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1、Particle and Symmetry,Lecturer：Wei-Zhou Jiang,References,1L.Ryder,Elementary particles and symmetries(粒子物理与对称性，宋孝同等译）2W.M.Gibson,B.R.Pollard,Symmetry principles in elementary particle physics,（基本粒子物理学中的对称性原理，丁里译）3李政道，场论与粒子物理,19794黄克孙，夸克、轻子与规范场,19825许咨宗，课件：粒子物理中的守恒定律（中科大）;核与粒子物理导论,中国科技大学出版社6戴又善，粒子物理讲
2、义（浙大）6 R.Casalbuoni,Quantum Field Theory,(1997)7来自Wikipedia的资料9郑恒阳，粒子物理中的对称性和对称性破缺（山大，PPT报告）10陆埮,罗辽复,物质探微 从电子到夸克,(2005,科普读物)11Ian Aitchison,Supersymmetry in Particle Physics:An Elementary Introduction(2007,Cambridge),Outline,1.Introduction to fundamental particles2.Classic and quantum symmetry princ
3、iples3.Lorentz invariance(covariance)4.Parity（）,space inflection,angular momentum5.Charge conjugate symmetry(C),CP symmetry and its breaking6.Time inversion symmetry（）、theorem7.Isospin,gauge,chiral symmetries and their spontaneous breakings Below are possible lectures:夸克模型、标准模型、强子共振态，介子衰变、G宇称(?)超对称A
4、ds/CFT（？）iggs 粒子与重正化（？）手征对称性与标量场（？）超对称,粒子物理的基本内容,与量子力学和量子场论相关 微观粒子（原子、分子）性质；薛定谔方程；定态及散射基本粒子遵循之对称性基本粒子及其运动规律基本粒子及其相互作用 物质世界的基本构成(结构与相互作用）、宇宙学等，beyond quantum mechanics,1.基本粒子简介1.1 发展简史,物质的基本单元和基本结构的思辨探索殷（前1600年）周（前1027）时期的古代五行说，金木水火土战国 墨子：“端”是无同也，莫能破古印度：风火水土，四大皆空古希腊：恩培多克勒（约公元前490430）柏拉图（公元前427347）水、气
5、、火、土四元素。宋朝:朱熹,理气说,理在气先古希腊：德谟克利特（前四世纪），原子近代：1807年道尔顿，提出原子论 1869年 门捷列夫，元素周期律,现代粒子物理与核物理的发展,1895年，放射性：X射线（W.C.Rontgen伦琴）1896、1898年 天然放射性（A.H.Becquerel贝克勒尔；M.Curie 居里夫妇)1897年，电子（J.J.Tohmson汤姆生）1911年，Rutherford：散射实验-原子核式结构；R.A.Millikan 油滴实验1926年，P.A.Dirac:相对论量子力学，真空，反粒子1930年，正电子发现：赵忠尧；1932年，Anderson（1936
6、年，Nobel Prize)1932年，中子的发现：Chadwick 1930年，中微子：泡利 Pauli，费米Fermi（理论），王淦昌（实验建议），莱茵斯（1955年,Nobel Prize）1935年，介子：汤川秀树 H.Yukawa1950年代，强子共振态,200多种（宇宙线、加速器）1954年，杨-Mills规范场，W,Z介子,胶子:弱、强作用1957年,李政道，杨振宁：Nobel Prize,弱作用宇称不守恒,1964年，M.Gell-Mann 强子结构的夸克模型1967年，S.Wemberg,A.Salam,S.L.Glashow,弱电统一理论，W，Z波色子1983年，西欧核子中
7、心（CERN）发现W，Z波色子1970年代，量子色动力学（QCD）亚夸克，前子（Preon），毛子(Maon,1977 Glashow基于Onion-layer straton model的提议)？公孙龙：一尺之棰，日取其半，万世不竭物质从哪里来？真空与物质，心经，色不异空，空不异色，色即是空，空即是色。,1.2 粒子分类,轻子 e,;；及其反粒子强子 a)重子：b)介子：规范波色子Higgs粒子?,共振态,右图：Kerson Huang,Quarks，Leptons&Gauge Fields,p5(1992,World Scientific Publishing),Denoted as Hu
8、ang1992 later on.,高能物理实验 宇宙线：其中包括约87%质子，12%粒子（氦核子），其余大部分是原子核、电子、射线以及超高能中微子也构成一小部分宇宙射线。右图来自Wikipedia。中国：云南落雪山 3180米云室，在川3222米 大型磁云室；西藏甘巴拉山5500米，高山乳胶室，羊八井4300米，国际宇宙线观测站（中日、中意）；高空热气球，卫星（AMS，东南大学）,地球实验室,加速器1932年，高压加速器，质子0.7MeV1939年，回旋加速器，质子20MeV1946年，稳相加速器（变电场），190MeV1953年，质子同步加速器（变磁场），23GeV现有著名加速器，高真空，
9、强流，超导强磁右图：张闯，漫谈对撞机，现代物理知识2007年第二期,1.3 相互作用,From Huang1992,四种相互作用,一些例子,以交换虚粒子实现相互作用A)力程,B)衰变寿命,Interactions and scattering cross sections Rutherford scattering,S matrix in general cases：,All reactions including have the electromagnetic interactionReactions including come from the weak interactionWith
10、 e,included are reactions of the weak or electric interactions All mesons decay eventually into pairs of the electron an d positron,neutrino,an diphotons；All baryons,except protons,will decay.,From Huang1992,Questions：1。How to produce more particles?2。How to classify these particles?3。How are partic
11、les arranged into the structure of bulk matter that is determined by the interactions?4。More fundamental interactions?new physics?,0到双光子的衰变？,+g q+qbar?,1.4 Natural unit,Small energy scale for microscopic particles short time scale in the process of interactions.Its more convenient to use the natural
12、 unit:,1.5 Particles,celestrial bodies and cosmos,Big bang,inflation,dark matter,dark energy,表格来自 陆埮教授,What are dark matter and energy?,Dark Matter23%,Dark Energy73%,“Normal Matter”4%,Are they related to large-mass celestial body?,From Big Bang to Black Holes,10-10-100 s,Protonneutron,After 1 Billio
13、n years,Neutrson Star,Proton,Neutron,Black hole,(R10km),The energy resources in nature are from the combustion of PROTONS!,习题,掌握粒子物理发展的主要事件。加速器在粒子物理发展中的作用是什么？简述四种相互作用。说明相互作用与散射截面、寿命的关系。基本粒子是如何分类的？举例说明自然单位制的时空和物质度量单位及与国际单位制的关系。,Symmety,Conservation law,Rotational symmetry,Angular momentumBaryon numbe
14、rLepton numberIsospin,Spatial translation,Momentum conservation,Temporal translation,Energy conservation,Global symmetry Conservation law,Chapter 2:Classical and quantum symmetry princples,Symmetry:Invariance of the physical laws under the transformation of interior and exterior degrees of freedom(i
15、ndistinguishability),2.1 Symmetry and conservation laws，Noether theorem,U（1），Charge,Electromagnetic interaction,SU（2），Weak Charge,weak interaction*,SU（3），color(charge),Strong interaction,Local symmetry Interaction,*SU(2)对称性首先是杨-Mills规范场中引入以研究强相互作用的同位旋对称性的，见C.N.Yang and R.L.Mills,Phys.Rev.96,191(1954
16、).,Above is the continuous symmetryConcrete symmetry：Space reflection（P）Time inversion（T）Charge conjugate（C）particle and antiparticle Explicit breaking of symmetry,Breakings of parity conservation and charge conjugate symmetry in weak interaction,(弱作用的宇称不守恒、电荷共轭对称破坏等)；Related to the spontaneous symm
17、etry breaking？(与自发破缺的关系？)Spontaneous breaking of symmetry（caused by vacuum asymmetry）breakings of gauge and chiral symmetries.Two modes:Goldstone TheoremJ.Goldstone,Nuovo Cimento,19,154(1961)；Higgs mechanism。,2.2 Examples of conservation lawsBaryon number and lepton number,In any process,the baryon
18、and lepton numbers should be conserved.Because Fermions are real particles，the stability of matter requiresthat the creation and annihilation be in pairs.,2.3 Symmetry in classical mechanics,1。Invariance of spatial translation,namely,an absolute position is unmeasurable Momentum conservation 1）Examp
19、le:two-particle system Interaction potential:displacement:a,？,2）General case:Lagrange equation in Analytical Mechanics,2。Energy conservation，namely,absolute time is unmeasurable,?,2.3 Symmetry in quantum mechanics,在量子力学中已有讨论，如见曾谨言量子力学上册Generally speaking,Conserved quanta are the expectation value of
20、 operators,different from the classical mechanics From Schroedinger equation,it has,1。Translational transformation Infinitesimal transformation,Finite transformation,2。Temporal translation 3。Invariance of rotation,4.Invariance of gauge transformationHere,we are limited to the global symmetry that is
21、 independent of space and time.,习题,1。在经典情形证明时间平移不变性导致能量守恒；在量子情形下，无穷下变换和有限变换下分别证明时间平移不变性导致能量守恒。2。如1题证明转动不变性导致角动量守恒。,3.Lorentz invariance(covariance),Lorentz GroupEquation of relativistic quantum mechanicsRequirements for Lagrangian,3.1 Lorentz Group,Concept of the group：The operations or the set that
22、 have closeness.,Lorentz transformation,The event interval is a Lorentz scalar：,Lorentz group,Lorentz group also includes the space-time reflection for the invariance of s2.If not included,it is dubbed Lorentz boost洛仑兹换速。If the translation is added to the Lorentz rotation,then it forms the Poincare
23、group.,3.2 Simple relativistic mechanics,Lorentz Scalar,3.3 Requirements for Lagrangian,All equations of motion are derived from the principle of least action,i.e.,Euler-Lagrange equaiton。Lagrangian must be the Lorentz scalar，so that not changed with the transformation of the inertial frame:,Free fi
24、elds and interactions,Is the mass the Lorentz scalar？,3.4 More content of covariance,CPT（discuss later on）Generalised covariance:covariant derivative,习题,1.,2.,3.,About learning method:to have goals,苍龙：粒子物理，Sky dragon地龙：量子力学,Earth dragon,Self-confidence to dig out new physics beyond quantum mechanics
25、,元音老人碧岩录讲座昔五祖演会下有一僧请益五祖：如何是末后句？祖云：你师兄会末后句，问他去。僧问师兄，适逢游山回，僧为打水洗脚次，进问云：如何是末后句？师兄以脚挑水洒其面斥云：什么末后句？！僧哭诉祖，祖云：我向你道，他会末后句！僧于言下大,悟。,陈献章、王守仁,4.Parity（）、Space reflection symmetry,angular momentum,4.1 Space reflection,（夫思妻）枯眼望遥山隔水，往来曾见几心知。壶空怕酌一杯酒，笔下难成和韵诗。途路阻人离别久，讯音无雁寄回迟。孤灯夜守长寥寂，夫忆妻兮父忆儿。,（妻想夫）儿忆父兮妻忆夫，寂寥长守夜灯孤。迟回寄
26、雁无音讯，久别离人阻路途。诗韵和成难下笔，酒杯一酌怕空壶。知心几见曾来往，水隔山遥望眼枯。,夫妻相思宋李禺,（夫思妻）枯眼望遥山隔水，往来曾见几心知。壶空怕酌一杯酒，笔下难成和韵诗。途路阻人离别久，讯音无雁寄回迟。孤灯夜守长寥寂，夫忆妻兮父忆儿。,DNA shows the breaking of mirror image.,Chirality,长瓣兜兰paphiopedilum：The helixes at both sides have the left-right symmetry:the right is left-handed helix and the left right-han
27、ded.,DNA,自然界的许多分子，手性分子占去了很大的比例。构成蛋白质的氨基酸都是 L 型氨基酸，多糖和核酸的单糖是 R 型糖。人们甚至发现，1969年坠落在澳大利亚默奇森的陨石(aerolite)中的氨基酸(amino acid)也主要是L 型的。,Chirality of biological molecules,4.2 Angular momentum and Parity,xyz xyz-,+,Spatial wave function:,习题：,An example：Electric dipole transition,Probability,4.3 Identification
28、of the intrinsic parity of(static)particles,Single particle with given momentum is not the eigenstate of parity(?why),1。Identification of intrinsic parity of meson,-Deuteron reaction，the final state produces two neutrons.This reaction can be accompanied by the radiation of KX-ray from the deuteron-p
29、ion atom，,-,L=0,KX-ray,i=L=0,Odevity of angular momentum from the relative motion of two neutrons,All possible states of two identical neutrons,0，1，2,Only one state meetsthe conservation of angular momentum and the antisymmetry of for fermionic system：,Initial state：,Possible final states of（n,n）,，0
30、 belong to the same isospin mulplet and they should have the same parity:,meson:pseudoscalar meson,2。Identification of photon intrinsic parity,P,Ry(),x,y,z,z,y,x,y,z,x,Spin&parity quantum numbers of particles,4.3 Parity violation in the weak interaction,We should know that the parity conservation re
31、mains in the strong and electromagnetic interactions.（1）-puzzle,Angular momentum conservation of identification of parity,JP 0-0-0-0-0-0-0-L L+L-L,Jf=L+L-=0,L+=L-=L,Jf=L=0,(f)=P3()(-1)2L=-1,(f)=P2()(-1)L=+1,A.M.,Parity,Dalitz diagram analysis,Lee-Yangs work,If the weak interaction conserves parity,m
32、ust be two kinds of particles having different parity.But they share the same spin,mass,yield and lifetime.So,should be like the same particle,while the parity is violated then.This is the puzzle.After reviewing the experimental data of particles and nuclides before 1956,Lee and Yang found that the
33、parity is conserved in the strong and electromagnetic interaction,while in the process of the weak interaction,like the decay of the particles,-decay of nuclides，no data can elaborate that the parity is conserved.is thus the final-state particles of some particle which is produced through the strong
34、 interaction,and decey into different final states via the weak interaction that violates the parity.,-就是粒子K+,Experimental verification,Theoretic probe,Measurement of longitudinal polarization of particle,The spin orientation of final-state electron and anti-neutrino should be along the orientation
35、of polarization:,Longitudinal polarization of e is defined as：,For positron+1，of right-hand priority；for electron 1，of left-hand priority.,（2）Neutrino helicity in the weak interaction,1958年M.Goldhaber等人利用 核素的 K电子俘获特殊的衰变方式,巧妙地从实验证明了中微子的螺旋度。衰变级联过程为,&Sm*have opposite momentumand angular momentum(AM)for
36、 AM conservation，h of thusconforms with that of Sm*，while the latter is determined by thehelicity of.实验上测得左旋光子。,（3）production&decay:parity conservation or not?,强产生的粒子是横向极化的。横向极化态的空间反射具有不变性,产生平面法线 z：,（4）,For parity conservation,peudoscalar must be zero,习题,5.Charge conjugation（）、CP symmetry and its br
37、eaking5.1Charge conjugate symmetry,the operator C：transformation between the particle and antiparticle，changes all intrinsic quanta,e.g.,Charge Q，baryon no.B，lepton no.L，strange no.S，hypercharge G，the 3rd component of isospin I3.C does not change the spin;自旋虽然是内禀自由度,但与时空性质相关.内部自由度对称性给出additive quant
38、um numbers.,Charge parity of photons:,charge parity of 0,Generalized Pauli principle,5.3 Verification of C conjugate symmetry,1.C-parity conservation in electromagnetic interaction:,C(-1)L+S(-1)n,Oddevity of photon number is decided by the(L+S)of positionium,In the electromagnetic process,the C-pari
39、ty conservation is verified up toa quite high precision.,Compare two mutually conjugate process:,Meson and anti-meson in the f.s.feature a perfect symmetry.Especially for the exclusive process+（-），C-parity symmetry givessymmetric angular distributionof cross section:and 0 produced by P-Pbar annhilat
40、ion is symmetric about=90。,Strong decay of vector meson:,J PC 1 0-0-0-+L 1 1C 1-1+1P-1-1+1,2.C-parity conservation in strong interaction process,3.C-parity breaking in the weak interaction process，conservation of the joint CP transformtion,P：l.h.r.h.C：particle-antiparticle,作业：分析下列反应的荷称是否守恒,J PC 1 0-
41、0-0-+L 1 1,5.4 CP symmetry breaking and neutral Kaon decay,1.Background,However,the difference comes up for the neutral K decay.,-,纯K0,S（Y）+1 0 1,Strangeness is not a conserved number of the weak interaction,while K0&K0bar are eigenstates of the strong interaction,instead of the weak interaction,（见M
42、.Gell-Mann and A.Pais的工作（Phys.Rev.97,1387,1955.）,The weak interaction eigenstates should come from the mixing of them:,The oscillation observation：in pure K0 beam there is the reaction arising from K0bar,-+p,-,纯K0,p,纯K0,K2,S=-1,3.CP breaking,In 1964，Christenson,Cronin,Fitch,Turlay found in the neutr
43、al Kaon decays the symmetry breaking of the joint CP operation(Phys.Rev.Lett.,13,138(1964).),The same meson decays into states with opposite CPCP breaking！,Solution：,（1）Mixing leads to CP breaking,Phenomenologic theory may use 3 parameters related to the amplitude and width to describe to describe t
44、he CP breakingof the decay of the long-lived KL,如果KL中K0K0Bar等幅混合，0,K1&K2 have the definite CP oddevity:,Odd and even CP mixing states:KS,KL,The unequal mixing of that leads to the CP breaking is the so-called superweak theory for CP breaking,p=q，equal mixing，CP symmetric,Gw,Gw,Gsw,K0,K0,（2）Direct CP
45、 breaking,直接比较K0反K0到达同位旋为I的介子末态的衰变振幅的差异,the final state phase shift。For the CP invariance，must be real.The observable of CP breaking,mixing parameters and decay amplitude meet following relations,The data indicate：,1,Extraction from experiments：,In the neutral K decay,direct CP breaking is unimporta
46、nt.,If has a tiny imaginary part,of 2008 Nobel PrizeCP&3rd generation of quarks,3.Microscopic model for CP breakingCKM model,CabibboKobayashiMaskawa,In 1963，Cabibbo introduced the Cabibbo angle to keep the universality of the quark model in the weak interaction，After Charm quark found,the strength o
47、f the flavor changing decay can be expressed by the 2X2 matrix,1973年KM发现2X2的四夸克模型不能解释CP破缺，把Cabibbo矩阵一般化为3X3的如下形式：,三代夸克。带撇的是弱作用的本征态，右边不带撇的是质量本征态，弱作用里它们不一样,From Wikipedia,But in KM theory,CP breaking is not enough to interpret the matter-antimatter asymmetry.Must look for new physics beyond the standa
48、rd model,Why in the Universe,still no anti-matter found？CP symmetry breaking，e.g.,Who is the future Hopeful of the Nobel Prize?,6.Time reversal symmetry（）、theorem,Time reversal:The macroscopic time direction can be defined by the irreversible process,like the antropy evolution,Time reversal is,in fa
49、ct,the reversal of the motion.Time reversal invariance is just the invariance of the motion.,6.1 Time reversal in Classical mechanics,注意：FT的自变量为-t.,角动量L与动量p一致.,Time reversal Motion reversal,见 W.M.吉布森，B.R.波拉德，(丁里译）基本粒子物理学中的对称性原理，p197.,6.2 Time reversal in quantum mechanics,Expectation value after tim
50、e reversal：,Tanti-unitary operator：,可令T=UK，K为取复共轭且t-t，,T transformation for operator A:,6.3 Detailed balance principle,This indicates that for the motion reversal,probability is invariant:Time reversal invariance.,2.The principle of detailed balance For the space-time reflection symmetry,the transit
