An collider scans the hadronic cross section near the meson

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

An e+e−e^+e^- collider scans the hadronic cross section near the ϕ(1020)\phi(1020) meson, varying s\sqrt{s} in small steps. The beam energy spread contributes a resolution of only 0.1 MeV0.1\,\mathrm{MeV} to s\sqrt{s}, negligible compared with the structure seen. The measured cross sections are given in the data below. Data (s\sqrt s in MeV, σ\sigma in nb): (1015.0,18.6)(1015.0,18.6), (1017.35,50.0)(1017.35,50.0), (1019.5,100.0)(1019.5,100.0), (1021.65,50.0)(1021.65,50.0), (1024.0,18.6)(1024.0,18.6). ((a)) Read off the mass of the resonance responsible for this peak. ((b)) Read off its full width at half maximum Γ\Gamma. ((c)) Convert Γ\Gamma into a lifetime τ\tau, and state briefly why this Γ\Gamma can be taken as the particle's natural width rather than an instrumental blur.

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