Two experiments study the baryon

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

Two experiments study the

\Delta(1232)

baryon. Experiment A (

\pi N

elastic scattering, momentum resolution contributing only

2\,\mathrm{MeV}

\sqrt{s}

) measures a peak with full width at half maximum

118\,\mathrm{MeV}

. Experiment B (photoproduction with a calorimeter of resolution

30\,\mathrm{MeV}

, full width at half maximum) measures a peak of full width at half maximum

125\,\mathrm{MeV}

, at the same mass. Someone argues: "these must be two different particles, or at least two different widths: Experiment A gives

\Gamma = 118\,\mathrm{MeV}

but Experiment B gives

\Gamma = 125\,\mathrm{MeV}

. Also, since the

\Delta(1232)

is only ever inferred from a bump and is never seen directly the way a proton track is seen, it should not be called a real particle at all." ((a)) Show that the two measurements are consistent with a single natural width once each is corrected for its own resolution. ((b)) Give the grounds on which the

\Delta(1232)

resonance is nonetheless identified as a genuine particle.

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