B − L

"B-L" redirects here. For other uses, see BL (disambiguation).

Flavour in particle physics
Flavour quantum numbers
Isospin: I or I3 Charm: C Strangeness: S Topness: T Bottomness: B′
Related quantum numbers
Baryon number: B Lepton number: L Weak isospin: T or T3 Electric charge: Q X-charge: X
Combinations
Hypercharge: Y Y = (B + S + C + B′ + T) Y = 2 (Q − I3) Weak hypercharge: YW YW = 2 (Q − T3) X + 2YW = 5 (B − L)
Flavour mixing
CKM matrix PMNS matrix Flavour complementarity

In high energy physics, B − L (pronounced "bee minus ell") is the difference between the baryon number (B) and the lepton number (L).

Details

This quantum number is the charge of a global/gauge U(1) symmetry in some Grand Unified Theory models, called U(1)_B − L. Unlike baryon number alone or lepton number alone, this hypothetical symmetry would not be 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 gauge bosons associated to this symmetry are commonly called X and Y bosons.

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

Weak hypercharge Y
W is related to B − L via:

X + 2Y
W = 5(B − L)

where X is the U(1) symmetry Grand Unified Theory-associated conserved quantum number.

See also

• Baryogenesis
• Leptogenesis
• Majoron
• Proton decay
• X and Y bosons
• X (charge)
• Leptoquark