A free neutron undergoes beta-minus decay and a neutral pion decays into two photons. (a) Write both reactions, including the antineutrino. (b) Give proton and neutron quark compositions. (c) State the quark-level change and weak boson. (d) Check charge, baryon and lepton number. (e) Explain why photons carry no baryon number.

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Accepted Answer

n → p + e⁻ + electron antineutrino; π⁰ → γ + γ; neutron udd, proton uud; d → u + W⁻, then W⁻ → e⁻ + antineutrino. The reactions are n → p + e⁻ + anti-νₑ and π⁰ → γ + γ. Two photons can conserve momentum in the pion rest frame by leaving oppositely. Neutron valence composition is udd and proton is uud. Converting one d to u raises the hadron charge by one elementary unit. At the weak vertex d → u + W⁻; the virtual W⁻ produces e⁻ + anti-νₑ. The electron is created rather than stored inside the neutron. Charge is 0 = +1 − 1; baryon number remains 1; electron and antineutrino lepton numbers +1 and −1 cancel. Energy and momentum also remain conserved. Photons are gauge bosons, not three-quark baryons, so baryon number is zero. The neutral pion is a quark–antiquark meson and also has baryon number zero.

Quark bookkeeping in two decays

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