The resonance has mass

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

The ϕ(1020)\phi(1020) resonance has mass Mc2=1019.46 MeVMc^2 = 1019.46\,\mathrm{MeV}, full width at half maximum Γ=4.25 MeV\Gamma = 4.25\,\mathrm{MeV}, and peak cross section σpeak=1.20 μb\sigma_{\rm peak} = 1.20\,\mu\mathrm{b} in a kaon-pair production scan. Use the Breit-Wigner form σ(E)=σpeak1+(2(E−Mc2)Γ)2.\sigma(E) = \dfrac{\sigma_{\rm peak}}{1 + \left(\dfrac{2(E-Mc^2)}{\Gamma}\right)^2}. ((a)) Find the mean lifetime of the ϕ\phi. ((b)) Predict the cross section at E−Mc2=Γ/2=2.125 MeVE - Mc^2 = \Gamma/2 = 2.125\,\mathrm{MeV}.

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