em decay of hadrons

P461 - particles III 1

EM Decay of Hadrons

• 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

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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)

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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)

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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

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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)

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Decays of Leptons• Transition leptonneutrino emits virtual W

which then “decays” to all kinematically available doublet pairs

• For taus, mass=1800 MeV and W can decay into e and u+d (s by mixing). 3 colors for quarks and so rate ~3 times higher.

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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

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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

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Top Quark Decay• Very small rate of ts or td• the quark states have a color factor of 3•

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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

• 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

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Decay Rates: Pions

• 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

MeVms

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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

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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

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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

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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

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Muon Decay

• Almost 100% of the time muons decay by

• Q(muon decay) > Q(pionmuon 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

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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, 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:

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Parity violation in + + e+ decay

• Experiment by Garwin, Lederman, Weinrich aimed to confirm parity violation through the measurements of I() 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.


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 s.

• Goal: to measure I() for positrons.

• Conventional way: move detecting system (telescope 3-4) around carbon target measuring intensities at various . 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.


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:

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em decay of hadrons

Documents

strong decay

t quark decays

em decays

uubar quark

virtual photon

virtual w

pi decay

quarkantiquark pairs