# Georgi–Glashow model

In particle physics, the **Georgi–Glashow model**^{[1]} is a particular grand unified theory (GUT) proposed by Howard Georgi and Sheldon Glashow in 1974. In this model the standard model gauge groups SU(3) × SU(2) × U(1) are combined into a single simple gauge group SU(5). The unified group SU(5) is then thought to be spontaneously broken into the standard model subgroup below a very high energy scale called the grand unification scale.

Since the Georgi–Glashow model combines leptons and quarks into single irreducible representations, there exist interactions which do not conserve baryon number, although they still conserve the quantum number *B – L* associated with the symmetry of the common representation. This yields a mechanism for proton decay, and the rate of proton decay can be predicted from the dynamics of the model. However, proton decay has not yet been observed experimentally, and the resulting lower limit on the lifetime of the proton contradicts the predictions of this model. However, the elegance of the model has led particle physicists to use it as the foundation for more complex models which yield longer proton lifetimes, particularly SO(10) in basic and SUSY variants.

(For a more elementary introduction to how the representation theory of Lie algebras are related to particle physics, see the article Particle physics and representation theory.)

Similar motivations apply to Pati-Salam, and to SO(10), E6, and other supergroups of SU(5).

The explicit embedding can be found in eg.^{[2]} or in the original paper by Georgi and Glashow.^{[1]}

When this occurs, SU(5) is spontaneously broken to the subgroup of SU(5) commuting with the group generated by *Y*.

giving the gauge bosons of the standard model plus the new X and Y bosons. See restricted representation.

giving precisely the left-handed fermionic content of the standard model, where for every generation d^{c}, u^{c}, e^{c} and ν^{c} stand for anti-down-type quark, anti-up-type quark, anti-down-type lepton and anti-up-type lepton, respectively, and q and l stand for quark and lepton. Fermions transforming as a **1** under SU(5) are now thought to be necessary because of the evidence for neutrino oscillations, unless a way is found to introduce a tiny Majorana coupling for the left-handed neutrinos.

These monopoles have quantized Y magnetic charges. Since the electromagnetic charge Q is a linear combination of some SU(2) generator with Y/2, these monopoles also have quantized magnetic charges, where by magnetic here, we mean electromagnetic magnetic charges.

The first column is an Abbreviation of the second column (neglecting proper normalization factors), where capital indices are SU(5) indices, and i and j are the generation indices.

The vacua correspond to the mutual zeros of the F and D terms. Let's first look at the case where the VEVs of all the chiral fields are zero except for Φ.

In other words, there are at least three different superselection sections, which is typical for supersymmetric theories.

Only case III makes any phenomenological sense and so, we will focus on this case from now onwards.

It can be verified that this solution together with zero VEVs for all the other chiral multiplets is a zero of the F-terms and D-terms. The matter parity remains unbroken (right up to the TeV scale).

The sterile neutrinos, if any exists, would also acquire a GUT scale Majorana mass coming from the superpotential coupling ν^{c2}.

Unification of the Standard Model via an SU(5) group has significant phenomenological implications. Most notable of these is proton decay, which is present in SU(5) with and without supersymmetry. This is allowed by the new vector bosons introduced from the adjoint representation of SU(5), which also contains the gauge bosons of the standard model forces. Since these new gauge bosons are in (3,2)_{−5/6} bifundamental representations, they violated baryon and lepton number. As a result, the new operators should cause protons to decay at a rate inversely proportional to their masses. This process is called dimension 6 proton decay and is an issue for the model, since the proton is experimentally determined to have a lifetime greater than the age of the universe. This means that an SU(5) model is severely constrained by this process.

As well as these new gauge bosons, in SU(5) models the Higgs field is usually embedded in a **5** representation of the GUT group. The caveat of this is that since the Higgs field is an SU(2) doublet, the remaining part, an SU(3) triplet, must be some new field - usually called D or T. This new scalar would be able to generate proton decay as well and, assuming the most basic Higgs vacuum alignment, would be massless, allowing the process at very high rates.

While not an issue in the Georgi–Glashow model, a supersymmeterised SU(5) model would have additional proton decay operators due to the superpartners of the standard model fermions. The lack of detection of proton decay (in any form) brings into question the veracity of SU(5) GUTs of all types, however, while the models are highly constrained by this result, they are not in general ruled out.

In the lowest-order Feynman diagram corresponding to the simplest source of proton decay in SU(5), a left-handed and a right-handed up quark annihilate, yielding an X^{+} boson, which decays to a right-handed (or left-handed) positron and a left-handed (or right-handed) anti-down quark:

On the other hand, on can just parametrize the ignorance about neutrinos using the dimension 5 Weinbergoperator: