331 model
Encyclopedia
The 331 model in particle physics
offers an explanation of why there must exist three families of quarks and leptons. One curious feature of the Standard Model
is that the anomaly
cancels exactly, for each quark-lepton family, of which we know three. The standard model thus offers no explanation of why there are three families, or indeed why there is more than one family.
One idea, therefore, is to extend the standard model such as to destroy the perfect cancellation of the anomaly, per family, and to make the three families transform differently under an extended gauge group, and to arrange that the anomaly cancel, only for three families. But the cancellation will persist for 6, 9, ... families, so then there is a new super-family problem, which is best avoided by having only three families.
Such a construction necessarily requires the addition of further gauge bosons and chiral fermions, which then provide testable predictions of the new model, in the form of elementary particles, to be sought experimentally, at masses above the weak scale, of about 100 GeV. The minimal 331 model predicts singly and doubly charged spin-one bosons, bilepton
s, which could show up in electron-electron scattering when it is studied at TeV energy scales and may also be produced in multi-TeV proton–proton scattering at the Large Hadron Collider
as early as 2011.
The 331 model offers an explanation of why there must exist three families of quarks and leptons, a fact which is put in "by hand" in the Standard Model. The 331 model is an extension of the electroweak gauge symmetry from
to 
with 
and the hypercharge 
and the electric charge 
where T3 and T8 are the Gell-Mann matrices
of SU(3)L and β and I are parameters of the model. The name 331 comes from the full gauge symmetry group
.
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
offers an explanation of why there must exist three families of quarks and leptons. One curious feature of the Standard Model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
is that the anomaly
Anomaly (physics)
In quantum physics an anomaly or quantum anomaly is the failure of a symmetry of a theory's classical action to be a symmetry of any regularization of the full quantum theory. In classical physics an anomaly is the failure of a symmetry to be restored in the limit in which the symmetry-breaking...
cancels exactly, for each quark-lepton family, of which we know three. The standard model thus offers no explanation of why there are three families, or indeed why there is more than one family.
One idea, therefore, is to extend the standard model such as to destroy the perfect cancellation of the anomaly, per family, and to make the three families transform differently under an extended gauge group, and to arrange that the anomaly cancel, only for three families. But the cancellation will persist for 6, 9, ... families, so then there is a new super-family problem, which is best avoided by having only three families.
Such a construction necessarily requires the addition of further gauge bosons and chiral fermions, which then provide testable predictions of the new model, in the form of elementary particles, to be sought experimentally, at masses above the weak scale, of about 100 GeV. The minimal 331 model predicts singly and doubly charged spin-one bosons, bilepton
Bilepton
A bilepton is a hypothetical particle predicted by the minimal 331 model. It is a spin one gauge boson which appears with single and double electric charge and with lepton number L=+2 and L=-2. It can mediate exotic processes such as V+A muon decay and muonium-antimuonium conversion...
s, which could show up in electron-electron scattering when it is studied at TeV energy scales and may also be produced in multi-TeV proton–proton scattering at the Large Hadron Collider
Large Hadron Collider
The Large Hadron Collider is the world's largest and highest-energy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....
as early as 2011.
The 331 model offers an explanation of why there must exist three families of quarks and leptons, a fact which is put in "by hand" in the Standard Model. The 331 model is an extension of the electroweak gauge symmetry from
to with and the hypercharge and the electric charge where T3 and T8 are the Gell-Mann matricesGell-Mann matrices
The Gell-Mann matrices, named for Murray Gell-Mann, are one possible representation of the infinitesimal generators of the special unitary group called SU....
of SU(3)L and β and I are parameters of the model. The name 331 comes from the full gauge symmetry group
.See also
- Standard ModelStandard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
- Standard model (basic details)Standard model (basic details)This is a detailed description of the standard model of particle physics. It describes how the leptons, quarks, gauge bosons and the Higgs particle fit together...
- Beyond the Standard ModelBeyond the Standard ModelPhysics beyond the Standard Model refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the origin of mass, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy...