The 331 model in
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
is an extension of the
electroweak
In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very differe ...
gauge symmetry which offers an explanation of why there must be three
families
Family (from la, familia) is a group of people related either by consanguinity (by recognized birth) or affinity (by marriage or other relationship). The purpose of the family is to maintain the well-being of its members and of society. Ideal ...
of
quarks
A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly ...
and
leptons
In particle physics, a lepton is an elementary particle of half-integer spin (spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutr ...
. The name "331" comes from the full gauge symmetry group
.
Details
The 331 model in
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
is an extension of the
electroweak
In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very differe ...
gauge symmetry from
to
with
.
In the 331 model, hypercharge is given by
:
and electric charge is given by
:
where
and
are the
Gell-Mann matrices
The Gell-Mann matrices, developed by Murray Gell-Mann, are a set of eight linearly independent 3×3 traceless Hermitian matrices used in the study of the strong interaction in particle physics.
They span the Lie algebra of the SU(3) group in t ...
of SU(3) and
and
are parameters of the model.
Motivation
The 331 model offers an explanation of why there must be three
families
Family (from la, familia) is a group of people related either by consanguinity (by recognized birth) or affinity (by marriage or other relationship). The purpose of the family is to maintain the well-being of its members and of society. Ideal ...
of
quarks
A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly ...
and
leptons
In particle physics, a lepton is an elementary particle of half-integer spin (spin ) that does not undergo strong interactions. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons or muons), and neutr ...
. One curious feature of the
Standard Model is that the
gauge anomalies
In theoretical physics, a gauge anomaly is an example of an anomaly: it is a feature of quantum mechanics—usually a one-loop diagram—that invalidates the gauge symmetry of a quantum field theory
In theoretical physics, quantum field theo ...
independently exactly cancel for each of the three known quark-lepton families. The Standard Model thus offers no explanation of why there are three families, or indeed why there is more than one family.
The idea behind the 331 model is to extend the standard model such that all three families are required for anomaly cancellation. More specifically, in this model the three families transform differently under an extended gauge group. The perfect cancellation of the anomalies within each family is ruined, but the anomalies of the extended gauge group cancel when all three families are present. The cancellation will persist for 6, 9, ... families, so having only the three families observed in nature is the least possible matter content.
Such a construction necessarily requires the addition of further gauge bosons and chiral fermions, which then provide testable predictions of the model in the form of elementary particles. These particles could be found experimentally at masses above the
electroweak scale
In particle physics, the electroweak scale, also known as the Fermi scale, is the energy scale around 246 GeV, a typical energy of processes described by the electroweak theory. The particular number 246 GeV is taken to be the vacuum expectation ...
, which is on the order of 10
2 - 10
3 GeV. The minimal 331 model predicts singly and doubly charged spin-one bosons,
bileptons, 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 which can reach 10
4 GeV.
See also
*
Physics beyond the Standard Model
References
*
*
*
Physics beyond the Standard Model
Electroweak theory
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