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EM Decay of Hadrons

EM Decay of Hadrons. u. g. 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)

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EM Decay of Hadrons

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  1. EM Decay of Hadrons u g • 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 g ubar P461 - particles III

  2. 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) m+ c g m- cbar P461 - particles III

  3. 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

  4. 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 q e+ g qbar e- P461 - particles III

  5. P461 - particles III

  6. 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 d u d u W e n P461 - particles III

  7. 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

  8. Weak Decays of Hadrons • 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

  9. Top Quark Decay • 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

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

  11. 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

  12. The First Top Quark Event muon electron P461 - particles III

  13. The First Top Quark Event jet P461 - particles III

  14. Another Top Quark Event jets electron P461 - particles III

  15. 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 P461 - particles III

  16. Pi Decay to e-nu vs mu-nu nu L+ • 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 P461 - particles III

  17. 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

  18. 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

  19. 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

  20. 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

  21. Jm Jn p+ n m+ Jn Je Jm n e+ m+ n Jn 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: p+ m+ + nm m+e+ + ne +nm P461 - particles III

  22. 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

  23. 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

  24. 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

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