Pati–Salam model

Pati–Salam model
Name	Pati–Salam model
Type	Grand unified theory
Introduced	1974
Proponents	Jogesh Pati, Abdus Salam
Gauge group	SU(4) × SU(2)_L × SU(2)_R

Pati–Salam model The Pati–Salam model is a proposed extension of the Standard Model that unifies quarks and leptons within a larger gauge group and introduces left–right symmetry, developed by Jogesh Pati and Abdus Salam in 1974. It aims to address anomalies in grand unification proposals by linking features of Georgi–Glashow schemes with left–right symmetric frameworks related to work by Mohapatra and Senjanović. The model has motivated searches in experiments such as Large Hadron Collider programs and informed theoretical studies in supersymmetry, string theory, and neutrino physics.

Introduction

The model organizes fermions into multiplets of an extended gauge symmetry SU(4) × SU(2)_L × SU(2)_R, connecting ideas from Georgi–Glashow model, SO(10), and Left–right symmetry frameworks influenced by Sheldon Glashow and Howard Georgi. It proposes lepton number as a fourth color, inspired by early proposals by Pati and Salam that echo patterns in Gell-Mann’s flavor symmetries and in explorations by Harari and Shupe. The structure preserves features relevant for proton decay constraints considered in analyses by Wilczek and Weinberg and offers mechanisms compatible with seesaw mechanism ideas attributed to Minkowski and Yanagida.

Gauge Structure and Symmetry Breaking

The gauge group SU(4) × SU(2)_L × SU(2)_R extends the SU(3) color of QCD to SU(4) by treating leptons as a fourth color, paralleling symmetry considerations found in Pati and Salam’s contemporaries. The SU(2)_R factor restores parity at high energies similar to proposals by Mohapatra and Senjanović and interacts with left-handed SU(2)_L reminiscent of Glashow–Weinberg electroweak unification. Symmetry breaking chains often reduce the group to SU(3) × SU(2) × U(1) via intermediate stages analogous to SO(10) breaking routes studied by Fritzsch and Minkowski. The breaking scales are constrained by experimental limits from Super-Kamiokande, LHCb, and ATLAS searches for heavy gauge bosons and rare processes analyzed by groups including CMS.

Fermion Content and Representations

Fermions are placed in left- and right-handed multiplets transforming as (4,2,1) and (4,1,2), grouping generations in a manner analogous to representations in SO(10) and reflecting classification schemes used by Georgi and Glashow. Each family unifies quarks and leptons similarly to how Gell-Mann organized hadrons, allowing charge quantization related to patterns discussed by Weinberg and Salam. The model accommodates three generations as observed by experiments at CERN and Fermilab and connects to flavor studies led by Cabibbo, Kobayashi, and Maskawa through mass mixing matrices. Right-handed neutrinos naturally appear, tying into neutrino oscillation results from Super-Kamiokande and SNO and theoretical seesaw implementations related to Minkowski and Yanagida.

Higgs Sector and Mass Generation

The Higgs sector employs multiplets that break SU(4) and SU(2)_R at high scales and SU(2)_L at the electroweak scale, paralleling scalar choices in SO(10) and Left–right symmetric model studies by Mohapatra. Typical scalar representations include fields analogous to those used in analyses by Senjanović and Deshpande for parity restoration and for generating Majorana masses for right-handed neutrinos, implementing variants of the Type I seesaw explored by Gell-Mann collaborators. Yukawa couplings linking fermion multiplets to scalars produce quark and lepton masses and mixing matrices similar to textures investigated by Fritzsch and Ramond. Radiative corrections and threshold effects, topics developed by Weinberg and Dimopoulos, affect unification predictions and Higgs mass parameters, with implications probed by experimental collaborations such as ATLAS and CMS.

Phenomenological Implications

The model predicts new gauge bosons (often denoted W_R and heavy SU(4) gauge bosons) whose signatures overlap with searches at Large Hadron Collider and flavor experiments like LHCb; limits derive from studies by ATLAS, CMS, and Belle II. It offers mechanisms for small neutrino masses linking to oscillation results from SNO, KamLAND, and Daya Bay, and has implications for leptogenesis scenarios considered by Fukugita and Yanagida. Proton stability constraints relate to bounds from Super-Kamiokande and are cross-referenced in grand unification analyses by Langacker and Murayama. Flavor-changing neutral currents and rare decays examined in work by Buras and Isidori constrain parameter space, while cosmological consequences intersect with studies by Kolb and Turner on baryogenesis and dark matter searches by Planck and Fermi Gamma-ray Space Telescope collaborations.

Variants and Unification Connections

Variants include supersymmetric versions inspired by Dimopoulos and Susskind and embeddings into larger groups such as SO(10) and E6 studied by Georgi and Gursey, connecting to string-derived constructions explored by Green and Schwarz. Left–right symmetric descendants relate to work by Mohapatra and Senjanović, and non-supersymmetric unifications draw on renormalization group analyses by Jones and Weinberg. The model’s compatibility with proton decay limits, gauge coupling unification studied by Langacker, and neutrino mass generation mechanisms continues to motivate phenomenology in collaborations like CERN and theoretical programs at institutions such as Perimeter Institute and Institute for Advanced Study.

Category:Grand Unified Theories