A detector reconstructs the invariant mass and finds a peak at

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Particles, interactions and experiment

Particle Physics, Ch Resonances, widths and the Breit-Wigner line shape

Problem

A detector reconstructs the π+π−π0\pi^+\pi^-\pi^0 invariant mass and finds a peak at 782.7 MeV/c2782.7\,\mathrm{MeV}/c^2, the ω\omega meson, with an observed full width at half maximum of 30.0 MeV/c230.0\,\mathrm{MeV}/c^2. The detector's mass resolution at this mass, calibrated on a reference peak of known negligible width, is 25.0 MeV/c225.0\,\mathrm{MeV}/c^2 (full width at half maximum). Someone argues: "the observed full width at half maximum is the ω\omega meson's own decay width, so Γ=30.0 MeV\Gamma = 30.0\,\mathrm{MeV}, and τ=ℏ/Γ=2.19×10−23 s\tau = \hbar/\Gamma = 2.19\times10^{-23}\,\mathrm{s}." ((a)) Explain what is wrong with this reasoning. ((b)) Find the largest natural width Γ\Gamma this plot allows and the matching lower limit on the lifetime τ\tau, and state by at least what factor the argued lifetime is too short.

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