B−L

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Flavour in particle physics v • d • e
Flavour quantum numbers: Lepton number: L Baryon number: B Strangeness: S Charm: C Bottomness: B' Topness: T Isospin: I_z or I Weak isospin: T_z Electric charge: Q Combinations: Hypercharge: Y Y=2(Q-I_z) Y=B+S+C+B'+T Weak hypercharge: Y_W Y_W=2(Q-T_z) Y_W=B−L Related topics: CPT symmetry CKM matrix CP symmetry Chirality

In high energy physics, B−L (pronounced "bee minus ell") is the baryon number minus the lepton number. This quantum number is the charge of a global/gauge U(1) symmetry in some GUT models, called U(1)_B−L. Unlike baryon number alone or lepton number alone, this hypothetical symmetry is not broken by chiral anomalies or gravitational anomalies, as long as this symmetry is global, which is why this symmetry is often invoked. If B−L exists as a symmetry, it has to be spontaneously broken to give the neutrinos a nonzero mass if we assume the seesaw mechanism.

The anomalies that break baryon number conservation and lepton number conservation individually cancel in way that B−L is always conserved. One example is proton decay where proton (B=1, L=0) decays into a pion (B=0, L=0) and positron (B=0, L=−1).