In a fixed-target experiment a beam of momentum strikes protons at rest

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

In a fixed-target experiment a

K^-

beam of momentum

800\,\mathrm{MeV}/c

strikes protons at rest, and the

K^-p

cross section shows a peak at this beam momentum. Someone argues: "The beam momentum

800\,\mathrm{MeV}/c

corresponds to a

K^-

total energy of

\sqrt{800^2+493.7^2}=940\,\mathrm{MeV}

. Since the peak occurs at this beam energy, the resonance produced there has mass

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

." ((a)) Find the error in this reasoning. ((b)) Using

m_{K^-}c^2=493.7\,\mathrm{MeV}

and

m_pc^2=938.3\,\mathrm{MeV}

, compute the correct mass of the resonance produced.

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