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 Incoming links: Accidental symmetry

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

B - L

is anomaly free when a right-handed neutrino is included in each generation.

Below the strange-quark threshold, the gauge-field and two-flavour quark terms are

L = - \frac{1}{4} G_{μν}^{a} G^{a μν} - \frac{1}{4} F_{μν} F^{μν} + \sum_{q = u, d} \overline{q} (i γ^{μ} D_{μ} - m_{q}) q,

where

D_{μ} = \partial_{μ} - i g_{s} G_{μ}^{a} T^{a} - i e Q_{q} A_{μ}, Q_{u} = \frac{2}{3}, Q_{d} = - \frac{1}{3} .

Every renormalizable gauge-invariant term contains equal numbers of quark and antiquark fields. The common phase symmetry

q \mapsto e^{i β /3} q

is therefore automatic rather than imposed in constructing the Lagrangian. Its conserved charge is baryon number, making

U (1)_{B}

an accidental symmetry of the renormalizable low-energy theory.