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Decay Rates: Pions

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 gives partial width(-1) T=1600/F=1 sec or partial width = 1 sec-1. Pi Decay to e-nu vs mu-nu.

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Decay Rates: Pions

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  1. 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 • gives partial width(-1) T=1600/F=1 sec or partial width = 1 sec-1 P461 - particles IV

  2. 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. But easier for muon as heavier mass P461 - particles IV

  3. 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 IV

  4. 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 IV

  5. 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 IV

  6. 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 IV

  7. Jm Jn p+ n m+ Jn Je Jm n e+ m+ n Jn Detecting Parity Violation in muon decay • Massless neutrinos are fully polarised, 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 polarisation when they come to rest, the electrons from muon decay should also be polarised and have an angular dependence: p+ m+ + nm m+e+ + ne +nm P461 - particles IV

  8. 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 IV

  9. 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 IV

  10. 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 IV

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