A collider experiment records the invariant mass spectrum near

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 collider experiment records the

\mu^+\mu^-

invariant mass spectrum near

9.46\,\mathrm{GeV}/c^2

, where the

\Upsilon(1S)

meson is known to appear. The observed peak has a full width at half maximum of

(71 \pm 3)\,\mathrm{MeV}/c^2

, read from the histogram. The same detector's mass resolution at this mass, calibrated using a resonance of known narrow width, is

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

(full width at half maximum), essentially independent of which particle is produced. ((a)) State the mass read from the peak position. ((b)) Using the upper edge of the measured full width at half maximum,

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

(

71+3

), place an upper limit on the natural width

\Gamma

of the

\Upsilon(1S)

. ((c)) Convert this upper limit on

\Gamma

into a lower limit on the lifetime

\tau

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