A histogram of the invariant mass from many collisions shows a peak at

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

A histogram of the

K\pi

invariant mass from many collisions shows a peak at

895\,\mathrm{MeV}/c^2

, identified as the

K^{*}(892)^0

meson. The count rises to a maximum and falls to half of that maximum at bin centres

871\,\mathrm{MeV}/c^2

and

919\,\mathrm{MeV}/c^2

. The detector's mass resolution, measured separately using a narrow reference peak, contributes a full width at half maximum of

8.0\,\mathrm{MeV}/c^2

to any observed peak, independent of the particle's own width. ((a)) State the mass and the observed full width at half maximum of the peak. ((b)) Use the resolution to estimate the natural width

\Gamma

of the

K^{*}(892)^0

. ((c)) Convert

\Gamma

into a lifetime

\tau

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