EM Decay of Hadrons u g g ubar If a photon is involved in a decay (either final state or virtual) then the decay is at least partially electromagnetic Can’t have u-ubar quark go to a single photon as have to conserve energy and momentum (and angular momentum) Rate is less than a strong decay as have coupling of 1/137 compared to strong of about 0.2. Also have 2 vertices in pi decay and so (1/137)2 EM decays always proceed if allowed but usually only small contribution if strong also allowed u g g ubar P461 - particles III

c-cbar and b-bbar Mesons Similar to u-ubar, d-dbar, and s-sbar “excited” states similar to atoms 1S, 2S, 3S…1P, 2P…photon emitted in transitions. Mass spectrum can be modeled by QCD If mass > 2*meson mass can decay strongly But if mass <2*meson decays EM. “easiest” way is through virtual photons (suppressed for pions due to spin) c g m+ m- cbar P461 - particles III

c-cbar and b-bbar Meson EM-Decays Can be any particle-antiparticle pair whose pass is less than psi or upsilon: electron-positron, u-ubar, d-dbar, s-sbar rate into each channel depends on charge2(EM coupling) and mass (phase space) Some of the decays into hadrons proceed through virtual photon and some through a virtual (colorless) gluon) c g cbar P461 - particles III

Electromagnetic production of Hadrons Same matrix element as decay. Electron-positron pair make a virtual photon which then “decays” to quark-antiquark pairs. (or mu+-mu-, etc) electron-positron pair has a given invariant mass which the virtual photon acquires. Any quark-antiquark pair lighter than this can be produced The q-qbar pair can acquire other quark pairs from the available energy to make hadrons. Any combination which conserves quark counting, energy and angular momentum OK e+ g q qbar e- P461 - particles III

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Weak Decays If no strong or EM decays are allowed, hadrons decay weakly (except for stable proton) Exactly the same as lepton decays. Exactly the same as beta decays Charge current Weak interactions proceed be exchange of W+ or W-. Couples to 2 members of weak doublets (provided enough energy) U d u d W e n P461 - particles III

Decays of Leptons Transition leptonneutrino emits virtual W which then “decays” to all kinematically available doublet pairs For taus, mass=1800 MeV and W can decay into e+n, m+n, and u+d (s by mixing). 3 colors for quarks and so rate ~3 times higher. W e P461 - particles III

Weak Decays of Hadrons W e Can have “beta” decay with same number of quarks in final state (semileptonic) or quark-antiquark combine (leptonic) or can have purely hadronic decays Rates will be different: 2-body vs 3-body phase space; different spin factors W e P461 - particles III

Top Quark Decay t b W c u Simplest weak decay (and hadronic). M(top)>>Mw (175 GeV vs 81 GeV) and so W is real (not virtual) and there is no suppression of different final states due to phase space the t quark decays before it becomes a hadron. The outgoing b/c/s/u/d quarks are seen as jets t b W c u P461 - particles III

Top Quark Decay t b W Very small rate of ts or td the quark states have a color factor of 3 t b W P461 - particles III

How to Discover the Top Quark make sure it wasn’t discovered before you start collecting data (CDF run 88-89 top mass too heavy) build detector with good detection of electrons, muons, jets, “missing energy”, and some B-ID (D0 Run I bm) have detector work from Day 1. D0 Run I: 3 inner detectors severe problems, muon detector some problems but good enough. U-LA cal perfect collect enough data with right kinematics so statistically can’t be background. mostly W+>2 jets Total: 17 events in data collected from 1992-1995 with estimated background of 3.8 events P461 - particles III

The First Top Quark Event muon electron P461 - particles III

The First Top Quark Event jet P461 - particles III

Another Top Quark Event jets electron P461 - particles III

Decay Rates: Pions u dbar Look at pion branching fractions (BF) The Beta decay is the easiest. ~Same as neutron beta decay Q= 4.1 MeV. Assume FT=1600 s. LogF=3.2 (from plot) F= 1600 for just this decay gives “partial” T=1600/F=1 sec or partial width = 1 sec-1 u dbar P461 - particles III

Pi Decay to e-nu vs mu-nu Depends on phase space and spin factors in pion rest frame pion has S=0 2 spin=1/2 combine to give S=0. Nominally can either be both right-handed or both left-handed But parity violated in weak interactions. If m=0  all S=1/2 particles are LH and all S=1/2 antiparticles are RH neutrino mass = 0  LH electron and muon mass not = 0 and so can have some “wrong” helicity. Antparticles which are LH.But easier for muon as heavier mass L+ nu P461 - particles III

Polarization of Spin 1/2 Particles Obtain through Dirac equation and polarization operators. Polarization defined the degree of polarization then depends on velocity. The fraction in the “right” and “wrong” helicity states are: fraction “wrong” = 0 if m=0 and v=c for a given energy, electron has higher velocity than muon and so less likely to have “wrong” helicity P461 - particles III

Pion Decay Kinematics 2 Body decay. Conserve energy and momentum can then calculate the velocity of the electron or muon look at the fraction in the “wrong” helicity to get relative spin suppression of decay to electrons P461 - particles III

Pion Decay Phase Space Lorentz invariant phase space plus energy and momentum conservation gives the 2-body phase space factor (partially a computational trick) as the electron is lighter, more phase space (3.3 times the muon) Branching Fraction ratio is spin suppression times phase space P461 - particles III

Muon Decay Almost 100% of the time muons decay by Q(muon decay) > Q(pionmuon decay) but there is significant spin suppression and so muon’s lifetime ~100 longer than pions spin 1/2 muon  1/2 mostly LH (e) plus 1/2 all LH( nu) plus 1/2 all RH (antinu) 3 body phase space and some areas of Dalitz plot suppressed as S=3/2 electron tends to follow muon direction and “remember” the muon polarization. Dirac equation plus a spin rotation matrix can give the angular distribution of the electron relative to the muon direction/polarization P461 - particles III

Detecting Parity Violation in muon decay Massless neutrinos are fully polarized, P=-1 for neutrino and P=+1 for antineutrino (defines helicity) Consider + + e+ decay. Since neutrinos are left-handed PH=-1, muons should also be polarised with polarisation P= -v/c (muons are non-relativistic, so both helicity states are allowed). If muons conserve polarization when they come to rest, the electrons from muon decay should also be polarized and have an angular dependence: n m+ p+ Jn Jm p+  m+ + nm e+ n m+ Je Jn Jm m+  e+ + ne + nm P461 - particles III

Parity violation in + + e+ decay Experiment by Garwin, Lederman, Weinrich aimed to confirm parity violation through the measurements of I(q) for positrons. 85 MeV pion beam (+ ) from cyclotron. 10% of muons in the beam: need to be separated from pions. Pions were stopped in the carbon absorber (20 cm thick) Counters 1-2 were used to separate muons Muons were stopped in the carbon target below counter 2. P461 - particles III

Parity violation in + + e+ decay Positrons from muon decay were detected by a telescope 3-4, which required particles of range >8 g/cm2 (25 MeV positrons). Events: concidence between counters 1-2 (muon) plus coincidence between counters 3-4 (positron) delayed by 0.75-2.0 ms. Goal: to measure I(q) for positrons. Conventional way: move detecting system (telescope 3-4) around carbon target measuring intensities at various q. But very complicated. More sophisticated method: precession of muon spin in magnetic field. Vertical magnetic field in a shielded box around the target. The intensity distribution in angle was carried around with the muon spin. P461 - particles III

Results of the experiment by Garwin et al. Changing the field (the magnetising current), they could change the rate (frequency) of the spin precession, which will be reflected in the angular distribution of the emitted positrons. Garwin et al. plotted the positron rate as a function of magnetising current (magnetic field) and compared it to the expected distribution: P461 - particles III