B − L

B − L is the difference between baryon number and lepton number, a quantum number conserved by many particle interactions. It is central to theories of neutrino mass, grand unification, and the matter–antimatter asymmetry.

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Baryon number: A quantum number equal to one-third the net number of quarks in a system. B − L subtracts this charge from lepton number.
Quark: An elementary fermion that combines with other quarks to form hadrons. Each quark carries baryon number one-third, contributing to B.
Grand unified theory: A theory that seeks to unify the strong, weak, and electromagnetic interactions at high energy. Many grand unified models place B − L within a larger gauge structure.
Leptogenesis: A proposed origin of the cosmic matter excess through lepton-number-generating processes in the early universe. B − L produced by leptogenesis can survive electroweak sphaleron processes.
B − L gauge symmetry: A gauge symmetry in which the difference between baryon and lepton number is a local charge. It promotes the global quantum number B − L to a gauge interaction.
Lepton number: A quantum number that distinguishes leptons from antileptons and tracks their net number. It is the second charge in the difference B − L.
Lepton: An elementary fermion that does not undergo the strong interaction. Leptons and antileptons determine the net lepton number L.
SO(10) grand unified theory: A grand unified model based on the gauge group SO(10), which accommodates one fermion generation in a 16-dimensional representation. Its particle multiplets naturally include a right-handed neutrino and a B − L generator.
Baryogenesis: The collection of mechanisms proposed to explain the universe’s excess of matter over antimatter. B − L violation can provide a starting asymmetry for generating baryon excess.
B − L symmetry breaking: The spontaneous breaking of a gauge or global B − L symmetry by a nonzero scalar field value. Breaking the symmetry can generate Majorana neutrino masses and a massive gauge boson.