The resonance

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 Υ(1S)\Upsilon(1S) resonance, produced in e+e−e^+e^- annihilation, has mass Mc2=9460.30 MeVMc^2 = 9460.30\,\mathrm{MeV}, full width at half maximum Γ=54.02 keV\Gamma = 54.02\,\mathrm{keV}, and peak cross section σpeak=1.00 nb\sigma_{\rm peak} = 1.00\,\mathrm{nb}. 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 Υ(1S)\Upsilon(1S). ((b)) Predict the cross section at E−Mc2=3Γ=162.1 keVE - Mc^2 = 3\Gamma = 162.1\,\mathrm{keV}.

Browse the problem library