Misplaced Pages

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "B − L" – news · newspapers · books · scholar · JSTOR (January 2021) (Learn how and when to remove this message)

In particle physics, B − L (pronounced "bee minus ell") is a quantum number which is the difference between the baryon number (B) and the lepton number (L) of a quantum system.

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, then for the seesaw mechanism to work B – L has to be spontaneously broken to give the neutrinos a nonzero mass.

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).

The weak hypercharge Y_W is related to B – L via

$${\displaystyle X+2\,Y_{\text{W}}=5\,(B-L),}$$

where X charge (not to be confused with the X boson) is the conserved quantum number associated with the global U(1) symmetry Grand Unified Theory.

See also

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

References

1. Wilczek, Frank; Zee, A. (1979). "Operator analysis of nucleon decay". Physical Review Letters. 43 (21): 1571–1573. Bibcode:1979PhRvL..43.1571W. doi:10.1103/PhysRevLett.43.1571.

This particle physics–related article is a stub. You can help Misplaced Pages by expanding it.

• v
• t
• e

• Conservation laws
• Flavour (particle physics)
• Particle physics stubs