介子但小于质子。

科学探索How Science Works不同寻常的预言An unusual prediction在发现上述三种粒子之前，日本物理学家汤川秀树（Hideki Yukawa）就预言，核子间的强核力存在交换粒子。

他认为交换粒子的作用范围不超过10－15m，并推断其质量在电子与质子之间。

由于这种离子的质量介于电子与质子之间，所以汤川就将这种粒子称为“介子”（mesons）。

一年后，卡尔·安德森拍摄的云室照片显示一条异常轨迹可能就是这类粒子所产生。