GAUGE THEORIES IN PARTICLE PHYSICS ed.3rd vol1. Solutions外文书

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1、SolutionstoproblemsinGaugeTheoriesinParticlePhysics",ThirdEdition,volume1:FromRelativisticQuantumMechanicstoQED"Chapter22.1Thequantumnumbersofthe`anything'mustbeB=1;Q=0inbothcases,togetherwithS=1intherstcaseandS=+1inthesecond;considerwhatarethelightestsingle-particleortwo-particlestate

2、swiththesequantumnumbers.002.2(i)4-momentumconservationgivesp+k=p+kwhichmaybewritten20002022asp=(kk)+p;squaringbothsidesgivesp=q+2p
(kk)+Mc,andtheresultfollowsbyevaluatingthedotproductintheframesuch0thatp=(Mc;0).ForhighlyrelativisticelectronsEcjkj;E0022022200cjkj,whenceqc=(EE)c(kk)

3、2E+2Ecos=2200224Esin=2.Forelasticscatteringp=Mc,andhencefromthe20rstresultq=2M(EE).Combiningthiswiththe(approximate)20formulaforqintermsofgivestheformulaforE.0(ii)E=4:522GeV(negelectingtheelectronmass).2021=2(iii)Theinvariantmassoftheproducedhadronicstateis(p=c);usingtherstdisplay

4、edequationandthe(approximate)expressionfor22qintermsofgives1238MeV=c(approximatelyequaltothemassoftheI=3=2
resonance).0(iv)Theterm`quasi-elasticpeak'inthiscontextmeansthevalueofEcorrespondingtoacollisionbetweentheincidentelectronandasinglenucleonintheHenucleus,ignoringthebindingenergyofth

5、estrucknucleon(i.e.itistreatedlikeelasticscattering).Sincethebindingenergyisoforder10MeV,verymuchlessthantheelectronenergy,thisisexpectedtobeagoodrstapproximationtothekinematics.It0givesE=355:6MeV.Thestrucknucleonis,however,movingbyvirtueofbeingboundinsidetheHenucleus(ithasaboundstatewave

6、functionandanassociatedmomentumdistribution).Ratherthanattemptingamorerealisticcor-rectionbasedonthenucleonwavefunction,wecangetafairideaofatypicalnucleonmomentumbyusingthe`uncertaintyrelation'esti-mateph=RwhereRisthenuclearradius.HereR1:5fm,andp130MeV=c,whichgivesastrucknucleonspeedof

7、orderv=c0:14.(NotethatHeisatightlyboundnucleus,andtheformulaforthenu-1=3clearradiusR=1:1(A)isnotreallyapplicable-ofcourse,wearemakingroughestimatesanyway.)Consideringcongurationswiththeoutgoingelectronmovingparallel/antiparalleltothestrucknucleon0givesatypi