Georgi–Glashow model

Georgi–Glashow model
Name	Georgi–Glashow model
Classification	Grand Unified Theory
Symmetry	SU(5)
Theorized by	Howard Georgi and Sheldon Glashow
Year	1974
Subsequent theories	Minimal Supersymmetric Standard Model, SO(10)

Georgi–Glashow model. The Georgi–Glashow model is a particular Grand Unified Theory (GUT) based on the simple Lie group SU(5). It was proposed in 1974 by physicists Howard Georgi and Sheldon Glashow, unifying the electromagnetic, weak, and strong forces into a single gauge theory. The model makes several definitive predictions, most notably the instability of the proton, but has been challenged by experimental results from facilities like Super-Kamiokande.

Overview

The Georgi–Glashow model was the first realistic and simplest Grand Unified Theory proposed, aiming to describe all known fundamental particle interactions except gravity within the framework of a single gauge theory. It embeds the Standard Model gauge group, SU(3) × SU(2) × U(1), into the simple Lie group SU(5). This unification elegantly explains the quantization of electric charge and predicts relationships between the coupling constants of the different forces. The work of Howard Georgi and Sheldon Glashow built upon earlier ideas in quantum field theory and was contemporaneous with other unification efforts following the success of the Weinberg–Salam model.

Mathematical formulation

The mathematical foundation of the model is the special unitary group SU(5), whose generators correspond to the gauge bosons of the unified force. The Lie algebra of SU(5) contains the algebras of the Standard Model groups as subalgebras. The breaking of the SU(5) symmetry to the Standard Model group is typically achieved through the Higgs mechanism, employing a scalar field in the adjoint representation of SU(5). This symmetry breaking pattern dictates the masses of the new X and Y bosons and sets the unification scale.

Particle content and interactions

The fermions of one generation are arranged into two irreducible representations of SU(5): a \(\overline{5}\) and a \(10\). The \(\overline{5}}\) contains the down-type quarks and the lepton doublet, while the \(10\) contains the up-type quarks, the charged lepton, and the neutrino. The gauge bosons reside in the adjoint representation, the \(24\), which includes the familiar gluons, W and Z bosons, photon, and twelve new X and Y bosons that mediate interactions causing baryon number violation.

Proton decay and experimental status

A dramatic prediction of the Georgi–Glashow model is proton decay, mediated by the X and Y bosons, with a dominant expected decay channel such as \(p \rightarrow e^+ \pi^0\). Early calculations suggested a lifetime on the order of \(10^{30}\) years. Extensive searches for this decay have been conducted by experiments like Super-Kamiokande in Japan, IMB in the United States, and the Sudbury Neutrino Observatory in Canada. The non-observation of proton decay at the predicted rate has ruled out the minimal, non-supersymmetric version of the Georgi–Glashow model.

Unification scale and coupling constants

In the model, the three coupling constants of the Standard Model are projected to merge at a single energy scale, the unification scale, which is calculated to be approximately \(10^{15}\) GeV. This extrapolation uses the renormalization group equations of quantum field theory. However, precise measurements of the couplings at facilities like CERN and SLAC show that, in the minimal model, they do not quite meet at a single point, a problem resolved by introducing supersymmetry as in the Minimal Supersymmetric Standard Model.

Relation to other grand unified theories

The Georgi–Glashow model is the prototype for subsequent GUTs. It is a subgroup of larger unifying groups like SO(10), which can incorporate a right-handed neutrino and predict neutrino masses. Other alternatives include models based on E6 and Pati–Salam symmetry. While the minimal model is experimentally disfavored, its core ideas and structure remain highly influential in particle physics, motivating ongoing research at laboratories including Fermilab and the planned Future Circular Collider.

Category:Grand Unified Theories Category:Particle physics