In annihilation the resonance is produced with 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

In e+e−e^+e^- annihilation the ω(782)\omega(782) resonance is produced with mass Mc2=782.66 MeVMc^2 = 782.66\,\mathrm{MeV}, full width at half maximum Γ=8.68 MeV\Gamma = 8.68\,\mathrm{MeV}, and peak cross section σpeak=1.50 μb\sigma_{\rm peak} = 1.50\,\mu\mathrm{b}. The line shape is 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 ω\omega. ((b)) Predict the cross section at a centre-of-mass energy 8.68 MeV8.68\,\mathrm{MeV} above the peak.

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