Pati–Salam

Pati–Salam
Name	Pati–Salam model
Introduced	1974
Founders	Jogesh Chandra Pati, Abdus Salam
Type	Grand Unified-like model
Gauge group	SU(4)_{C} × SU(2)_{L} × SU(2)_{R}

Pati–Salam is a unified framework proposed by Jogesh Chandra Pati and Abdus Salam in 1974 that arranges quarks and leptons in common multiplets under an extended color group, aiming to explain charge quantization and fermion family structure. It sits between the Standard Model and larger unification schemes such as SU(5), SO(10), and E6, providing a natural origin for B−L and left–right symmetry that connects to ideas in neutrino mass generation and proton decay. The framework has influenced model-building related to seesaw mechanism, left–right symmetric model, and Peccei–Quinn theory-inspired solutions to the strong CP problem.

History and motivation

The proposal by Jogesh Chandra Pati and Abdus Salam built on earlier concepts from Glashow–Weinberg–Salam model and the successes of Quantum Chromodynamics to unify color and flavor by embedding leptons as a fourth color in an SU(4) group; contemporaneous work on Grand Unified Theory by Howard Georgi and Sheldon Glashow produced SU(5), while subsequent developments by Harvey Fritzsch and Peter Minkowski explored related neutrino mass mechanisms. Motivation drew on anomalies discussed in Adler–Bell–Jackiw anomaly contexts and the desire to account for charge quantization noted by Paul Dirac and formalized in GUT constructions. The Pati–Salam idea interlocks with left–right parity recovery from Lee and Yang parity violation observations and connects to CP violation studies by Kobayashi and Maskawa, inspiring embedding into SO(10) by Georgi, Fritzsch lines and later string-theory embeddings considered by Edward Witten and Michael Green.

Model structure and gauge group

The canonical gauge group is SU(4)_{C} × SU(2)_{L} × SU(2)_{R}, relating to groups studied in Lie algebra classifications and exploited in embeddings into SO(10), E6, and heterotic E8 × E8 string compactifications researched by Gross, Harvey, Martinec, Rohm. SU(4)_{C} unifies Quantum Chromodynamics color triplets with a lepton component analogous to structures in Georgi–Glashow and Pati–Salam-inspired left–right constructions examined alongside Left-right symmetry proposals by Mohapatra and Senjanović. The SU(2)_{L} and SU(2)_{R} factors mirror the electroweak chiral structure from Weinberg, Salam, and Glashow, and the model admits discrete symmetries considered in Parity (physics) restoration and CP symmetry analyses by Sakharov and others. Gauge coupling considerations relate to renormalization group studies by Gross and Wilczek.

Particle content and symmetry breaking

Fermions of one family reside in left- and right-handed multiplets transforming as (4,2,1) and (4,1,2), paralleling family assignments in SO(10) spinors used by Fritzsch and Minkowski. Scalar sectors often include multiplets in (1,2,2), (15,1,1), and (10,1,3) representations similar to Higgs constructions in Georgi–Jarlskog textures and Froggatt–Nielsen flavor models by Froggatt and Nielsen. Symmetry breaking chains to the Standard Model may proceed via intermediate groups such as SU(3)_{C} × SU(2)_{L} × SU(2)_{R} × U(1)_{B-L} studied in Mohapatra–Senjanović papers, or embed into SO(10) breaking paths explored by Babu and Barr. The model naturally accommodates Majorana masses through scalar multiplets enabling the type I seesaw and type II seesaw mechanisms developed by Minkowski, Yanagida, Gell-Mann, Ramond, Slansky, and Mohapatra.

Phenomenological implications

Pati–Salam predicts leptoquark gauge bosons that mediate transitions between quarks and leptons, a feature related to phenomena studied in rare decay searches and flavor physics anomalies reported by collaborations such as LHCb, Belle, and BaBar. The embedding of B-L ties into baryogenesis scenarios of the Sakharov type and leptogenesis frameworks developed by Fukugita and Yanagida. Neutrino mass patterns in Pati–Salam relate to oscillation results from Super-Kamiokande, SNO, and Daya Bay, and flavor textures draw on parameterizations used by Wolfenstein and Pontecorvo. Proton decay channels resemble those in SU(5) and SO(10) analyses by Weinberg and Wilczek–Zee but with different dominant operators discussed in papers by Zee and Langacker. The model impacts electric dipole moment estimates relevant to constraints from ACME and tests of CP violation.

Experimental tests and constraints

Collider searches at the Large Hadron Collider, guided by analyses from ATLAS and CMS, place limits on leptoquark masses and right-handed gauge bosons similar to searches inspired by W'' and Z'' models studied in CDF and D0 analyses at the Tevatron. Low-energy probes from MEG, Mu2e, and COMET constrain charged-lepton-flavor-violation operators discussed in theoretical work by Kuno and Okada. Precision electroweak fits by groups associated with LEP and SLD restrict scalar sector mixings analogous to constraints used in Higgs boson studies by ATLAS and CMS. Neutrinoless double beta decay searches by KamLAND-Zen, GERDA, and EXO constrain Majorana mass contributions predicted in seesaw realizations by Schechter and Valle. Cosmological limits from Planck and big-bang-nucleosynthesis work by Steigman impose bounds on additional relativistic degrees of freedom in extended versions examined by Kolb and Turner.

Extensions and variations

Models extend Pati–Salam via embedding into SO(10), E6, or string-theory constructions by Witten, Candelas, and Kachru, or by adding discrete flavor symmetries studied by Froggatt, Ma, and Altarelli. Supersymmetric versions relate to work by Dimopoulos and Georgi and connect to MSSM phenomenology explored by Nilles and Haber. Extra-dimensional realizations borrow techniques from Randall–Sundrum and Arkani-Hamed, Dimopoulos, Dvali scenarios, while orbifold breaking approaches echo methods of Kawamura and Hall. Recent interest ties Pati–Salam to flavor anomalies discussed by Altmannshofer and to dark-matter model building in lines investigated by Bertone and Feng.

Category:Grand unified theories