The spin-summed

PHYSICS · Subjective · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Particles, interactions and experiment

Symmetry and Flavour, Ch From amplitude to rate: Lorentz-invariant phase space, widths and cross sections

Problem

The spin-summed, spin-averaged squared amplitude for W−→e−νˉeW^-\to e^-\bar\nu_e, quoted from electroweak theory (label: asserted), is ∣M∣2‾=423GFMW4,\overline{|\mathcal{M}|^2} = \frac{4\sqrt2}{3}G_FM_W^4, treating the electron and neutrino as massless. Using GF=1.1663788×10−5 GeV−2G_F=1.1663788\times10^{-5}\,\mathrm{GeV^{-2}} and MW=80.377 GeVM_W=80.377\,\mathrm{GeV}, calculate Γ(W−→e−νˉe)\Gamma(W^-\to e^-\bar\nu_e) in MeV using the two-body width formula Γ=p∗∣M∣2‾/8πM2\Gamma = p^*\overline{|\mathcal{M}|^2}/8\pi M^2, with p∗=MW/2p^*=M_W/2 for massless decay products.

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