AdnanAdnan BashirBashir, IFM, UMSNH, Mexico, IFM, UMSNH, Mexico August 2013August 2013

HadronHadron Physics & Physics & Quantum Quantum ChromodynamicsChromodynamics

HermosilloHermosillo SonoraSonora

Part 1Part 1: : First Encounter With Hadrons:First Encounter With Hadrons: Introduction to Mesons & Baryons, The Quark Model, Introduction to Mesons & Baryons, The Quark Model, Goldstone Theorem & Goldstone Bosons, Sigma Model, Goldstone Theorem & Goldstone Bosons, Sigma Model,

Part 2Part 2: : From Hadrons to QCD:From Hadrons to QCD: QCD QCD LagrangianLagrangian and its Symmetries, QCD as a Gauge and its Symmetries, QCD as a Gauge Theory, Feynman Rules, Asymptotic FreedomTheory, Feynman Rules, Asymptotic Freedom

HadronHadron Physics & QCDPhysics & QCD

Part 3Part 3: : From QCD Back to Hadrons:From QCD Back to Hadrons: Symmetries, Their Breaking, Current Algebra and Low Symmetries, Their Breaking, Current Algebra and Low Energy ResultsEnergy Results

Part 4Part 4: : Modern Challenges:Modern Challenges: Transition From Low to High Energies. Lattice, Transition From Low to High Energies. Lattice, ChiralChiral Perturbation Theory, SchwingerPerturbation Theory, Schwinger--Dyson Equations, etc.Dyson Equations, etc.

1: 1: ““Introduction to Elementary ParticlesIntroduction to Elementary Particles”, D. Griffiths”, D. Griffiths ““Quarks and LeptonsQuarks and Leptons”, F. ”, F. HalzenHalzen & A. Martin& A. Martin ““Gauge Theory of Elementary ParticlesGauge Theory of Elementary Particles”, T. Cheng & L. Li”, T. Cheng & L. Li

2:2: ““Lecture Notes in PhysicsLecture Notes in Physics”, P. ”, P. PascualPascual & R. & R. TarrachTarrach, , ““Foundations of Quantum Foundations of Quantum ChromodynamicsChromodynamics”, T. ”, T. MutaMuta, , ““An Introduction to Quantum Field TheoryAn Introduction to Quantum Field Theory”, M. ”, M. PeskinPeskin & D. Schroeder.& D. Schroeder.

4:4: Theses, Reviews, Notes, SeminarsTheses, Reviews, Notes, Seminars

3: 3: ““Gauge Theory of Elementary ParticlesGauge Theory of Elementary Particles”, T. Cheng & L. Li”, T. Cheng & L. Li ““An Introduction to Quantum Field TheoryAn Introduction to Quantum Field Theory”, M. ”, M. PeskinPeskin & D. Schroeder.& D. Schroeder.

HadronHadron Physics & QCDPhysics & QCD

First Encounter With HadronsFirst Encounter With Hadrons

AdnanAdnan BashirBashir, IFM, UMSNH, Mexico, IFM, UMSNH, Mexico August 2013August 2013

ContentsContents

•• Particles and Quantum NumbersParticles and Quantum Numbers •• Particles and Quantum NumbersParticles and Quantum Numbers

•• Probing the StructureProbing the Structure •• Probing the StructureProbing the Structure

•• MesonsMesons •• MesonsMesons

•• More MesonsMore Mesons •• More MesonsMore Mesons

•• Protons and Neutrons Protons and Neutrons -- IsospinIsospin •• Protons and Neutrons Protons and Neutrons -- IsospinIsospin

•• StrangenessStrangeness •• StrangenessStrangeness

•• ResonancesResonances •• ResonancesResonances

•• IsospinIsospin RevisitedRevisited •• IsospinIsospin RevisitedRevisited

•• What Next?What Next? •• What Next?What Next?

Probing the StructureProbing the Structure

•• Scattering,Scattering, Spectroscopy,Spectroscopy, SplittingSplitting--upup experimentsexperiments •• Scattering,Scattering, Spectroscopy,Spectroscopy, SplittingSplitting--upup experimentsexperiments

•• Scattering:Scattering: Compton scattering, Rutherford experiment,Compton scattering, Rutherford experiment, crosscross--sections and interaction potentials. sections and interaction potentials. •• Scattering:Scattering: Compton scattering, Rutherford experiment,Compton scattering, Rutherford experiment, crosscross--sections and interaction potentials. sections and interaction potentials.

•• Splitting up Experiments:Splitting up Experiments: Bombarding Beryllium withBombarding Beryllium with alpha particles: discovery of alpha particles: discovery of neutronsneutrons. Modern. Modern accelerators involving hadrons. accelerators involving hadrons.

•• Splitting up Experiments:Splitting up Experiments: Bombarding Beryllium withBombarding Beryllium with alpha particles: discovery of alpha particles: discovery of neutronsneutrons. Modern. Modern accelerators involving hadrons. accelerators involving hadrons.

•• Spectroscopy:Spectroscopy: Atomic spectroscopy: Lyman, Atomic spectroscopy: Lyman, BalmerBalmer andand PaschenPaschen series. Bohr model. Fine structure (spinseries. Bohr model. Fine structure (spin--orbitorbit interaction). Hyperfine structure (electron spin interaction). Hyperfine structure (electron spin –– nuclearnuclear spin interaction, Lamb shift)spin interaction, Lamb shift)

•• Spectroscopy:Spectroscopy: Atomic spectroscopy: Lyman, Atomic spectroscopy: Lyman, BalmerBalmer andand PaschenPaschen series. Bohr model. Fine structure (spinseries. Bohr model. Fine structure (spin--orbitorbit interaction). Hyperfine structure (electron spin interaction). Hyperfine structure (electron spin –– nuclearnuclear spin interaction, Lamb shift)spin interaction, Lamb shift)

NuclearNuclear degreesdegrees ofof freedomfreedom areare frozenfrozen inin atomicatomic physicsphysics.. (Atomic(Atomic excitationsexcitations:: ~~eVeV,, NuclearNuclear excitationsexcitations:: ~~MeVMeV)) NuclearNuclear degreesdegrees ofof freedomfreedom areare frozenfrozen inin atomicatomic physicsphysics.. (Atomic(Atomic excitationsexcitations:: ~~eVeV,, NuclearNuclear excitationsexcitations:: ~~MeVMeV))

Probing the StructureProbing the Structure

Probing the StructureProbing the Structure

From Atom to From Atom to NucleusNucleus: : From Atom to From Atom to NucleusNucleus: :

Probing the StructureProbing the Structure

From Atom to Nucleus: From Atom to Nucleus: From Atom to Nucleus: From Atom to Nucleus:

•• UntilUntil aboutabout 19301930,, atomatom waswas merelymerely electronselectrons andand protonsprotons.. •• UntilUntil aboutabout 19301930,, atomatom waswas merelymerely electronselectrons andand protonsprotons..

Protons and NeutronsProtons and Neutrons

•• HeHe isis 44 timestimes asas heavyheavy asas HH withwith onlyonly 22 electronselectrons.. LiLi hashas 33 electronselectrons butbut 77 timestimes asas heavyheavy asas HH.. WhyWhy soso heavy?heavy? •• HeHe isis 44 timestimes asas heavyheavy asas HH withwith onlyonly 22 electronselectrons.. LiLi hashas 33 electronselectrons butbut 77 timestimes asas heavyheavy asas HH.. WhyWhy soso heavy?heavy?

•• ThereThere couldcould notnot bebe allall protonsprotons inin thethe nucleusnucleus withwith somesome electronselectrons necessarynecessary toto cancelcancel thethe additionaladditional chargecharge.. ConfiningConfining electronselectrons inin aa nucleusnucleus ofof 55 FermiFermi requiresrequires ~~ 250250 MeVMeV.. ElectromagneticElectromagnetic interactioninteraction ofof electronselectrons withwith nucleusnucleus providesprovides muchmuch lessless energyenergy..

•• ThereThere couldcould notnot bebe allall protonsprotons inin thethe nucleusnucleus withwith somesome electronselectrons necessarynecessary toto cancelcancel thethe additionaladditional chargecharge.. ConfiningConfining electronselectrons inin aa nucleusnucleus ofof 55 FermiFermi requiresrequires ~~ 250250 MeVMeV.. ElectromagneticElectromagnetic interactioninteraction ofof electronselectrons withwith nucleusnucleus providesprovides muchmuch lessless energyenergy..

•• BotheBothe && BeckerBecker bombardedbombarded berylliumberyllium withwith energeticenergetic alphaalpha particlesparticles inin 19301930.. ItIt producedproduced neutralneutral radiationradiation whichwhich waswas penetratingpenetrating butbut nonnon--ionizingionizing.. LedLed toto discoverydiscovery ofof neutronsneutrons..

•• BotheBothe && BeckerBecker bombardedbombarded berylliumberyllium withwith energeticenergetic alphaalpha particlesparticles inin 19301930.. ItIt producedproduced neutralneutral radiationradiation whichwhich waswas penetratingpenetrating butbut nonnon--ionizingionizing.. LedLed toto discoverydiscovery ofof neutronsneutrons..

Protons and NeutronsProtons and Neutrons

•• Heisenberg’sHeisenberg’s proposalproposal isis toto identifyidentify:: •• Heisenberg’sHeisenberg’s proposalproposal isis toto identifyidentify::

andand callcall thisthis isospinisospin.. SpinSpin cancan alsoalso bebe 11 etcetc.. WhatWhat aboutabout isospinisospin?? WeWe shallshall comecome toto itit laterlater.. andand callcall thisthis isospinisospin.. SpinSpin cancan alsoalso bebe 11 etcetc.. WhatWhat aboutabout isospinisospin?? WeWe shallshall comecome toto itit laterlater..

•• StrongStrong interactionsinteractions appearedappeared independentindependent ofof thethe electricelectric chargecharge ofof pp andand nn.. HeisenbergHeisenberg proposedproposed inin 19321932 thatthat bothboth pp andand nn areare manifestationsmanifestations ofof thethe samesame statestate:: NucleonNucleon..

•• StrongStrong interactionsinteractions appearedappeared independentindependent ofof thethe electricelectric chargecharge ofof pp andand nn.. HeisenbergHeisenberg proposedproposed inin 19321932 thatthat bothboth pp andand nn areare manifestationsmanifestations ofof thethe samesame statestate:: NucleonNucleon..

•• TheThe symmetrysymmetry relatingrelating themthem isis calledcalled isospinisospin,, likelike spinspin.. StrongStrong interactionsinteractions areare invariantinvariant underunder aa transformationtransformation whichwhich interchangesinterchanges aa protonproton andand aa neutronneutron..

•• TheThe symmetrysymmetry relatingrelating themthem isis calledcalled isospinisospin,, likelike spinspin.. StrongStrong interactionsinteractions areare invariantinvariant underunder aa transformationtransformation whichwhich interchangesinterchanges aa protonproton andand aa neutronneutron..

•• ProtonsProtons andand neutronsneutrons areare boundbound insideinside aa nucleonnucleon throughthrough strongstrong interactionsinteractions andand havehave almostalmost identicalidentical massmass.. •• ProtonsProtons andand neutronsneutrons areare boundbound insideinside aa nucleonnucleon throughthrough strongstrong interactionsinteractions andand havehave almostalmost identicalidentical massmass..

Protons and NeutronsProtons and Neutrons

•• TheThe groupgroup structurestructure ofof thethe isospinisospin generatorsgenerators TTii satisfiessatisfies thethe SU(SU(22)) LieLie algebraalgebra.. •• TheThe groupgroup structurestructure ofof thethe isospinisospin generatorsgenerators TTii satisfiessatisfies thethe SU(SU(22)) LieLie algebraalgebra..

•• TheThe pp andand nn formform aa doubletdoublet:: •• TheThe pp andand nn formform aa doubletdoublet::

•• AsAs isospinisospin isis aa symmetrysymmetry ofof thethe strongstrong interactioninteraction withwith HamiltonianHamiltonian HHss:: •• AsAs isospinisospin isis aa symmetrysymmetry ofof thethe strongstrong interactioninteraction withwith HamiltonianHamiltonian HHss::

Protons and NeutronsProtons and Neutrons

•• SinceSince thethe membersmembers ofof thethe isospinisospin doubletdoublet havehave differentdifferent electricelectric charge,charge, itit isis notnot aa symmetrysymmetry ofof electromagneticelectromagnetic interactionsinteractions.. ThusThus itit isis notnot anan exactexact symmetrysymmetry..

•• SinceSince thethe membersmembers ofof thethe isospinisospin doubletdoublet havehave differentdifferent electricelectric charge,charge, itit isis notnot aa symmetrysymmetry ofof electromagneticelectromagnetic interactionsinteractions.. ThusThus itit isis notnot anan exactexact symmetrysymmetry..

•• HowHow goodgood isis itit aa symmetrysymmetry ofof thethe totaltotal HamiltonianHamiltonian H?H? IfIf itit werewere exact,exact, thethe membersmembers willwill bebe massmass degeneratedegenerate.. ThusThus differencedifference inin massmass cancan provideprovide anan estimateestimate::

•• HowHow goodgood isis itit aa symmetrysymmetry ofof thethe totaltotal HamiltonianHamiltonian H?H? IfIf itit werewere exact,exact, thethe membersmembers willwill bebe massmass degeneratedegenerate.. ThusThus differencedifference inin massmass cancan provideprovide anan estimateestimate::

•• ThusThus itit isis aa fairlyfairly goodgood symmetrysymmetry andand wewe cancan writewrite:: •• ThusThus itit isis aa fairlyfairly goodgood symmetrysymmetry andand wewe cancan writewrite::

•• ElectromagneticElectromagnetic interactionsinteractions belongbelong toto HH11.. •• ElectromagneticElectromagnetic interactionsinteractions belongbelong toto HH11..

MesonsMesons

•• WhatWhat holdsholds thethe positivelypositively chargedcharged protonsprotons insideinside anan atomatom togethertogether inin aa closeclose proximityproximity withinwithin aa nucleus?nucleus? •• WhatWhat holdsholds thethe positivelypositively chargedcharged protonsprotons insideinside anan atomatom togethertogether inin aa closeclose proximityproximity withinwithin aa nucleus?nucleus?

•• ThereThere mustmust bebe aa forceforce strongerstronger thanthan thethe electromagneticelectromagnetic repulsionrepulsion betweenbetween protonsprotons andand aa shortshort rangerange oneone.. •• ThereThere mustmust bebe aa forceforce strongerstronger thanthan thethe electromagneticelectromagnetic repulsionrepulsion betweenbetween protonsprotons andand aa shortshort rangerange oneone..

•• YukawaYukawa inin 19341934 proposedproposed aa massivemassive bosonboson beingbeing exchangedexchanged betweenbetween nucleons,nucleons, explainingexplaining thethe shortshort rangerange ofof strongstrong forcesforces.. YukawaYukawa estimatedestimated itsits massmass:: 300300--400400 mmee..

•• YukawaYukawa inin 19341934 proposedproposed aa massivemassive bosonboson beingbeing exchangedexchanged betweenbetween nucleons,nucleons, explainingexplaining thethe shortshort rangerange ofof strongstrong forcesforces.. YukawaYukawa estimatedestimated itsits massmass:: 300300--400400 mmee..

•• ItIt waswas calledcalled aa mesonmeson,, “the“the middlemiddle weight”weight”.. BaryonsBaryons (e(e..gg..,, protonsprotons andand neutrons)neutrons) areare “the“the heavyheavy weights”weights” andand leptonsleptons (e(e..gg..,, electrons)electrons) areare thethe “light“light weights”weights”..

•• ItIt waswas calledcalled aa mesonmeson,, “the“the middlemiddle weight”weight”.. BaryonsBaryons (e(e..gg..,, protonsprotons andand neutrons)neutrons) areare “the“the heavyheavy weights”weights” andand leptonsleptons (e(e..gg..,, electrons)electrons) areare thethe “light“light weights”weights”..

MesonsMesons •• PowellPowell usedused photographicphotographic emulsionsemulsions onon mountainmountain topstops toto observeobserve pionspions decayingdecaying intointo muonsmuons observedobserved atat seasea levellevel.. •• PowellPowell usedused photographicphotographic emulsionsemulsions onon mountainmountain topstops toto observeobserve pionspions decayingdecaying intointo muonsmuons observedobserved atat seasea levellevel..

•• PionPion waswas laterlater foundfound toto comecome inin threethree versionsversions:: ππ++,, ππ--,, ππ00 •• PionPion waswas laterlater foundfound toto comecome inin threethree versionsversions:: ππ++,, ππ--,, ππ00

•• TheThe pionspions camecame outout toto havehave isospinisospin 11:: •• TheThe pionspions camecame outout toto havehave isospinisospin 11::

•• Similarly,Similarly, thethe compoundcompound statesstates ofof nn andand pp cancan inin principleprinciple bebe isoiso--triplettriplet andand isoiso--singletsinglet.. ButBut nono nnnn oror pppp statesstates areare foundfound inin naturenature.. JustJust anan isoiso--singletsinglet deuterondeuteron isis foundfound..

•• Similarly,Similarly, thethe compoundcompound statesstates ofof nn andand pp cancan inin principleprinciple bebe isoiso--triplettriplet andand isoiso--singletsinglet.. ButBut nono nnnn oror pppp statesstates areare foundfound inin naturenature.. JustJust anan isoiso--singletsinglet deuterondeuteron isis foundfound..

•• TheThe quantumquantum numbernumber ofof isospinisospin isis foundfound toto bebe conservedconserved inin strongstrong interactionsinteractions.. •• TheThe quantumquantum numbernumber ofof isospinisospin isis foundfound toto bebe conservedconserved inin strongstrong interactionsinteractions..

MesonsMesons

More MesonsMore Mesons

•• InIn 19471947,, RochesterRochester andand ButlerButler observedobserved thethe existenceexistence ofof aa newnew KK00 particleparticle decayingdecaying intointo aa ππ++ andand aa ππ-- inin anan upsideupside downdown VV--patternpattern..

•• InIn 19471947,, RochesterRochester andand ButlerButler observedobserved thethe existenceexistence ofof aa newnew KK00 particleparticle decayingdecaying intointo aa ππ++ andand aa ππ-- inin anan upsideupside downdown VV--patternpattern..

•• TheThe massmass ofof thethe KK00 hadhad toto bebe atat leastleast doubledouble thatthat ofof pionspions.. •• TheThe massmass ofof thethe KK00 hadhad toto bebe atat leastleast doubledouble thatthat ofof pionspions..

•• TheyThey werewere likelike heavyheavy pionspions butbut livedlived muchmuch longerlonger thanthan pionspions.. ππ00 lifelife timetime ==88..44 1010--1717 secsec KK00

SS--KK00LL lifelife time=time=

((88..99 xx 1010--1111 –– 55..1212 xx 1010--88)) ss

•• TheyThey werewere likelike heavyheavy pionspions butbut livedlived muchmuch longerlonger thanthan pionspions.. ππ00 lifelife timetime ==88..44 1010--1717 secsec KK00

SS--KK00LL lifelife time=time=

((88..99 xx 1010--1111 –– 55..1212 xx 1010--88)) ss

•• WeakWeak interactions?interactions? •• WeakWeak interactions?interactions?

More MesonsMore Mesons

•• InIn 19491949,, PowelPowel discovereddiscovered chargedcharged KaonKaon inin thethe decaydecay.. •• InIn 19491949,, PowelPowel discovereddiscovered chargedcharged KaonKaon inin thethe decaydecay..

•• ItIt tooktook tilltill 19561956 toto figurefigure outout KK++ belongedbelonged toto samesame categorycategory asas KK00..

•• ItIt tooktook tilltill 19561956 toto figurefigure outout KK++ belongedbelonged toto samesame categorycategory asas KK00..

•• WithWith time,time, moremore mesonsmesons werewere discovereddiscovered:: ηη,, φφ,, ωω andand ρρ mesonsmesons..

•• WithWith time,time, moremore mesonsmesons werewere discovereddiscovered:: ηη,, φφ,, ωω andand ρρ mesonsmesons..

•• ItsIts massmass hadhad toto bebe moremore thanthan threethree timestimes pionpion massmass.. •• ItsIts massmass hadhad toto bebe moremore thanthan threethree timestimes pionpion massmass..

Particles & Quantum NumbersParticles & Quantum Numbers

•• InIn 19501950 anotheranother strangestrange particleparticle waswas discovereddiscovered inin decaydecay:: •• InIn 19501950 anotheranother strangestrange particleparticle waswas discovereddiscovered inin decaydecay::

•• ΛΛ waswas heavierheavier thanthan pp.. ItIt waswas categorizedcategorized asas aa baryonbaryon.. •• ΛΛ waswas heavierheavier thanthan pp.. ItIt waswas categorizedcategorized asas aa baryonbaryon..

•• OtherOther BaryonsBaryons decaydecay butbut whywhy isis protonproton soso stable?stable? WeWe don’tdon’t observeobserve::

•• OtherOther BaryonsBaryons decaydecay butbut whywhy isis protonproton soso stable?stable? WeWe don’tdon’t observeobserve::

•• BeforeBefore leptonlepton nono.. violationviolation waswas noticed,noticed, StuckelbergStuckelberg proposedproposed BaryonBaryon quantumquantum numbernumber toto explainexplain thisthis..

•• BeforeBefore leptonlepton nono.. violationviolation waswas noticed,noticed, StuckelbergStuckelberg proposedproposed BaryonBaryon quantumquantum numbernumber toto explainexplain thisthis..

Particles and Quantum NumbersParticles and Quantum Numbers

•• TheThe followingfollowing assignmentsassignments werewere mademade forfor thethe baryonbaryon nono:: •• TheThe followingfollowing assignmentsassignments werewere mademade forfor thethe baryonbaryon nono::

•• BetaBeta--decaydecay waswas allowedallowed byby baryonbaryon nono.. conservationconservation:: •• BetaBeta--decaydecay waswas allowedallowed byby baryonbaryon nono.. conservationconservation::

•• AlsoAlso thethe reactionreaction whichwhich ledled toto thethe discoverydiscovery ofof antianti-- protonproton waswas allowedallowed:: •• AlsoAlso thethe reactionreaction whichwhich ledled toto thethe discoverydiscovery ofof antianti-- protonproton waswas allowedallowed::

•• ProtonProton beingbeing thethe lightestlightest baryonbaryon couldcould notnot decaydecay intointo anythinganything lighterlighter.. •• ProtonProton beingbeing thethe lightestlightest baryonbaryon couldcould notnot decaydecay intointo anythinganything lighterlighter..

•• NoNo conservedconserved numbernumber existsexists forfor mesonsmesons:: •• NoNo conservedconserved numbernumber existsexists forfor mesonsmesons::

StrangenessStrangeness

•• ItIt soonsoon becamebecame clearclear thatthat strangestrange particlesparticles ((kaonskaons andand Lambdas)Lambdas) areare producedproduced copiouslycopiously (time(time scalescale ofof 1010--2323 sec)sec) butbut decaydecay slowlyslowly (time(time scalescale ofof 1010--1010 sec)sec)..

•• ItIt soonsoon becamebecame clearclear thatthat strangestrange particlesparticles ((kaonskaons andand Lambdas)Lambdas) areare producedproduced copiouslycopiously (time(time scalescale ofof 1010--2323 sec)sec) butbut decaydecay slowlyslowly (time(time scalescale ofof 1010--1010 sec)sec)..

•• ForFor strongstrong interactionsinteractions:: •• ForFor strongstrong interactionsinteractions::

•• TheThe electromagneticelectromagnetic decaysdecays areare expectedexpected toto bebe inin timestimes nono moremore thanthan aroundaround 1010--1616 secsec:: •• TheThe electromagneticelectromagnetic decaysdecays areare expectedexpected toto bebe inin timestimes nono moremore thanthan aroundaround 1010--1616 secsec::

•• DecayDecay timestimes ofof 1010--1010 secsec correspondcorrespond toto weakweak forceforce:: •• DecayDecay timestimes ofof 1010--1010 secsec correspondcorrespond toto weakweak forceforce::

•• ItIt waswas obviousobvious thatthat strangestrange particlesparticles werewere producedproduced inin strongstrong interactionsinteractions andand decayeddecayed throughthrough weakweak interactionsinteractions.. •• ItIt waswas obviousobvious thatthat strangestrange particlesparticles werewere producedproduced inin strongstrong interactionsinteractions andand decayeddecayed throughthrough weakweak interactionsinteractions..

StrangenessStrangeness

•• StrangeStrange particlesparticles werewere producedproduced inin pairspairs.. •• StrangeStrange particlesparticles werewere producedproduced inin pairspairs..

•• InIn 19531953 GellGell--MannMann andand NishijimaNishijima coinedcoined anotheranother quantumquantum numbernumber strangenessstrangeness andand assignedassigned::

•• InIn 19531953 GellGell--MannMann andand NishijimaNishijima coinedcoined anotheranother quantumquantum numbernumber strangenessstrangeness andand assignedassigned::

•• StrangenessStrangeness waswas seenseen toto conserveconserve inin strongstrong interactionsinteractions andand hencehence strangersstrangers werewere nevernever producedproduced inin onesones:: •• StrangenessStrangeness waswas seenseen toto conserveconserve inin strongstrong interactionsinteractions andand hencehence strangersstrangers werewere nevernever producedproduced inin onesones::

•• StrangeStrange particlesparticles decaydecay throughthrough weakweak interactionsinteractions andand dodo notnot conserveconserve strangenessstrangeness..

•• StrangeStrange particlesparticles decaydecay throughthrough weakweak interactionsinteractions andand dodo notnot conserveconserve strangenessstrangeness..

StrangenessStrangeness

•• GellGell--MannMann andand NishijimaNishijima observedobserved aa relationrelation betweenbetween quantumquantum numbersnumbers:: •• GellGell--MannMann andand NishijimaNishijima observedobserved aa relationrelation betweenbetween quantumquantum numbersnumbers::

•• ForFor BaryonsBaryons ofof B=B=11,, itit waswas seenseen:: •• ForFor BaryonsBaryons ofof B=B=11,, itit waswas seenseen::

StrangenessStrangeness

ResonancesResonances

•• ManyMany particlesparticles havehave longlong lifelife timestimes toto bebe observedobserved directlydirectly inin thethe bubblebubble chamberschambers.. ((ττ >> 1010--1212 secsec)).. •• ManyMany particlesparticles havehave longlong lifelife timestimes toto bebe observedobserved directlydirectly inin thethe bubblebubble chamberschambers.. ((ττ >> 1010--1212 secsec))..

•• ManyMany otherother particlesparticles havehave muchmuch shortershorter lifetimeslifetimes.. TheirTheir directdirect detectiondetection isis impossibleimpossible.. TheirTheir existenceexistence mustmust bebe inferredinferred indirectlyindirectly..

•• ManyMany otherother particlesparticles havehave muchmuch shortershorter lifetimeslifetimes.. TheirTheir directdirect detectiondetection isis impossibleimpossible.. TheirTheir existenceexistence mustmust bebe inferredinferred indirectlyindirectly..

•• TheseThese transienttransient particlesparticles appearappear asas intermediatesintermediates statesstates.. TheyThey areare typicallytypically formedformed whenwhen collidingcolliding twotwo particlesparticles andand decaydecay veryvery quicklyquickly..

•• TheseThese transienttransient particlesparticles appearappear asas intermediatesintermediates statesstates.. TheyThey areare typicallytypically formedformed whenwhen collidingcolliding twotwo particlesparticles andand decaydecay veryvery quicklyquickly..

•• TheyThey respectrespect conservationconservation lawslaws.. If,If, ee..gg..,, thethe isospinisospin ofof collidingcolliding particlesparticles isis 33//22,, thethe resonanceresonance mustmust havehave isospinisospin 33//22 (( ΔΔ resonance)resonance)..

•• TheyThey respectrespect conservationconservation lawslaws.. If,If, ee..gg..,, thethe isospinisospin ofof collidingcolliding particlesparticles isis 33//22,, thethe resonanceresonance mustmust havehave isospinisospin 33//22 (( ΔΔ resonance)resonance)..

ResonancesResonances

•• IndicationIndication ofof theirtheir emergenceemergence isis thethe stronglystrongly peakingpeaking crosscross sectionsection (probability(probability ofof thethe processprocess aa bb -->> cc dd toto happen)happen) whenwhen plottingplotting σσ vsvs thethe centrecentre ofof massmass energyenergy ofof thethe collisioncollision..

•• IndicationIndication ofof theirtheir emergenceemergence isis thethe stronglystrongly peakingpeaking crosscross sectionsection (probability(probability ofof thethe processprocess aa bb -->> cc dd toto happen)happen) whenwhen plottingplotting σσ vsvs thethe centrecentre ofof massmass energyenergy ofof thethe collisioncollision..

•• TheThe meanmean lieslies atat EEcmcm((abab)) withwith aa widthwidth givengiven byby ΔE=ΔE=11/τ/τ,, wherewhere ττ isis thethe lifelife timetime ofof thethe resonanceresonance.. •• TheThe meanmean lieslies atat EEcmcm((abab)) withwith aa widthwidth givengiven byby ΔE=ΔE=11/τ/τ,, wherewhere ττ isis thethe lifelife timetime ofof thethe resonanceresonance..

•• CrossCross--sectionssections forfor thethe resonancesresonances areare ofof thethe typetype:: •• CrossCross--sectionssections forfor thethe resonancesresonances areare ofof thethe typetype::

wherewhere isis thethe centrecentre ofof massmass energyenergy squaredsquared ofof thethe incomingincoming particlesparticles aa andand b,b, MM isis thethe massmass andand ГГ==11//ττ isis thethe widthwidth ofof thethe resonanceresonance..

wherewhere isis thethe centrecentre ofof massmass energyenergy squaredsquared ofof thethe incomingincoming particlesparticles aa andand b,b, MM isis thethe massmass andand ГГ==11//ττ isis thethe widthwidth ofof thethe resonanceresonance..

ResonancesResonances

IsospinIsospin RevisitedRevisited

•• AsAs thethe strongstrong interactioninteraction isis invariantinvariant inin thethe isospinisospin space,space, thethe HamiltonianHamiltonian commutescommutes withwith allall componentscomponents ofof isospinisospin.. •• AsAs thethe strongstrong interactioninteraction isis invariantinvariant inin thethe isospinisospin space,space, thethe HamiltonianHamiltonian commutescommutes withwith allall componentscomponents ofof isospinisospin..

•• ThisThis symmetrysymmetry allowsallows usus toto findfind ratiosratios amongamong scatteringsscatterings:: •• ThisThis symmetrysymmetry allowsallows usus toto findfind ratiosratios amongamong scatteringsscatterings::

•• UsingUsing ClebschClebsch--GordonGordon coefficients,coefficients, wewe findfind:: •• UsingUsing ClebschClebsch--GordonGordon coefficients,coefficients, wewe findfind::

IsospinIsospin RevisitedRevisited

•• LetLet TT bebe thethe operatoroperator whosewhose matrixmatrix elementselements <<f|T|if|T|i>> givegive usus thethe scatteringscattering amplitudeamplitude forfor ii -->> ff.. ThenThen:: •• LetLet TT bebe thethe operatoroperator whosewhose matrixmatrix elementselements <<f|T|if|T|i>> givegive usus thethe scatteringscattering amplitudeamplitude forfor ii -->> ff.. ThenThen::

•• TT cannotcannot connectconnect statesstates ofof differentdifferent II && II33.. AnyAny membermember ofof aa givengiven multipletmultiplet II hashas thethe samesame matrixmatrix elementelement TTII:: •• TT cannotcannot connectconnect statesstates ofof differentdifferent II && II33.. AnyAny membermember ofof aa givengiven multipletmultiplet II hashas thethe samesame matrixmatrix elementelement TTII::

•• ThusThus:: •• ThusThus::

IsospinIsospin RevisitedRevisited

•• IfIf TT11//22 <<<< TT33//22,,:: •• IfIf TT11//22 <<<< TT33//22,,::

•• ThisThis conditioncondition isis satisfiedsatisfied nearnear thethe I=I=33//22 resonanceresonance threshold,threshold, ii..ee..,, M=M=12321232 MeVMeV.. ThisThis correspondscorresponds toto thethe wellwell--knownknown ΔΔ resonanceresonance..

•• ThisThis conditioncondition isis satisfiedsatisfied nearnear thethe I=I=33//22 resonanceresonance threshold,threshold, ii..ee..,, M=M=12321232 MeVMeV.. ThisThis correspondscorresponds toto thethe wellwell--knownknown ΔΔ resonanceresonance..

•• Experimentally,Experimentally, thethe totaltotal thresholdthreshold isis easiereasier toto measuremeasure:: •• Experimentally,Experimentally, thethe totaltotal thresholdthreshold isis easiereasier toto measuremeasure::

IsospinIsospin RevisitedRevisited

IsospinIsospin invarianceinvariance:: IsospinIsospin invarianceinvariance::

What next?What next?

•• InIn 19601960ss itit waswas clearclear thatthat hundredshundreds ofof elementaryelementary resonancesresonances existedexisted.. TheyThey allall hadhad definitedefinite quantumquantum numbersnumbers suchsuch asas spin,spin, isospinisospin,, strangeness,strangeness, baryonbaryon number,number, etcetc..

•• InIn 19601960ss itit waswas clearclear thatthat hundredshundreds ofof elementaryelementary resonancesresonances existedexisted.. TheyThey allall hadhad definitedefinite quantumquantum numbersnumbers suchsuch asas spin,spin, isospinisospin,, strangeness,strangeness, baryonbaryon number,number, etcetc..

•• Typically,Typically, widthswidths increasedincreased withwith massmass oror lifetimeslifetimes decreaseddecreased withwith thethe massmass ofof thethe resonanceresonance.. •• Typically,Typically, widthswidths increasedincreased withwith massmass oror lifetimeslifetimes decreaseddecreased withwith thethe massmass ofof thethe resonanceresonance..

•• ThereThere waswas aa diredire needneed forfor thethe classificationclassification ofof newnew particlesparticles andand resonancesresonances.. •• ThereThere waswas aa diredire needneed forfor thethe classificationclassification ofof newnew particlesparticles andand resonancesresonances..

•• WereWere allall thesethese particlesparticles andand resonancesresonances elementaryelementary oror theythey werewere composedcomposed ofof anotheranother layerlayer ofof elementaryelementary particles?particles?

•• WereWere allall thesethese particlesparticles andand resonancesresonances elementaryelementary oror theythey werewere composedcomposed ofof anotheranother layerlayer ofof elementaryelementary particles?particles?

WhenWhen thethe NobelNobel prizesprizes werewere firstfirst awardedawarded inin 19011901,, physicistphysicist knewknew somethingsomething ofof justjust twotwo objectsobjects whichwhich areare nownow calledcalled “elementary“elementary particles”,particles”, thethe electronelectron andand thethe protonproton.. AA delugedeluge ofof otherother “elementary”“elementary” particlesparticles appearedappeared afterafter 19301930;; neutron,neutron, neutrino,neutrino, μμ meson,meson, ππ meson,meson, heavierheavier mesonsmesons andand variousvarious hyperonshyperons.. II havehave heardheard itit saidsaid thatthat “the“the finderfinder ofof aa newnew elementaryelementary particleparticle usedused toto bebe rewardedrewarded byby aa NobelNobel prize,prize, butbut suchsuch aa discoverydiscovery nownow oughtought toto bebe punishedpunished byby aa $$1010,,000000 fine”fine”..

WhenWhen thethe NobelNobel prizesprizes werewere firstfirst awardedawarded inin 19011901,, physicistphysicist knewknew somethingsomething ofof justjust twotwo objectsobjects whichwhich areare nownow calledcalled “elementary“elementary particles”,particles”, thethe electronelectron andand thethe protonproton.. AA delugedeluge ofof otherother “elementary”“elementary” particlesparticles appearedappeared afterafter 19301930;; neutron,neutron, neutrino,neutrino, μμ meson,meson, ππ meson,meson, heavierheavier mesonsmesons andand variousvarious hyperonshyperons.. II havehave heardheard itit saidsaid thatthat “the“the finderfinder ofof aa newnew elementaryelementary particleparticle usedused toto bebe rewardedrewarded byby aa NobelNobel prize,prize, butbut suchsuch aa discoverydiscovery nownow oughtought toto bebe punishedpunished byby aa $$1010,,000000 fine”fine”..

•• WillisWillis LambLamb onon receivingreceiving isis NobelNobel prizeprize:: •• WillisWillis LambLamb onon receivingreceiving isis NobelNobel prizeprize::

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What next?What next?

What next?What next?