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) and ...

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 In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups ...

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. Idea ...

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 neut ...

. The name "331" comes from the full gauge symmetry group

SU(3)_C \times SU(3)_L \times U(1)_X\,

Details

The 331 model in

is an extension of the

from

SU(2)_W \times U(1)_Y

\,SU(3)_L \times U(1)_X\,

with

SU(2)_W \subset SU(3)_W

. In the 331 model, hypercharge is given by :

Y = \beta\,T_8 + I\,X

and electric charge is given by :

Q = \frac

where

T_3

and

T_8

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 th ...

of SU(3) and

\beta

and

I

are parameters of the model.

Motivation

The 331 model offers an explanation of why there must be three

and

. One curious feature of the

Standard Model The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. I ...

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; i.e. of a gauge theory In physics, a gauge ...

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, which is on the order of 10² - 10³ 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 The Large Hadron Collider (LHC) is the world's largest and highest-energy particle collider. It was built by the European Organization for Nuclear Research (CERN) between 1998 and 2008 in collaboration with over 10,000 scientists and hundr ...

which can reach 10⁴ GeV.

References

* * * Physics beyond the Standard Model Electroweak theory {{Particle-stub

Details

Motivation

See also

References