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 K∗(892)0K^{*}(892)^0 resonance has mass Mc2=895.55 MeVMc^2 = 895.55\,\mathrm{MeV}, full width at half maximum Γ=47.3 MeV\Gamma = 47.3\,\mathrm{MeV}, and peak cross section σpeak=10.0 mb\sigma_{\rm peak} = 10.0\,\mathrm{mb} in a kaon-pion scattering 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 K∗(892)0K^{*}(892)^0. ((b)) Predict the cross section at E−Mc2=2Γ=94.6 MeVE - Mc^2 = 2\Gamma = 94.6\,\mathrm{MeV}.

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