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.

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.

Nevertheless, 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.)

splitting restricts SU(5) to S(U(2)×U(3)), yielding matrices of the form with kernel

Thus the Standard Model's representation F ⊕ F* of one generation of fermions and antifermions lies within

, GUTs can be written in terms of vectors and matrices which allows for an intuitive understanding of the Georgi–Glashow model.

For that we recall a gauge field transforms as an adjoint, and thus can be written as

The Standard Model's quarks and leptons fit neatly into representations of SU(5).

Under the unbroken subgroup these transform as to yield precisely the left-handed fermionic content of the Standard Model where every generation dc, uc, ec, and νc correspond to anti-down-type quark, anti-up-type quark, anti-down-type lepton, and anti-up-type lepton, respectively.

The number of sterile neutrino generations need not be three, unless the SU(5) is embedded in a higher unification scheme such as SO(10).

The F zeros corresponds to finding the stationary points of W subject to the traceless constraint

The gauge algebra 24 decomposes as This 24 is a real representation, so the last two terms need explanation.

However, the direct sum of both representation decomposes into two irreducible real representations and we only take half of the direct sum, i.e. one of the two real irreducible copies.

acquire GUT scale masses coming from self pairings of the superpotential,

The sterile neutrinos, if any exist, would also acquire a GUT scale Majorana mass coming from the superpotential coupling νc  2  .

Unification of the Standard Model via an SU(5) group has significant phenomenological implications.

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.

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 so allowing the process at very high rates.

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: This process conserves weak isospin, weak hypercharge, and color.

and SU(5) defines left-handed normal leptons as "white" and right-handed antileptons as "black".

Since protons seem to be quite stable such a triplet has to acquire a quite large mass in order to suppress the decay.

For that consider the scalar part of the Greorgi-Glashow Lagrangian: We here have denoted the adjoint used to break

[2] As the SM the original Georgi–Glashow model proposed in[1] does not include neutrino masses.

The solutions to this problem follow the same ideas which have been applied to the SM: One on hand on can include a

As in the SM one can also implement the type-I seesaw mechanism which then generates naturally light masses.

The pattern of weak isospins , weak hypercharges , and strong charges for particles in the Georgi–Glashow model, rotated by the predicted weak mixing angle , showing electric charge roughly along the vertical. In addition to Standard Model particles, the theory includes twelve colored X bosons, responsible for proton decay .
Schematic representation of fermions and bosons in SU(5) GUT showing 5 + 10 split in the multiplets. Row for 1 (the sterile neutrino singlet) is omitted, but would likewise be isolated. Neutral bosons (photon, Z-boson, and neutral gluons) are not shown but occupy the diagonal entries of the matrix in complex superpositions.
The most common 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 positron and an anti- down quark of opposite handedness.