Consider photoproduction of a neutral pion on a proton at rest,

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

Particle Physics, Ch Invariant mass: decays, thresholds and the collider frame

Problem

\gamma + p \to p + \pi^0

, where the incoming photon has energy

E_\gamma

in the laboratory. Use

m_pc^2 = 938.27\,\mathrm{MeV}

and

m_{\pi^0}c^2 = 134.98\,\mathrm{MeV}

. ((a)) Compute the correct threshold photon energy

E_\gamma^{\rm thr}

for this reaction. ((b)) Someone argues that the threshold photon energy must simply equal the rest energy of the particle being created,

134.98\,\mathrm{MeV}

. Compare this with your answer to part (a) and explain, in terms of what must be true of the final-state particles at threshold, why it is wrong.

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