SO(10) GUT

SO(10) GUT
Name	SO(10) GUT
Type	Grand unified theory
Introduced	1970s
Notable people	Howard Georgi, Abdus Salam, Steven Weinberg, Sheldon Glashow, Graham Ross, Richard Slansky, Hitoshi Murayama, Rabi Mohapatra, Goran Senjanović
Related theories	SU(5), E6, Pati–Salam model, Left–right symmetry, Supersymmetry, String theory
Key concepts	Grand unification, Gauge symmetry, Spinor representation, Seesaw mechanism

SO(10) GUT SO(10) GUT is a class of Grand unified theory proposals embedding the Standard Model gauge group into the Lie group SO(10). It unifies a single family of fermions into a single irreducible representation and offers mechanisms for neutrino masses, baryogenesis, and gauge coupling unification, motivating connections to Supersymmetry, String theory, and collider phenomenology.

Overview

SO(10) models were developed in the context of the post-1964 unification effort by researchers such as Howard Georgi, Sheldon Glashow, Abdus Salam, and Steven Weinberg and were advanced by Graham Ross and Richard Slansky. The framework embeds SU(3)×SU(2)×U(1) into SO(10), accommodates the right-handed neutrino, and relates quark and lepton quantum numbers, connecting to ideas from the Pati–Salam model and larger groups like E6. SO(10) variants interface with MSSM, Left–right symmetry, and Grand Desert paradigms while informing searches at facilities such as the Large Hadron Collider and informing cosmological scenarios tied to Big Bang nucleosynthesis.

Mathematical Structure and Representations

The gauge group SO(10) is a rank-5, real, compact Lie group studied in the tradition of Élie Cartan and classified in the Cartan classification. Its algebra is associated with the D5 Dynkin diagram and admits representations including the vector 10, the adjoint 45, and the spinors 16 and 126. The spinor 16 representation famously contains the Standard Model family: left-handed electron, muon, tau, their neutrinos, and the corresponding quarks together with a sterile right-handed neutrino. Representation theory for SO(10) builds on methods used by Élie Cartan, Weyl group, and later expositions by Richard Slansky. Tensor product decompositions link SO(10) to subgroups like SU(5), Spin(10), and the Pati–Salam model's SU(4)×SU(2)×SU(2), while branching rules guide model-building studied by groups working at CERN, SLAC National Accelerator Laboratory, and Fermilab.

Model Building and Symmetry Breaking

SO(10) model building employs scalar sectors with multiplets such as 10, 45, 54, 126, and 210 to implement spontaneous symmetry breaking to the Standard Model via intermediate steps exemplified by Pati–Salam model or Left–right symmetry. The Higgs structure and vacuum expectation values are arranged to give intermediate gauge groups like SU(5), SU(4)×SU(2)×SU(2), or SU(3)×SU(2)×U(1)×U(1), with classical techniques borrowed from Peter Higgs's mechanism and radiative corrections discussed in work by Howard Georgi and A. Masiero. Supersymmetric extensions leverage soft-breaking sectors analyzed in studies by Rabi Mohapatra, Hitoshi Murayama, and Goran Senjanović, with renormalization group running connecting unification scales studied by collaborations at DESY and KEK.

Fermion Masses, Mixings, and Neutrinos

Yukawa couplings in SO(10) couple fermion spinors to Higgs multiplets (10, 120, 126), producing mass matrices that relate CKM and PMNS parameters. The inclusion of the 126 or 16̄×16̄ channels enables the type-I and type-II Seesaw mechanism for small neutrino masses, building on ideas from Minkowski, Yanagida, Glashow, Mohapatra, and Senjanović. Realistic textures often invoke flavor symmetries studied by research groups at Institut des Hautes Études Scientifiques, Max Planck Institute for Physics, and Perimeter Institute, and confront precision data from Super-Kamiokande, SNO, and Daya Bay. Fitting charged fermion hierarchies uses techniques developed in works by Graham Ross, Stuart Raby, and Alberto Masiero.

Proton Decay and Phenomenological Constraints

SO(10) predicts baryon-number violating processes such as proton decay via heavy gauge bosons or color-triplet Higgs exchange, leading to channels scrutinized by experiments like Super-Kamiokande, Soudan Mine, and future detectors such as Hyper-Kamiokande and DUNE. Predicted lifetimes depend on unification scale and model details; constraints influence choices of intermediate symmetry and supersymmetric spectra considered by groups at CERN and Fermilab. Phenomenological limits also incorporate flavor-changing neutral current bounds from Belle II, LHCb, and collider searches at ATLAS and CMS.

Cosmological Implications and Baryogenesis

SO(10) frameworks offer baryogenesis mechanisms including leptogenesis via decays of heavy right-handed neutrinos, connecting with thermal history topics addressed by Alan Guth and Andrei Linde in inflationary scenarios. Topological defects such as monopoles or cosmic strings may form during symmetry breaking, linked to analyses by Tom Kibble and Alexander Vilenkin, with cosmological bounds from measurements by Planck and WMAP. Dark matter candidates arise in supersymmetric SO(10) variants (neutralino, gravitino) studied by teams at SLAC, CERN, and Kavli Institute for Cosmological Physics.

Experimental Tests and Signatures

Tests of SO(10) include proton decay searches at Super-Kamiokande and proposed Hyper-Kamiokande and DUNE detectors, neutrino oscillation precision at T2K and NOvA, rare decay and flavor measurements at Belle II and LHCb, and direct searches for supersymmetric partners at ATLAS and CMS. Indirect probes come from precision gauge coupling unification fits using data from LEP, Tevatron, and LHC, and cosmological constraints from Planck and BICEP2. Connections to String theory lead to model realizations studied at Institute for Advanced Study and in collaborations with groups at Princeton University and Harvard University.

Category:Grand unified theories