Georgi–Glashow model

Georgi–Glashow model
Cjean42 · CC BY-SA 3.0 · source
Name	Georgi–Glashow model
Introduced	1974
Originators	Howard Georgi; Sheldon Glashow
Type	Grand unified theory
Gauge group	Georgi–Glashow model (SU(5))

Georgi–Glashow model The Georgi–Glashow model is a prototype Grand Unified Theory proposed in 1974 by Howard Georgi and Sheldon Glashow that embeds the Standard Model gauge group into an SU(5) gauge symmetry. It unifies electroweak and strong interactions at high energy scales and predicts novel gauge bosons and baryon-number violating processes. The model motivated searches at facilities such as CERN, Fermilab, and informed theoretical programs at institutions like SLAC National Accelerator Laboratory and Princeton University.

Introduction

The original proposal by Howard Georgi and Sheldon Glashow aimed to unify SU(3) color and SU(2) weak isospin with U(1) hypercharge into an SU(5) gauge group, drawing on ideas from earlier work by Hermann Weyl, Oskar Klein, and Paul Dirac. It posits a single gauge coupling at a grand unification scale influenced by renormalization group running first computed in contexts developed by Kenneth Wilson and David Gross. The formulation generated intense theoretical activity involving researchers at Harvard University, Massachusetts Institute of Technology, Yale University, and University of Cambridge to confront predictions such as gauge boson spectra, fermion embedding, and proton decay, shaping programs at experimental collaborations including Super-Kamiokande, IMB, and SNO.

Gauge structure and field content

The model is based on a simple Lie group SU(5) with adjoint gauge fields analogous to constructions by Élie Cartan and uses representations studied in the classification by Cartan. Gauge bosons live in the 24-dimensional adjoint representation, decomposing under the Standard Model subgroup into octet gluons associated with QCD, triplet weak bosons tied to electroweak symmetry, and heavy X and Y bosons that mediate baryon-number violation; these features were analyzed further in work at CERN and by theorists including Steven Weinberg and Abdus Salam. The scalar sector contains a 24-dimensional Higgs field for breaking SU(5) to the Standard Model and a 5-dimensional Higgs to break electroweak symmetry, drawing on symmetry-breaking techniques similar to those used by Peter Higgs and François Englert.

Spontaneous symmetry breaking and Higgs mechanism

Spontaneous symmetry breaking is realized by a vacuum expectation value of the adjoint 24 representation that reduces SU(5) to SU(3)×SU(2)×U(1), paralleling mechanisms in the Higgs mechanism developed by Peter Higgs and Gerald Guralnik. The residual electroweak symmetry is subsequently broken by a 5 representation acquiring a vacuum expectation value, mirroring the scalar sector phenomenology studied in contexts at University of Oxford and Caltech. The masses of X and Y gauge bosons, computed via gauge coupling normalization influenced by renormalization group analysis by Howard Georgi and colleagues, set the grand unification scale relevant for proton decay lifetimes considered by experimental groups at Super-Kamiokande and Kamiokande.

Fermion representations and Yukawa couplings

Fermions of a single Standard Model family are embedded in the 10 and 5̄ representations of SU(5), a structure noted in early grand unification literature by Howard Georgi and studied in model-building by Savas Dimopoulos and Stuart Raby. The 10 contains the up-type quark singlets and quark doublets related to quark mixing investigated by Nicola Cabibbo, Makoto Kobayashi, and Toshihide Maskawa, while the 5̄ contains down-type quarks and lepton doublets relevant to experiments at Brookhaven National Laboratory and DESY. Yukawa couplings derive from SU(5)-invariant operators producing mass relations such as m_b = m_τ at the unification scale, relations examined in precision studies by groups at CERN and SLAC. Attempts to reproduce realistic fermion masses and mixings motivated extensions by researchers at Stanford University and University of Chicago.

Proton decay and phenomenological implications

A hallmark prediction is proton decay mediated by heavy X and Y bosons, producing modes like p → e+ π0, motivating searches by Super-Kamiokande, IMB, and Soudan Underground Mine State Park collaborations. Early estimates by Sheldon Glashow and contemporaries predicted lifetimes in tension with nonobservations, prompting refinements from renormalization group analyses by Georgi and Howard Georgi's collaborators and influencing detector designs at Kamiokande and Sudbury Neutrino Observatory. The model also yields neutrino mass textures and baryogenesis scenarios that connect to work by Andrei Sakharov and experimental neutrino programs at NOνA and DUNE. Electroweak precision data from Particle Data Group compilations and collider searches at Large Hadron Collider placed further constraints, guiding theoretical searches at Perimeter Institute and Institute for Advanced Study.

Extensions and unification contexts

The Georgi–Glashow construction spurred extensions including supersymmetric SU(5) developed by Howard Georgi and Savas Dimopoulos, SO(10) unification championed by Harvey Georgi and Rabi Mohapatra, and higher-rank frameworks explored by Edward Witten and Michael Green. Supersymmetric extensions were motivated by hierarchy problem discussions involving Leonard Susskind and by results from LEP and Tevatron experiments. String theory embeddings by David Gross and Joseph Polchinski and studies at Institute for Advanced Study linked SU(5) patterns to compactification schemes used by Cumrun Vafa. Modern model-building incorporates flavor symmetries investigated at Institute for Nuclear Theory and grand desert scenarios constrained by precision cosmology from Planck (spacecraft) and dark matter searches at XENON collaborations.

Category:Grand unified theories