The meson has a measured mean lifetime

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Particles, interactions and experiment

Particle Physics, Ch Decay rates, cross sections and phase space

Problem

The

D^0

meson has a measured mean lifetime

\tau = 4.101\times10^{-13}\,\mathrm{s}

, and

3.95\%

of its decays go to the channel

K^-\pi^+

. ((a)) Find the total decay width

\Gamma

of the

D^0

, in eV. ((b)) Find the partial width

\Gamma(D^0\to K^-\pi^+)

, in eV. ((c)) Separately, a beam of

K^+

mesons arrives at a liquid hydrogen target at a rate

\dot N_{\rm beam} = 5.0\times10^{7}\,\mathrm{s^{-1}}

. The target is

\ell = 20\,\mathrm{cm}

of liquid hydrogen, with proton number density

\rho_n = 4.2\times10^{28}\,\mathrm{m^{-3}}

, and the relevant cross section is

\sigma = 25\,\mathrm{mb}

. Find the interaction rate

\dot N

, assuming the thin-target approximation applies.

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