B−L

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Flavour in particle physics

Flavour quantum numbers: Baryon number: B Lepton number: L Strangeness: S Charmness: C Bottomness: B′ Topness: T Isospin: I or I3 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).

[edit] Details

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 such a way that B − L is always conserved. One example is proton decay where a proton (B = 1; L = 0) decays into a pion (B = 0, L = 0) and positron (B = 0; L = −1).

Weak hypercharge is related to B−L via:

where X is the U(1) symmetry GUT-associated conserved quantum number.

[edit] See also

• Baryogenesis
• Leptogenesis
• Majoron
• Proton decay
• X and Y bosons

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