HadronsIsospin, StrangenessQuark Model3 Flavours u, d, sMesonsPseudosc - PDF document

Quark Model Quark Model HadronsIsospin, StrangenessQuark Model3 Flavours u, d, sMesonsPseudoscalarand vector mesonsBaryonsDecuplet, octetHadronMassesSpin-spin couplingHeavy QuarksCharm, bottom, Heavy quark MesonsTop quarkMotivation for Quark ModelParticle “Zoo”proliferates“…the finder of a new particle used to be rewarded by a Nobel prize, but such a discovery ought to be punished by a $10000 fine”Lamb, 1955Outline OutlineHadrons known in 1960 Nuclear and Particle PhysicsFranz Muheim2 Isospin Isospin Nucleons Protonand neutronhave almost equal massStrong nuclear forceis charge independentVppVpnVnnIsospin p and n form part of single entity withisospin½analogous to and of spin ½IsospinI is conservedin strong interactionsAdditionby rules of angular momentumIsospinMultiplets Useful for classification of hadrons, see slide 12I+1 states in a isospinmuliplet|I, I3�Quark Model Gives natural explanationfor Isospinninumber of i quarksIsospinworks wellMassesof u and d quark are almost equal uddunnnnI 213 Nuclear and Particle PhysicsFranz Muheim3 Isospin Isospin Conservation Conservation Conservation Law IsospinI is conservedin strong interactionsAllows to calculate ratiosof cross sectionsand branching fractionsin strong interactionsDelta(1232) Resonance Cross sections In agreement withI=3/2 Isospinprediction nppppp000 1xmb 233xmb 70all9x mb 20000pppppProductionIsospinadditionMatrix elementdepends on I, not I3 21213121233221210212132212331212123232121,,,0,1:,,,1,1:,,1,1:npp 1323320013233103MMnpMMMppMMppM Mass 1232 MeVWidth 120 MeV 211211233233HMHM 2M Nuclear and Particle PhysicsFranz Muheim4 Strangeness Strangeness Strange Particles Discovered in 1947Rochester and ButlerV, “fork”,and K, “kink”Productionof V(K0, ) and Kvia strong interaction, weak decayAssociated Production Strange particles produced in pairsPaisStrangeness S Additive quantum numberGell-Mann NishijimaConservedin strongand electromagneticinteractionsViolatedin weakdecaysNon-zero for Kaonsand hyperonsNaturally explained in quark model spsKsOKpK101002301063.21089.0100 :2...,,,,:1,:1...,,,,:000SKKSKKSnpS ssnnS Nuclear and Particle PhysicsFranz Muheim5 Quark Model Quark Model 3 Quark Flavours u, d, s 1964 -introduced by Gell-Mann & ZweigCharge, Isospinand Strangeness Additive quark quantum numbersare relatedQ = I3+ ½(S + B)not all independentGell-Mann Nishijimapredates quark modelvalid also for hadronsBaryon number Bquarks B = +1/3anti-quarks B = -1/3HyperchargeY = S + Bis useful quantum numberQuark model givesnatural explanationfor Isospinand Strangeness QuarkChargeQ[e]Isospin|I, I3�Strange-ness Sup (u)+2/3|½, +½›|½, -½›|0,0›0down (d)-1/30strange (s)-1/3-1 Gell-MannZweig 3 Quark Flavours u, d, s 3 Quark Flavours u, d, s Nuclear and Particle PhysicsFranz Muheim6 Mesons Mesons Bound States Zeronet colourchargeZeronet baryonnumber B = +1/3 +(-1/3) = 0Angular Momentum L For lightest mesons Ground stateL = 0between quarksParity P Intrinsicquantum number of quarks and leptonsP=+1for fermionsP=-1for anti-fermionsTotal Angular Momentum J include quark spinsS = 0spins anti-aligned or JP= 0-Pseudo-scalar mesonsS = 1spins aligned or JP= 1-Vector mesonsQuark flavours non-zero flavourstateszero net flavourstates have identicaladditive quantum numbersPhysical statesare mixtures 0for 11111LPPqqPLLqq qq SLJ ssdduudsussdudsudu,,,,,,, q q q q Nuclear and Particle PhysicsFranz Muheim9 Baryon Octet Baryon Octet Baryon Wavefunction (space)symmetric (L = 0)(colour)antisymmetricMixed symmetric(spin, flavour) Flavourmixed symmetric: e.g. (ud-du) u/2Spinas flavour: e.g. (-) /2Spin-flavoure.g. (ud-du-ud+ du) u/6Symmetrisationby cyclic permutations(proton, s=+½) = ( 2uud-uud-uud+2duu-duu-duu+2udu-udu-udu) /18Baryon Octet JP= ½+ Lightestbaryonsstableor long-livedAntibaryonsalso form Octet and Decuplet ...,,npStrangeness SIsospin&#xMass;p,n938.9 MeVSigma1193 MeVLambda1116 MeVCascade1318 MeV(Xi) Nuclear and Particle PhysicsFranz Muheim10 Discovery of Discovery of - - -(sss) Hyperon Hyperon-baryon with at least one s quark Quark model predicted existence and mass Missing member of baryon decupletJP= 3/2+ discovered 1964 at Brookhaven K-beamonto hydrogentarget Bubble Chamberdetector peeeeKKpK0000. Nuclear and Particle PhysicsFranz Muheim11 Hadron Hadron Masses Masses Quark Masses u, d & s quark masseslightat short distanceq2� 1 GeV2mud~ 5 MeVms~ 100 MeVConstituent massis relevant for quark modelq22mu= md~ 300 MeVms~ 500 MeVMeson Masses �m(K) m()due to ms � mu, mdm(�) m()same quark content e.g. +, +: (u-dbar)Mass difference is due to quark spinsChromomagneticMass Splitting Spin-spin couplingof quarks S1= S2= 1/2analogous to hyperfine splitting in el. mag. interactionMeson Massesmu= md= 310 MeVms= 483 MeVA = (2mu)2 ·160 MeVExcellent agreementWhat about eta(‘)? 043430141431)1()1()1(2121221122212212121212121SSSSSSSSSSSSSSmmSSAmmqqmmmSSE Mass [MeV] 780 782 K* 896 894 Meson Prediction Experiment 140 138 K 484 496 780 770 1032 1019 212121mmSSAmmqqm Nuclear and Particle PhysicsFranz Muheim12 Heavy Quarks Heavy Quarks Charm and bottom quarks Charmonium(c-cbar)---see QCD lecture1977 Discovery of Upsilon StatesInterpretation isBottomonium(b-bar)SpectroscopyCharmoniumand Upsilonmc~ 1.1 …1.4 GeVmb~ 4.1 …4.5 GeVHeavy-light Mesons and Baryons Charmed (c-quark) hadronsBottom-quark hadronsTop quark Decays before forming bound statesmt~ 174 GeVdiscovered in 1995 at Fermilab cudJscDdcDucDJscDdcDucDJcPsPsP21,,,1,,,0**0*0 budJbsBbdBbuBJbsBbdBbuBJbPsPsP00*0**0021,,,1,,,0