Chapter 8
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Chapter8 8.1Introduction.........................................................179 8.2TheNeutrinoHypothesisandtheˇDecay........................180 8.2.1NuclearˇDecayandtheMissingEnergy..............180 8.2.2ThePauliDesperateRemedy............................181 8.2.3HowWorldWarIIAcceleratedtheNeutrinoDiscovery............183 8.3FermiTheoryofBetaDecay.......................................184 8.3.1NeutronDecay...........................................185 8.3.2TheFermiCouplingConstantfromNeutronˇDecay.....................186 8.3.3TheCouplingConstant˛WfromFermiTheory........187 8.4UniversalityofWeakInteractions(I)..............................187 8.4.1MuonLifetime...........................................187 8.4.2TheSargentRule.........................................189 8.4.3ThePuppiTriangle......................................189 8.5TheDiscoveryoftheNeutrino....................................190 8.5.1ThePoltergeistProject...................................190 8.6DifferentTransitionTypesinˇDecay.............................194 8.6.1TheCross-Sectionoftheˇ-InverseProcess...........197 8.7LeptonFamilies.....................................................198 8.8ParityViolationinˇDecays.......................................201 8.9TheTwo-ComponentNeutrinoTheory............................204 8.10ChargedPionDecay................................................205 8.11StrangeParticleDecays............................................208 8.12UniversalityofWeakInteractions(II).TheCabibboAngle.....211 8.13WeakInteractionNeutralCurrent.........................213 8.14WeakInteractionsandQuarkEigenstates.................215 8.14.1TheWIHamiltonianandtheGIMMechanism.....................215 8.14.2HintsontheFourthQuarkfromWINeutralCurrents 217 8.14.3TheSixQuarksandtheCabibbo–Kobayashi–MaskawaMatrix........218 ¡ WIs § Longlifetimes:10-10comparedto10-19(EM)and10-23(SI) § Verysmallcrosssections:10-43cm2(1MeV),10-38(1GeV)~1012smallerthanSI § NeutrinosonlysubjecttoWIs ¡ ¡ ¡ Violatevariousquantum numbers:P,C,T,CP,s,c,b,t Noroleinbinding microscopicsystems Responsibleformatter transformations § betadecays,nuclearchain reactionsinSundependon pp → de+ν e mW = 80GeV ⇒ R ≈ 10 −18 m ¡ WIàspin-1gaugebosons–forcecarriers betweenquarksandleptons § ChargedbosonsW+,W-àchargedcurrents § NeutralbosonZ0àneutralcurrents ▪ Observedin1973inabubblechamberexperiment νµ + N → νµ + X ¡ SuccessesofUnifiedtheoryofEWinteractions § Existenceofneutralcurrents § Predictionofexistenceofcharmquark,priorto discoveryin1974 § PredictionofmassesofW+,W-andZ0,priorto discoveryin1983 ¡ EWtheorypredictsexistenceofnewspin-0boson– Higgs…confirmedatLHC… 18/04/16 F. Ould-Saada 4 ¡ Neutrinointroducedby Paulitoexplainbetadecay spectrum § 2-bodydecay:(Z,N)à(Z +1,N-1)+e- § 3-bodydecay (Z, N ) → (Z +1, N −1) + e− + ν e (Z, N ) → (Z −1, N +1) + e+ + ν e − n → p + e +νe d → u + e− + ν e 18/04/16 F. Ould-Saada • Eν inferredfromEe • withoutν, uniqueEevalueà • withν nouniqueEevalueà 5 ¡ Fermi § Transitionprobabilityfromperturbationtheory § AtlowenergiesweakandEMinteractionsclearlyseparated § FromgeneralAmplitude ¡ NeutronlifetimeàGF ¡ Neutrondecay 1 2π 2 2 dN =W = GF M τ ! dE0 n → p + e− + ν e ! ! ! ! p p + pe + pν = 0 Tp + Ee + Eν = E0 E0 = ( m p − mn ) c 2 = 1.294MeV Tp ≅ 10 −3 MeV ⇒ E0 ≅ Ee + Eν 18/04/16 F. Ould-Saada 6 dN e = dx dy dz dpx dpy dpz / h 3 Numberofstatesinphasespace ¡ V =1 VdΩ 2 pe2 dpe Ω=4 π dN e = p dpe " "" → 2 3 3 2e 2 π 2π ! dω = ( 2π !Μ) fi nν (E 0 − E e )n e (E e )dE e ! pν2 dpν dNν = 2π 2 !3 pe2 pν2 dpe dpν dN = dN e dNν = 4π 4 ! 6 pν = Eν / c = (E0 − Ee ) / c → dpν = dE0 / c § Cartesian § Spherical ¡ FinalstatedensitydN/dE0 ¡ TransitionrateW–lifetimeτ € dN 1 2 2 = p (E − E ) dpe e 0 e 4 6 3 dE0 4π ! c ∫ E0 /c 0 pe2 (E0 − Ee )2 dpe = 5 0 E 30c 3 ¡ (pb.8.16) 2 ⎛ GF ⎞ E05 1 2π 2 E05 2 =W = GF M =⎜ 3 3⎟ 3 4 6 3 ! ⎝ ! c ⎠ 60π 3! τ ! 30c × 4 π ! c ≈1 18/04/16 F. Ould-Saada Fermicoupling’sconstant GF ≡ GF ! 3c 3 ¡ Dim(GF)=[E]-2 7 § GFfromneutron(mixedFermiandGamow-Tellertransitionsà8.6)andmuondecays 1/2 ⎛ 60π 3! ⎞ n −5 −2 GF = ⎜ ≅ 2 ×10 GeV ⎟ 5 ⎝ τ E0 ⎠ n (E 0 = 1.2MeV, τ n = 885.7s ) GFn (corrected) = (1.140 ± 0.002) ×10 −5 GeV −2 GFµ = (1.16639 ± 0.00001) ×10 −5 GeV −2 µ (E 0 ≈ 100MeV ) § Dimensionlesscouplingconstant(protonmassasreference) α w = ( m pc 2 2 ) GF = 1.027 ×10 −5 § Sargentrule § Universality 5 τ µ ⎛ E0n = mn − m p − me ≈ 1MeV ⎞ −10 ⎟ ≈ ⎜⎜ ≈ 10 ⎟ τ n ⎝ E0µ ≈ mµ ≈ 100MeV ⎠ 18/04/16 F. Ould-Saada W ≅ GF2 E05 ≅ GF2 Δm 5 8 ¡ Neutrinodetection νe + n → e− + p § extremelysmallinteractionprobabilities § 1MeV:meanfreepath106km § intenseneutrinofluxandhugedetectors requiredtoobserveandmeasurethem νe + p → e+ + n ¡ Nuclearreactorandantineutrinoflux § P=150MW=1.5x108J/s § Meannuenergy:20MeV=20x ¡ 1.6x10-13J § Nurate:R=P/E=1020/s § Expectedfluxatd=10m:1013/cm2.s Expectedratevscrosssection § 200kgtargetprotons:NT=0.6x1028p § Datataking900h(+250hreactoroff) § N(interactions/s) Nυ p (s −1 ) = φυ (cm −2 s −1 )⋅ σ (cm 2 )⋅ N T ⋅ ε Eυ ≈ MeV, N = 3 / h, ε ≈ 0.1 ⇒ σ = 1.3×10 −43 cm 2 ¡ SavannahRivernuclearreactor § Anti-neutrinofluxof5×1013ν’s/s.cm2 § Detector:largeliquidscintillator ν e + p → e+ + n 108 Cd + n → 109Cd * → 109Cd + γ ¡ 18/04/16 F. Ould-Saada Neutrinoνeobservedforthefirsttimeby R.Davisetal.inasolarneutrino experimentatHomestakeinthe60´s 10 ¡ Nuclearβdecaysmoredifficulttointerpretinaquantitativewaybecause § presenceofnucleonsnotdirectlyinvolvedindecay ¡ Classificationofnucleartransitions § onbasisofthechangeinthenucleustotalangularmomentum(spin)beforeandafterdecay § S(e)ands(ν)antiparallelànochangeinnuclearspinΔJ=|Ji-Jf|=0 § S(e)ands(ν)parallelàchangeinnuclearspinΔJ=±1 ¡ Calculationoftransitionprobabilitytakesintoaccountnumberofstatesallowedby angularmomentumthrough|M|2 const 2 GF2 M = f ~ E05 f ⋅τ 2 18/04/16 F. Ould-Saada Fermi: M ~ 1 11 ¡ ¡ 0à0,ΔP=0 § ¡ Fermi 0à1,ΔP=0 § ¡ Somemeasurednucleartransitions GT ½à½ § mixed Note GF2|M|2 variations 2 GF2 M = const f ⋅τ f ~ E05 ¡ (a)Fermitransitions 10 0 + → 0 +, ΔJ = 0 § ΔJ=0,ΔP=0,ΔI=0 14 C → 10 B* + e− + ν e O → 14 N * + e+ + ν e v 2 M F = mi,s gV2 ; gV2 ~ 1 → f (θ ) = 1 + cos θ c ¡ (b)Gamow-Tellertransitions 1+ → 0 +, ΔJ = 1: 12 B → 12C + e− + ν e § ΔJ=1,ΔP=0,ΔI=0,1 2 M GT = mi,s gA2 ; 18/04/16 F. Ould-Saada gA gV 2 = 1.26 → f (θ ) = 1 − 1v cos θ 3c 13 ¡ Nuclearβdecay:1stsuccessfultheorybyFermi,1934 § AnalogywithQED § Transitionamplitude Μ fi = ∫ ψ *f (gOˆ )ψ i dV ▪ Ô:combinationofLorentzinvariantforms:S,PS,V,A,T § CorrecthelicitypropertieswithV-Acombination(forpurelyleptonic decays) € ▪ Relativestrengthfromexperimentincaseofnuclei(extendedobjects) § V.Vcombinations:Fermitransitions § A.Acombinations:Gamow-Tellertransitions 18/04/16 F. Ould-Saada 14 8.7Thetwo-Neutrino experiment Lederman,Schwartz,Steinberger,1962 ¡ Proofforexistenceofνµusinghighenergy neutrinosproducedbyanaccelerator § AlternatingGradientSynchrotron,Brookhaven § ProtoncollidewithBetargettoproducelarge pionflux § Piondecaysleadto(mainly)muon-neutrinos § Passingbeamthrough20mofirontofilter outmuons++ ¡ π − → µ − vµ π + → µ +ν µ Ifnodistinctionbetweenelectron-andmuon-neutrinotypes § Thenratesofreactions(1)occurwithequallikelihood. § Idemforreactions(2) (1) : ν µ + n → µ − + p ; ν e + n → e − + p (2) : vµ + p → µ + + n ; ve + p → e + + n 18/04/16 F. Ould-Saada 15 ¡ Lederman,Schwartz,Steinberger,1962 § Muontypeneutrinointeractionspredominate (1) : ν µ + n → µ − + p ; ν e + n → e − + p (2) : vµ + p → µ + + n ; ve + p → e + + n ¡ 25daysofacceleratortime, § 1014neutrinostraversedsparkchamber § 51interactionsresultinginafinal-statemuon ¡ Ratioelectrons/muonslatermeasuredat CERN: 18/04/16 F. Ould-Saada Ne = 0.017 ± 0.005 Nµ 16 ¡ Soonafterdiscoveryofstrangeparticles,apuzzleappeared § twospin-0particles(thenreferredtoτ+andθ+),ofsamemassandsamelifetime,observedto ¡ ¡ ¡ decayintotwopionandthreepion: P(π)=-1è θ + → π +π 0 ; τ + → π +π +π − P(θ + ) = P(π +π 0 ) = +1 P(τ + ) = P(π +π +π − ) = −1 € C,PandTsymmetriesthoughttobe conservedinallparticleinteractions. € § Puzzle! § (θ+andτ+correspondchargedK-meson decayingweakly(in10-8s)accordingto: K + → π +π 0 BR = 21.16 ± 0.14% K + → π +π +π − BR = 5.59 ± 0.05% T.D.Lee,C.N.Yang,1956, § Weakinteractionsdonotconserveparity! € § Proposedtomeasuresomepseudo-scalarquantity ▪ Helicityofsomeparticleorscalarproductofthespinofa particleandthemomentumofsomeotherparticle 60 Co→60Ni * + e − + νe ¡ ¡ ¡ ¡ ¡ ¡ Detector2countsevents–electrons withspinalignedopposite2. antineutrinostraveltodetector1 (undetected);spinisparalleltothe directionofmomentum. Mirrorimage:Detector2counts nothing! Right-handedelectronsshouldreach counter2becausealeft-handed antineutrinoisgoingtocounter1. However,theleft-handedantineutrinos haveneverbeenobserved,andcounter 2countsnothing. Thereflectioninthemirrorofthis physicalprocessgivesadifferentresult fromtherealexperiment! ¡ Parityviolation:Wuetal.1957 60 Co→60Ni * + e − + νe § Inmagneticsolenoidat0.01K § NuclearspinsalignparalleltoBfielddirection § Theemittedelectronswerecountedinthedirectionsparalleland antiparalleltothenuclearmagnetization ¡ ¡ Ifnoasymmetryweredetectedintheemissionofthedecayelectrons, therealworldandthemirrorworldwouldbeindistinguishable Experimentobserved“forward-backwarddecayasymmetry”,fewer electronsemittedinforwardhemispheretheninthebackwardwrtspins ofdecayingnuclei 18/04/16 F. Ould-Saada 19 ¡ Resultoftheearliest experimentshowingparity non-conservation.A normalisedcountingrateis shownfortwodirectionsofthe externalmagneticfield. ¡ Afteradiabatic demagnetisation,thesource warmsup,thepolarisation decreases,andthefield disappears. ! ! Parity ! ! sco ⋅ pe " "" → − sco ⋅ pe cosθ e "Parity "" → −cosθ e ! ! s ⋅p Measured: 〈cosθ e 〉 = 〈 !co ! e 〉 < 0 sco pe Expected if parity conserved: 〈cos θ e 〉 = 0 " σ! co ⋅ p!e % v I(θ ) = 1+ α $ ' = 1+ α e cosθ c # Ee & ! ! s I −I v σ = ! ; Λ = + − = α ; α = −1 s I+ + I− c ¡ ¡ SoonaftertheobservationoftheWI’sviolationofparity,itwasdiscovered thatitdoesnotpreservechargeconjugationsymmetry,C,either. Thiswasdemonstratedbyexaminingthespinsoftheelectronsand positronsemittedinthedecaysofpositivelyandnegativelychargedmuons µ − → e−ν e vµ ≠ µ + → e+ν e vµ ¡ Angulardistributionobservedforµ+and µ-decaysofform ¡ Cinvariancewouldrequirethat ratesandangulardistributions aresameforµ+andµ- ¡ Pinvariance wouldrequire 18/04/16 1 Γ µ ± (cosθ ) = Γ ± (1− a± cosθ ) 2 −1 ± Γ± ≡ τ = ∫ +1 −1 Γ µ ± (cosθ )dcosθ Γ+ = Γ− a+ = a− Γ µ ± (cosθ ) = Γ µ ± (−cosθ ) F. Ould-Saada 21 ¡ CandPconservationwouldrequire ¡ Measuredvalueswere ¡ ¡ Butwhydoµ+andµ-havethesamelifetimeifCisviolated? …becausethecombinedsymmetryCPisconserved a+ = a− = 0 −a+ = a− = 1.00 ± 0.04 § ViolationofPbeingexactlycompensatedbythatofP ¡ CPinvariancerequires ¡ …inagreementwithexperimentalobservations Γ µ + (cosθ ) = Γ µ − (−cosθ ) Γ+ = Γ− τ+ = τ− a+ = −a− ¡ Howtosurviveinastrangeworldwithoutsymmetryasguidance! 18/04/16 F. Ould-Saada 22 Helicity-states:right-handedR(a),left-handedL(b) ¡ § spincomponentalongdirectionofmotionofspin-1/2 particle NonconservationofPandChasanimportant consequenceonweakinteractions. ¡ § Masslessneutrinosgiveusagoodpicture: § “Almost”onlyleft-handedneutrinosandright- handedanti-neutrinosexistinnature. ¡ AsAbduSalamsaid:“Onreflectinganeutrinoin amirror,oneseesnothing, § theprocessbeingforbiddenbyPnon- conservation. § Butif,inadditiontoP,theneutrinoisturnedinto ananti-neutrinobyCoperation,the“image" comesback!” 18/04/16 F. Ould-Saada 23 ¡ Relativisticfermionsdescribedby2-componentspinor(and another2-componentspinorfortheantiparticle) § Slowfermions:2spinstates(upanddown) à2descriptionsforrelativisticfermions: ¡ helicityascomponentofspinindirectionofmotionoffermion § § § § ¡ Spincaneitherbealignedwithoragainstmomentum Fermionreferredtoasbeinginh=+orh=-staterespect. Measurementofsandpàhelicity However,helicityNOTinvariantunderproperLorentztransformations(2 observerscanmeasureoppositehelicities) chiralityorhandednesstoclassifythe2possiblestatesofa relativisticfermion ▪ ChiralityisinvariantunderLorentztransformations ▪ Particleisleft-handedorright-handed ¡ Bothhelicityandchiralitystateshaveimportantpropertythattheyare interchangedunderparityoperation LH ⎯Parity ⎯⎯→ RH ; h + ⎯Parity ⎯⎯→ h − ¡ ¡ WIscoupleuniquelytoLH-fermionsandRH-antifermions Formasslessfermions,helicityandchiralitycoincide § AmasslessLHparticleandamasslessh-particleareoneandthesamething ¡ Chirality:propertyof4-componentspinor § 2 chiral states are eigenstates of γ5 with eigenvalues +1 (R) and -1 (L) § chiralityingeneralnotconservedbutgoodQNformasslessparticles ψ = ψL + ψR 1 (1− γ 5 ) ψ, 2 1 ψ R = (1+ γ 5 ) ψ, 2 ψL = γ 5ψ L = −ψ L γ 5ψ R = +ψ R Lm = m(ψ Rψ L + ψ L ψ R ) ¡ 4-fermioninteractionconstrains,verytightly,thespins whichcancouplethroughWIs § OnlyLHfermionsandRHanti-fermionscantakepartinWIs ν L and ν R § Neutrinosandantineutrinosofoppositechiralitiesarebelievedto existasmν>0 § Inthiscasetheywouldnottakepartinanyoftheknowninteractions exceptgravity… ¡ ¡ MeasureofNeutrinohelicity(àchiralityformasslessν’s) Useβ-decay,deduceν helicityfromhelicityofotherdecayproducts, usingangularmomentumconservation ¡ Electroncapture þ § Initial(Eu)andfinal(Sm)statenucleiarespin-0 § Experimentselectedeventsinwhichphoton ý wasemittedindirectionofSm*,oppositeto directionofneutrino(E≥960keV) ▪ γ+SmàSm*àSm+γ ¡ § Helicityofneutrinonegative Photonhelicitymeasured § NeutrinoisLeft-handed § helicityofneutrinoinferredthroughangular momentumconservation Read more about his experiment π + → µ + vµ π + → e+ ve µ + → e+ ve vµ ¡ Piondecayatrest § Momentumandspinconservation ! ! vl − LH ⇒ pν & sν antiparallel ⇒ l + − LH ? 18/04/16 F. Ould-Saada ! ! ! pl + pν = 0 " ! ! sl + sν = 0 § Butrelativisticl+isRH! 28 ¡ OnbasisofSargentrule,πàeshouldbefavoured W ≅ GF2 E05 ≅ GF2 Δm 5 § Largerenergyavailableinfinalstate(mµ>>me) § Butπàedisfavouredbyfactor104! ¡ 2cases: § l+=µ+:muonnon-relativistic,bothhelicitiesallowed § l+=e+ : electron relativistic , helicity suppression à PR = v / c ; PLH = (1− v / c) % v ( 2 dp m % ml2 ( Γ π →l ∝ '1− * p = '1− 2 * & c ) dE 4 & mπ ) 2 l Spin-dependence: V-A interaction - V: proper vector à sign chge under P - A: axial-vector à no sign change 18/04/16 F. Ould-Saada 2 Check this! p.207 Electromagnetic current (γ): transforms as V Weak current (W): as V-A because of P-violation 29 ¡ Themeasuredratiois ¡ π+àµ+νµ Γ(π + → e+ν e ) −4 = (1.230 ± 0.004) ×10 Γ(π + → µ +ν µ ) § AnotherdecaywherebothPandCareviolated ¡ CombinedCPisconserved 18/04/16 þ ý ý þ F. Ould-Saada 30 ¡ ¡ Muonsemittedinpiondecaysarepolarised Highestenergyelectronsemittedinmuon decaysatisfy(showthis) § Theelectronisrelativistic,contrarytothemuon µ − → e − veν µ mµ c 2 ⎛ me2 ⎞ ⎜1 + 2 ⎟ >> mec 2 Ee = 2 ⎜⎝ mµ ⎟⎠ Helicityarguments+factthate-Ris helicitysuppressed àElectronsemittedoppositethe muonspin à Theangulardistributionofhigh energyelectronsleadstoaforwardbackwardasymmetry 18/04/16 F. Ould-Saada 31 ¡ Weakinteractiondoesnotproduce“boundstates”.Thisis consequenceof: § itsweaknesscomparedtoEMandstronginteractions. § verysmallrangecomparedtogravitation ¡ 3vectorbosonsmediateWIs: § W±(chargedcurrents),Z˚(neutralcurrents) ¡ 3typesofprocesses § Leptonic,semi-leptonic,hadronic ¡ Leptonic CC: µ − → e−ν µν e ; ν µe− → ν e µ− ; NC : ν µe− → ν µe− CC : n → p + e − + ν e d →u + e − + ν e ¡ semi-leptonic " p"→n + e + + ν e "u"→d + e + + ν e € ¡ Hadronic/non-leptonic Λ0 → p + π − s→u+u +d Characteristics: Long decay times and flavour violation ¡ Lepton-quarksymmetryandquarkmixing ⎛ u ⎞ ⎛c⎞ ⎜⎜ ⎟⎟, ⎜⎜ ⎟⎟ ⎝d ⎠ ⎝ s⎠ ⎛ν e ⎞ ⎛ν µ ⎞ ⎜⎜ − ⎟⎟, ⎜⎜ − ⎟⎟ ⎝e ⎠ ⎝ µ ⎠ d → u + e− + ve ; π −(du ) → µ− + vµ ; K −(su ) → µ− + vµ ¡ Symmetryàgud=gcs=gW Allowed : d + u → W − ; s + c → W − Forbidden : s + u → W − ; d + c → W − But : K − decay observed! ¡ 18/04/16 àquarkmixing! F. Ould-Saada 34 ¡ Semileptonic § ΔQ=ΔSrule § ΔQ=-ΔSsuppressed Largely suppressed ExamplesofΔS=0 andΔS=1decays ¡ Hadronic § ΔS=1,ΔI=1/2 ¡ Beforeproceedingfurther…Apuzzlewithu,d,s quarksàneutralkaons K 0 (498) ≡ ds ; K 0 ≡ sd S = +1 S = −1 Chargedkaons § interpretedthetwoparticles“θ+(θ-)”and“τ+(τ-)”asdifferentdecaychannelsofK+(K-). € ▪ Theθ-τpuzzleledtoparitynon-conservation. ¡ θ + → π +π 0 ; τ + → π +π +π − + + 0 P(θ ) = P(π π ) = +1 K + → π +π 0 BR = 21.16 ± 0.14% K + → π +π +π − BR = 5.59 ± 0.05% P(τ + ) = P(π +π +π − ) = −1 θ 0 → π 0π 0 ; π +π − ¡ Whataretheanalogueneutraldecays? ¡ The question is how to assign particles θ0 and τ0 to states K0 and K0bar? § Production (through strong interactions) and decay (through WIs) of neutral kaons: K − + p →K 0 + n € € € K + + n →K 0 + p π − + p = Λ0 + K 0 τ 0 → π 0π 0π 0 ; π +π −π 0 ¡ ¡ Whatisthelifetimeoftheneutralkaon?Properdecays length? ▪ Awelldefinedeigenstateshouldhaveone characteristicdecaytime(oneexponential). ▪ Instead,thedatashowtwodifferentlifetimes! InterpretationpossibleifweassumeK0andK0barassuperpositionoftwostateswith differentlifetimes 0 0 0 0 + − −10 K1 ≡ θ → π π ; π π K 20 ≡ τ 0 → π 0π 0π 0 ; π +π −π 0 τ1 ≅ 0.9 × 10 τ 2 ≅ 5 × 10 −8 s s K10 ≡ θ 0 → π 0π 0 ; π +π − K 20 ≡ τ 0 → π 0π 0π 0 ; π +π −π 0 The neutral kaons K0 and K0 are 2 distinct particles (as€ they have different strangeness QNs), that can both decay into two pions (or three pions) è Possibilities of oscillations! τ1 ≅ 0.9 × 10 −10 s τ 2 ≅ 5 × 10 −8 s ¡ ¡ ¡ K-Kbaroscillations B-Bbaroscillations Exercise:DrawasimilardiagramforD0 18/04/16 F. Ould-Saada 40 ¡ ParityandChargeconjugation π 0 π 0 and π +π - ⇒ P = Pπ2 (−1)L = +1#% $ 2 ⇒ Cπ 0 = +1 %& ⇒ CP(ππ ) = +1 ! ! ! ! π π π and π π π : L ≡ L12 + L3 = 0 ⇒ L12 = L3 $ & L3 3 L12 ⇒ P = Pπ (−1) (−1) = −1 % ⇒ CP(πππ ) = −1 & ⇒ Cπ3 0 = +1 ' 0 18/04/16 0 0 + - 0 F. Ould-Saada 41 K10 = 1 " $ 2# K 0 + K 0 '& K 20 = 1 " $ 2# K 0 − K 0 '& % K 0 and K 0 % PK ¡ =−K ¡ ; PK 0 =−K 0 K10 and K 20 are eigenstates of CP : CP K10 = + K10 ; CP K 20 = − K 20 K01andK02arelikerealparticlestotheweakinteractionasareK0andK0bartothestrong € 0 CP : CP K 0 = K 0 ; CP K 0 = K 0 C K0 = − K 0 ; C K 0 = − K0 0 are not eigenstates of CP π 0 π 0 = + π 0 π 0 ; CP π +π − =€ + π +π − CP π 0 π 0 π 0 = − π 0 π 0 π 0 ; CP π +π −π 0 = − π +π −π 0 K01andK02havedifferentmasses! K10 → ππ K 20 → πππ +& K S0 ≡ K10 mK − 2mπ ≈ 220MeV $& % ⇒ Γ1 > Γ 2 → τ 1 < τ 2 ⇒ , 0 &- K L ≡ K 20 mK − 3mπ ≈ 90MeV &' Morein12.2 Backto quarkmixing " ν % " νµ $ e ', $ $ e− ' $ µ − # &# ¡ ¡ ¡ Quarksaremixed andLepton-quark symmetryapplies todoublets %" u ', $ ' $# d ' = d cosθ c + s sin θ c & ⎛ u ⎞ ⎛c⎞ ⎜⎜ ⎟⎟, ⎜⎜ ⎟⎟ ⎝ d ' ⎠ ⎝ s' ⎠ %" c ', $ ' $ s' = s cosθ c − d sin θ c &# d ' = d cosθC + s sin θC s' = s cosθC − d sin θC θC = 13! Withadditionalcouplings,theory agreeswithexperiment Cabbiboangleextractedfrom measurements θC 18/04/16 F. Ould-Saada 43 % ' ' & ¡ ¡ ¡ Allowedprocesses~ Suppressedprocesses~ cos2 θ C ≈ 0.95 sin 2 θ C ≈ 0.05 Charmquarkintroducedinordertoexplainthe suppressionofFlavourChangingNeutralCurrents (FCNC),suchasK0-K0baroscillations ¡ K0leptonicdecay GIM mechanism – 1971 Charm discovery – 1974 18/04/16 F. Ould-Saada 44 ¡ Semileptoniccharmdecay § ΔC=1,ΔQ=1fromctodcorscquark ¡ Transitionfromaninitialdcorscquark intoafinalubarorcbarandstate ¡ Selectionruleforneutralcurrents § ΔS=0 § ΔS=1notobserved § With3quarlsu,d,s:ΔS=1isafeature! ¡ AddingCharmquark § ΔS=1contributionsfromsandccancel! ¡ Neutralcurrentinteractions conserveindividualquarknumbers § Strangeness-changingweakNC reactionsforbiddento1storder, § suchasKo-KobaroscillationsorK0àµ+µ- ν lν l Z 0 , l −l − Z 0 , l +l + Z 0 qqZ 0 , qqZ 0 ; q = u, d, c, s, t, b uuZ 0 , ccZ 0 , d 'd ' Z 0 , s's' Z 0 d 'd ' Z 0 = (d cosθ c + ssin θ c )(d cosθ c + ssin θ c )Z 0 = ddZ 0 cos2 θ c + ssZ 0 sin 2 θ c + (dsZ 0 + sdZ 0 )sin θ c cosθ c s's' Z 0 = ... ⇒ cancellation ⇒ ddZ 0 , ssZ 0 18/04/16 F. Ould-Saada 47 ¡ 2à3quarkgenerations § morecomplicatedQuarkmixingscheme ! d ' $ ! Vud # & = ## " s' % " Vcd ¡ Vus $! d $ ! cosθC &# & = ## & Vcs %" s % " – sin θC sin θC $! d $ &# & cosθC &%" s % ⎛ u ⎞ ⎛c⎞ ⎛ t ⎞ ⎜⎜ ⎟⎟ ,⎜⎜ ⎟⎟ ,⎜⎜ ⎟⎟ ⎝ d ⎠ ⎝ s ⎠ ⎝b⎠ ⎛ νe ⎞ ⎛ ν µ ⎞ ⎛ τ µ ⎞ ⎜⎜ − ⎟⎟ ,⎜⎜ − ⎟⎟ ,⎜⎜ − ⎟⎟ ⎝e ⎠ ⎝ µ ⎠ ⎝τ ⎠ GIMmechanismgeneralisedbyKobayashiandMaskawa(CKM,1972) § CKM3X3matrix § Unitary:VV+=1 ¡ Vij:transitionprobabilityiàj byWemission § 3mixinganglesandanimaginary phasetoaccountforCP-violation § CKMpredictionofquarksb,t… beforecwasdiscovered! ⎛ d '⎞ ⎛ Vud ⎜ s '⎟ = ⎜ V ⎜ ⎟ ⎜ cd ⎝ b ' ⎠ ⎝ Vtd Vus Vub ⎞ ⎛ d ⎞ Vcs Vcb ⎟ ⎜ s ⎟ ⎟⎜ ⎟ Vts Vtb ⎠ ⎝ b ⎠ Vij (i = u, c, t; j = d , s, b) http://nobelprize.org/nobel_prizes/physics/laureates/2008/index.html http://en.wikipedia.org/wiki/Cabibbo–Kobayashi–Maskawa_matrix ¡ CKMquark-mixingmatrix Vαi=probabili ty (αài+W transition) 18/04/16 F. Ould-Saada 49 ¡ CKMstandardparameterisation § 1.θ12aroundz § 2.θ13aroundy § 3.θ23aroundx ¡ Experimentalvalues s12 >> s23 >> s13 θ12=13.04±0.05°;θ13=0.201±0.011°;θ23=2.38±0.06°;δ13=1.20±0.08rad. s12~0.23,s13~0.003, s23~0.04 ¡ ¡ Wolfensteinparameterisation § λ=s12 § Aλ2=s23 § Aλ3(ρ−iη)=s13e−iδ Experimentalvalues λ = 0.22537 ± 0.00061 ; A = 0.814+0.023 −0.024 ; ρ = 0.117 ± 0.021 ; η = 0.353± 0.013 § CPviolationmostsignificantinB-decays:Vubplaysimportantrole § KandDdecays:VcdàCPviolationmuchsmaller § CPobservedforKnotyetforD § SMaccountsforCPviolationwith1phaseδ … However,notenoughto accountformatter-antimatterasymmetryobservedinUniverse ¡ ¡ VariousmeasurementstodetermineCKMparameters Unitarityconditions 2 2 2 1st row 2 2 2 2 nd row 2 2 2 1st column Vud + Vus + Vub = ( 0.9999 ± 0.0006 ) Vcd + Vcs + Vcb = (1.024 ± 0.032 ) Vud + Vcd + Vtd = (1.000 ± 0.004) 2 2 2 Vus + Vcs + Vts = (1.025 ± 0.032 ) 2 nd column ¡ Schemeoftopdecaychain § mt~172GeV,md~5MeV,mu~2.5MeV ( Γ (D Γ D0 → K +K – 0 → π +K – ), ) D0 = cu ( ( ( Γ (D Γ (D ) ) ) →π π ) V ∝ →π K ) V 2 ( Γ (D Γ D 0 → π +π – 0 → π +K – K + = us 0 + – 2 cd + – cs ( Γ (D Γ D 0 → K +π – 0 → π +K – ) ) s12 >> s23 >> s13 π + = ud π − = du K − = su 2 Γ D 0 → π + K – ∝ Vcs Vud 2 2 Γ D0 → K +K – Vcs Vus 2 ∝ ≈ tan θC ≈ 0.05 2 2 0 + – Γ D →π K Vcs Vud 0 ), ) 2 Vud 2 Vud 2 2 ≈ tan θC ≈ 0.05 ( Γ (D Γ D 0 → K +π – 0 + →π K – )∝ V ) V 2 cd cs 2 Vus 2 Vud 2 ≈ tan 4 θC ≈ 0.0025 Complete calculation taking into account phase space (easy) and colour field effects (difficult) à ( Γ (D Γ D0 → K +K – 18/04/16 0 → π +K – ) ≈ 0.10; Γ ( D Γ (D ) 0 → π +π – 0 → π +K – ) ≈ 0.04; Γ ( D Γ (D ) 0 → K +π – 0 → π +K – ) < 0.02 ) 54 ( ( ) ) Γ B − → D 0 K *− Ratio : Γ B − → D0 ρ − 2 2 B − = bu ; D 0 = cu ; ρ − = du ; K *− = su 2 Vus Γ(B − → D0 K *− ) Vus Vcb 2 ∝ = ∝ tan θc ≈ 0.05 2 2 2 Γ(B − → D0 ρ − ) Vud Vcb Vud 18/04/16 Experimental value ~0.05 55 #vµ e− → vµ e− %% NC : $vµ e− → vµ e− % + − + − %&e e → qq / µ µ #ve e− → ve e− % − NC + CC : $ve e → ve e− % + − νν → W W & 18/04/16 F. Ould-Saada 56 ν µ + e− →ν µ + e− ν µ + p →ν µ + p + π 0 CERN, 1973: First observation of “neutral currents" in the bubble chamber Gargamelle: an incident neutrino interacts with an electron in the liquid and disappears. p + p →W ± + X ∓ p + p →Z 0 + X 0 W ± → l ± + νl or νl ⎫⎪ MW = 80.4GeV / c 2 −25 τ ≈ 3 × 10 s ⎬ 2 0 + − Z → l l , νl νl ⎪⎭ M Z = 91.2GeV / c Questions: - Feynman graphs for proton anti-protons - how are W and Z produced in proton-proton collisions 18/04/16 F. Ould-Saada 58 ¡ Convertingaconventional”fixedtarget”proton acceleratorintoaproton-antiprotoncolliderinorderto providetheearliestpossibleopportunityfor discoveringmassivegaugebosons § C.Rubbiaetal.,1976 § S.vanderMeer,stochasticcoolingofantiprotons ¡ Betterchancethane+e-,…thattime p + p →W ± + X ∓ →l ± + ν l or ν l + X ∓ p + p →Z 0 + X 0 →l + l − + X 0 ¡ InputtoBreit-Wignerformula § § § § § MW=(80.22±0.26)GeV LeptonuniversalityinWdecays Γud/Γ=1/4(3*1/9withouttb) Γeν/Γ=1/12(1/9forrealWàeν νο, no tb) Onlyfermionswithdefinitehelicity states ▪ ¡ W,Zprocesses:rare~10-8,10-9 ¡ LHfermionsandRHantifermions Zcrosssection10xsmaller p + p → W ± + X ∓ → e± + νl or νl + X ∓ p + p → Z 0 + X 0 → e+e− + X 0 ¡ ¡ ManifestationofheavyWandZbosons § § distributionoftransversemomentumofemergingleptons Invariantmassdistributionofdi-leptons § Wdiscovery,January1983; UA1andUA2experiments109p-pbarcollisionsofwhich106 recorded ▪ § UA1:5Wàeνcandidates;UA2:4Wàeνcandidates Zdiscovery,June1983 http://cerncourier.com/cws/article/cern/29053 http://nobelprize.org/nobel_prizes/physics/laureates/1984/press.html ¡ QED § e+µ-àe+µ- § Transitionprobability § EM–vectornaturewithγµasoperators ¡ ExtensiontoWI § Makeuseofadditionalbilinearforms(relativisticinvariants) § Vectorandaxial-vectornatureofoperators ¡ ¡ Leptonicweak current Hadronicweak current § Universality:cV=-cA ¡ Electroweaktheoryoriginallyintroducedtosolve problemsrelatedtohigherorderdiagrams § Requiredbyexperiments § Leadtoinfinitecontributions(divergence) ¡ Problemssolvedwhencontributiondueto Z0andγ takenintoaccountinunifiedtheory § Cancellationofdivergences:T’Hooft,Veltman:1999Nobel prize ¡ Renormalisabilityisaconsequenceofafundamental symmetry–Gaugeinvariance § Cancellationfollowsif2fundamentalrelationshold ▪ Unificationcondition ▪ anomalycondition 18/04/16 F. Ould-Saada 64 ¡ Unificationcondition § InvolvesWeinbergangleθW § CouplingconstantgZàstrengthof neutralcurrentvertices § WeakandEMcouplingconstants related ¡ Anomalycondition § Relateselectricchargesofleptons andquarks e = gW sin θW = g Z cosθW 2 2ε 0 MW cosθW = , 0 < θW < π2 MZ ∑ Q + 3∑ Q l l q =0 q q = u, d , s, c, b, t 3= number of colours 18/04/16 F. Ould-Saada 65 ¡ StandardModelpredictions 2 2 3 2(!c) g πα (!c) W MW2 = = GF 2GF sin 2 θ W πα (!c) 3 M = 2GF sin 2 θ W cos 2 θ W 2 Z ¡ WeinbergangleθW § Fromcomparisonofneutralandcharged currentprocessesatlowenergiesà predictionofWandZmasses € sin 2 θW = 0.227 ± 0.014 M W = 78.3 ± 2.4 GeV / c 2 M Z = 89.0 ± 2.0 GeV / c 2 2 § Nowadays:fromvariousEWmeasurementsà sin θW = 0.2315 ± 0.0001 18/04/16 F. Ould-Saada 66 ¡ WeinbergangleθW § Fromcomparisonofneutralandcharged currentprocessesatlowenergiesà predictionofWandZmasses sin 2 θW = 0.227 ± 0.014 M W = 78.3 ± 2.4 GeV / c 2 M Z = 89.0 ± 2.0 GeV / c 2 § Nowadays:fromvariousEWmeasurementsà 3 2 ⎫ πα (! c ) M 2 2 W MW = ; MZ = ⎬⇒ 2 2 cos θW ⎭ 2GF sin θW § Notinagreementwithdirectmeasurementsof sin 2 θW = 0.2315 ± 0.0001 M W = 77.50 ± 0.03 GeV / c 2 M Z = 88.41 ± 0.04 GeV / c 2 gaugebosonmasses ▪ GFrelationusedvalidatlowenergies ▪ Ifhigherorders(loopswithW,Zandtop)takenintoaccount àagreementbetweentheoryandexperiment 18/04/16 F. Ould-Saada 67
