SO(10) grand unified theory

SO(10) grand unified theory
Name	SO(10) grand unified theory
Group	SO(10)
Introduced	1975
Proponents	Georgi, Fritzsch, Minkowski

SO(10) grand unified theory is a proposed unification framework that embeds the Standard Model gauge groups into a single simple Lie group, aiming to unify electroweak and strong interactions within a single symmetry. Developed in the mid-1970s contemporaneously with models by Howard Georgi, Sheldon Glashow, and related work by Harald Fritzsch and Pietro Minkowski, it seeks to explain charge quantization, family structure, and neutrino masses while connecting to ideas from Grand Unified Theory, Supersymmetry, and early String theory model building.

Introduction

SO(10) models arose in the era of unified theories alongside proposals by Howard Georgi and Sheldon Glashow for SU(5) Grand Unified Theory and were influenced by neutrino mass proposals from Pietro Minkowski. The framework fits within the broader historical development involving Gerard 't Hooft, Murray Gell-Mann, and the exploration of anomaly cancellation related to work by Edward Witten and Alberto Salvio. SO(10) attracted interest in studies by groups at institutions like CERN, Fermilab, and SLAC National Accelerator Laboratory and has been connected to phenomenology examined at collaborations such as ATLAS and CMS.

Group structure and representations

The gauge algebra of SO(10) is a rank-5 Lie algebra related to the classical group studied in mathematical physics by Élie Cartan. Its 45-dimensional adjoint representation parallels analyses by Weyl and later classification work by Dynkin, with root structures catalogued in the Cartan matrix formalism used in texts by Peter Goddard and David Olive. Fundamental representation choices include the 10, 16, 45, 54, 120, 126, and 210 multiplets; the 16-dimensional spinor representation famously accommodates a full Standard Model family, a structure analyzed in model-building papers from groups at Princeton University and Harvard University. Decompositions under subgroups like SU(5), SU(4)_C (Pati–Salam), and SU(3)_C×SU(2)_L×U(1)_Y are standard in reviews by researchers at KEK and INFN.

Fermion embedding and Yukawa couplings

Each generation of fermions fits in a single 16 spinor, unifying quarks and leptons in a manner reminiscent of family unification explored by Wolfgang Pauli-era algebraists and later by Georgi and Glashow. Right-handed neutrinos appear naturally, linking to seesaw discussions by Mohapatra and Gell-Mann. Yukawa sectors use Higgs representations (10, 120, 126) to generate mass matrices; model-building approaches by groups including University of Chicago and Massachusetts Institute of Technology address texture zeros and flavor symmetries informed by work from Fritzsch and Harvey B. Newman. Grand unification links to renormalization group studies performed by teams at Brookhaven National Laboratory and computational methods developed in collaborations like CERN–DESY.

Symmetry breaking and Higgs sectors

Symmetry breaking chains down to the Standard Model proceed through intermediate subgroups such as Pati–Salam, SU(5), or left–right symmetric groups studied in depth by Mohapatra and Senjanović. Higgs multiplets in 45, 54, 126, and 210 representations drive breaking patterns; vacuum expectation value analyses draw on techniques from Yoichiro Nambu and Jeffrey Goldstone, and subsequent effective potential calculations follow methods advanced by Steven Weinberg and Sidney Coleman. Supersymmetric SO(10) uses soft-breaking terms developed in the context of Minimal Supersymmetric Standard Model studies by Howard Haber and Gordon Kane, while non-supersymmetric variants recall renormalization work by Kenneth Wilson.

Proton decay and experimental constraints

Proton decay predictions arise from baryon-number-violating operators mediated by heavy gauge or Higgs bosons, a topic central to experimental searches at detectors like Super-Kamiokande, SNO, and proposed facilities inspired by Kamiokande and Hyper-Kamiokande. Lifetime limits constrain mass scales informed by computations from groups at Fermilab and KEK; limits challenge minimal non-supersymmetric scenarios similar to tensions seen in SU(5) analyses by Georgi and Glashow. Collider bounds from LHC experiments (ATLAS, CMS) and precision electroweak data from LEP further restrict parameter space, prompting alternative architectures in research from Perimeter Institute and Institute for Advanced Study.

Neutrino masses and seesaw mechanisms

SO(10) naturally contains right-handed neutrinos enabling Type I seesaw mechanisms originally proposed by Minkowski and elaborated by Gell-Mann, Ramond, and Slansky. Type II seesaw and hybrid scenarios involve triplet Higgs fields tied to works by Mohapatra and Senjanović and analyses performed at institutions like Caltech and Rutgers University. Leptogenesis proposals linking baryogenesis via CP-violating decays of heavy neutrinos connect to studies by A. D. Sakharov and phenomenological treatments in papers from groups at CERN and Harvard University.

Cosmological and phenomenological implications

SO(10) scenarios impact early-universe cosmology through monopole production and phase transitions analyzed in contexts developed by Alexander Vilenkin and Andrei Linde. Connections to dark matter candidates emerge in supersymmetric extensions studied at SLAC and dark-sector model papers from MIT collaborations. Flavor and CP violation predictions engage experimental programs at Belle II, BaBar, and neutrino facilities like T2K and NOvA, while grand unification ideas intersect with string compactification efforts by Edward Witten and Cumrun Vafa at institutions including Princeton University and Harvard University.

Category:Grand unified theory