Solution (source code)

= Solution

With the Standard Model field content, every gauge-invariant, Lorentz-invariant operator of dimension at most four automatically preserves <baryon number> and total <lepton number>. They are therefore <accidental symmetries>, rather than symmetries imposed in constructing the renormalizable Lagrangian. This explains perturbative conservation in ordinary reactions. They are not exact principles: the electroweak <chiral anomaly> violates $B+L$, the dimension-five <Weinberg operator> violates lepton number, and dimension-six <proton-decay operators> can violate baryon number. The combination $B-L$ is anomaly free when a <right-handed neutrino> is included in each generation.