The measured neutral-kaon parameters are ,

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Flavour, neutrinos and CP violation · Flavour, neutrinos and CP violation

Symmetry and Flavour, Ch Neutral kaons: mixing, strangeness oscillation and CP violation

Problem

The measured neutral-kaon parameters are τS=0.8954×10−10 s\tau_S = 0.8954\times10^{-10}\,\mathrm{s}, τL=5.116×10−8 s\tau_L = 5.116\times10^{-8}\,\mathrm{s}, and ΔmK=mL−mS=3.484×10−12 MeV\Delta m_K = m_L-m_S = 3.484\times10^{-12}\,\mathrm{MeV}. Take ℏ=6.582×10−22 MeV s\hbar = 6.582\times10^{-22}\,\mathrm{MeV\,s}. ((a)) Find the widths ΓS=ℏ/τS\Gamma_S = \hbar/\tau_S and ΓL=ℏ/τL\Gamma_L = \hbar/\tau_L, in MeV. ((b)) Verify that τL/τS=571\tau_L/\tau_S = 571. ((c)) Compute the width difference ΔΓK=ΓS−ΓL\Delta\Gamma_K = \Gamma_S-\Gamma_L and hence the phase ϕϵ=arctan⁡(2ΔmK/ΔΓK)\phi_\epsilon = \arctan(2\Delta m_K/\Delta\Gamma_K), and check it against the quoted value 43.5∘43.5^\circ.

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