B-L
Encyclopedia
In high energy physics, B − L is the difference between the baryon number (B) and the lepton number
(L).
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 neutrino
s a nonzero mass if we assume the seesaw mechanism
. The gauge boson
s 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 is related to B − L via:
where X
is the U(1) symmetry Grand Unified Theory-associated conserved quantum number
.
Lepton number
In particle physics, the lepton number is the number of leptons minus the number of antileptons.In equation form,so all leptons have assigned a value of +1, antileptons −1, and non-leptonic particles 0...
(L).
Details
This quantum numberQuantum number
Quantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...
is the charge of a global
Global symmetry
A global symmetry is a symmetry that holds at all points in the spacetime under consideration, as opposed to a local symmetry which varies from point to point.Global symmetries require conservation laws, but not forces, in physics.-See also:...
/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
Chiral anomaly
A chiral anomaly is the anomalous nonconservation of a chiral current. In some theories of fermions with chiral symmetry, the quantization may lead to the breaking of this chiral symmetry. In that case, the charge associated with the chiral symmetry is not conserved.The non-conservation happens...
or gravitational anomalies
Gravitational anomaly
In theoretical physics, a gravitational anomaly is an example of a gauge anomaly: it is an effect of quantum mechanics–usually a one-loop diagram—that invalidates the general covariance of a theory of general relativity combined with some other fields. The adjective "gravitational" is derived from...
, 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 neutrino
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...
s a nonzero mass if we assume the seesaw mechanism
Seesaw mechanism
In theoretical physics, the seesaw mechanism is a mechanism within grand unification theory, and in particular in theories of neutrino masses and neutrino oscillation, where it can be used to explain the smallness of observed neutrino masses relative to those of quarks and leptons.There are several...
. The gauge boson
Gauge boson
In particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles.-...
s associated to this symmetry are commonly called X and Y bosons
X and Y bosons
In particle physics, the X and Y bosons are hypothetical elementary particles analogous to the W and Z bosons, but corresponding to a new type of force predicted by the Georgi–Glashow model, a grand unified theory.-Details:The X and Y bosons couple quarks to leptons, allowing violation of the...
.
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
Proton decay
In particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron...
where a proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
(B = 1; L = 0) would decay into a pion
Pion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
(B = 0, L = 0) and positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...
(B = 0; L = −1).
Weak hypercharge
Weak hypercharge
The weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the Gell-Mann–Nishijima formula for the hypercharge of strong interactions...
Y is related to B − L via:
- X + 2Y = 5(B − L)
where X
X (charge)
In particle physics, the X-charge is a conserved quantum number associated with the SO grand unification theory....
is the U(1) symmetry Grand Unified Theory-associated conserved quantum number
Quantum number
Quantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...
.
See also
- BaryogenesisBaryogenesisIn physical cosmology, baryogenesis is the generic term for hypothetical physical processes that produced an asymmetry between baryons and antibaryons in the very early universe, resulting in the substantial amounts of residual matter that make up the universe today.Baryogenesis theories employ...
- LeptogenesisLeptogenesis (physics)In physical cosmology, leptogenesis is the generic term for hypothetical physical processes that produced an asymmetry between leptons and antileptons in the very early universe, resulting in the dominance of leptons over antileptons...
- MajoronMajoronIn particle physics, majorons are a hypothetical type of Goldstone boson that are theorized to mediate the neutrino mass violation of lepton number or B − L in certain high energy collisions such as...
- Proton decayProton decayIn particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron...
- X and Y bosonsX and Y bosonsIn particle physics, the X and Y bosons are hypothetical elementary particles analogous to the W and Z bosons, but corresponding to a new type of force predicted by the Georgi–Glashow model, a grand unified theory.-Details:The X and Y bosons couple quarks to leptons, allowing violation of the...
- X (charge)X (charge)In particle physics, the X-charge is a conserved quantum number associated with the SO grand unification theory....
- LeptoquarkLeptoquarkLeptoquarks are hypothetical particles that carry information between quarks and leptons given a generation and allowing quarks and leptons to interact. They are color-triplet bosons that carry both lepton and baryon numbers. They are encountered in various extensions of the Standard Model, such as...