The baryon has mass

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Non-abelian gauge theory and QCD · Non-abelian gauge theory and QCD

Particle Physics, Ch The Standard Model as a table you can predict from

Problem

The Δ+\Delta^+ baryon has mass 1232 MeV/c21232\,\mathrm{MeV}/c^2. Two decay channels are kinematically open: the strong channel Δ+→p π0\Delta^+\to p\,\pi^0 and the electromagnetic channel Δ+→p γ\Delta^+\to p\,\gamma, using the proton mass 938.3 MeV/c2938.3\,\mathrm{MeV}/c^2, the neutral pion mass 135.0 MeV/c2135.0\,\mathrm{MeV}/c^2, and treating the photon as massless. Someone argues: "the energy released in Δ+→pγ\Delta^+\to p\gamma is 1232−938.3=293.7 MeV1232-938.3=293.7\,\mathrm{MeV}, nearly twice the 1232−938.3−135.0=158.7 MeV1232-938.3-135.0=158.7\,\mathrm{MeV} released in Δ+→pπ0\Delta^+\to p\pi^0; the channel releasing more energy must dominate, so Δ+\Delta^+ decays mostly to pγp\gamma." ((a)) Check the two energy releases quoted. ((b)) State which channel is measured to dominate, and explain why the argument is wrong.

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