Georgi–Jarlskog

Georgi–Jarlskog
Name	Georgi–Jarlskog
Field	Particle physics, Theoretical physics
Known for	Georgi–Jarlskog mass relations
Notable works	Georgi and Jarlskog (1979)
Institutions	Harvard University, CERN, University of Stockholm

Georgi–Jarlskog

The Georgi–Jarlskog proposal is a set of specific Yukawa coupling and mass matrix relations introduced to relate quark and lepton masses within Grand Unified Theory frameworks, aiming to reconcile observed charged lepton and down-type quark mass patterns. The idea emerged in the context of SU(5), SO(10), and related unified schemes and influenced subsequent work in flavor physics, neutrino physics, and model building in the late 20th century. It has motivated tests involving Cabibbo–Kobayashi–Maskawa matrix, mass renormalization, and supersymmetry-augmented constructions.

Background

The origin of the Georgi–Jarlskog relations traces to efforts by practitioners in particle physics to embed Standard Model fermion masses in larger symmetry structures such as SU(5), SO(10), and E6. Early inputs included empirical patterns from measurements at facilities like CERN, SLAC National Accelerator Laboratory, and Fermilab, and theoretical constraints from pioneers such as Georgi, Howard, Jarlskog, Cecilia, Weinberg, Steven, Georgi, Howard's colleagues, and contemporaries in flavor symmetry model building. The relations were developed amid parallel approaches including Fritzsch textures, texture zeros, Froggatt–Nielsen mechanism, and Georgi–Glashow unification, while being tested against running with renormalization group equations influenced by work from Babu, K.S. and Raby, Stuart.

Georgi–Jarlskog Mass Relations

The core Georgi–Jarlskog pattern proposes modified grand-unified relations between down quark and charged lepton masses at the unification scale, replacing naive equalities from minimal SU(5) with factors such as 3 to accommodate empirical hierarchies. Typical relations include m_s ≈ m_μ/3 and m_d ≈ 3 m_e when evaluated at a high scale after accounting for renormalization group evolution driven by Quantum Chromodynamics and Quantum Electrodynamics effects. These relations were presented alongside proposals for specific Higgs representations and couplings that produce Clebsch–Gordan coefficients required by the pattern, drawing on algebraic structures known from group theory applied to Grand Unified Theory representations.

Theoretical Framework and Derivation

Derivations embed the relations within unified models where fermions reside in representations such as the 5 and 10 of SU(5) or the 16 of SO(10), and where Higgs fields transform as 5, 45, or 126 representations to generate needed Clebsch factors. The mechanism exploits nontrivial Yukawa contractions and antisymmetric couplings studied in the context of representation theory of Lie algebras and employs techniques similar to those used in analyses by Georgi, Howard, Jarlskog, Cecilia, Fritzsch, Harald, and Harari, H. to obtain off-diagonal texture structures. Implementation often invokes the Froggatt–Nielsen mechanism with heavy messenger fields and horizontal symmetries like U(1) or discrete groups familiar from analyses by Ishimori, H. and Altarelli, Guido to generate hierarchical entries. Radiative corrections and threshold effects at scales associated with supersymmetry breaking or intermediate scalars, as studied in work by Dimopoulos, S. and Susskind, Leonard, are incorporated via renormalization group flow computations pioneered by Machacek, M.E. and Babu, K.S..

Phenomenological Implications

If realized, the Georgi–Jarlskog relations influence low-energy observables including charged lepton mass ratios, down-type quark masses, and mixing parameters observable in flavor-changing neutral current processes explored at LHCb, Belle II, and BaBar. They affect predictions for proton decay branching ratios in unified setups tested at detectors like Super-Kamiokande and proposed experiments such as DUNE and Hyper-Kamiokande, since Higgs representations that generate the Clebsch factors can mediate baryon-number violating operators. The pattern constrains model-building choices relevant to leptogenesis scenarios framed by authors such as Fukugita, M. and Yanagida, T., and interacts with neutrino mass models developed by Minkowski, P. and Mohapatra, R.N..

Experimental Tests and Constraints

Testing requires extrapolation of low-energy masses to high scales using renormalization group equations that include inputs from Quantum Chromodynamics measured at LEP and Tevatron and electroweak parameters from Particle Data Group. Precision determinations of quark masses from lattice computations by collaborations such as HPQCD and RBC-UKQCD, along with charged lepton masses measured in experiments like LEP and storage-ring determinations, provide boundary conditions. Nonobservation of predicted proton decay modes constrains Higgs representations and coupling magnitudes, while flavor observables from LHCb, NA62, and MEG set limits on off-diagonal structures that could accompany Georgi–Jarlskog setups. Global fits performed by groups including CKMfitter and UTfit are used to test consistency with CKM matrix data.

Extensions and Variations

Extensions incorporate Georgi–Jarlskog-style Clebsch factors into SO(10) constructions, flavor symmetry models based on discrete groups such as A4 or S4, and supersymmetric frameworks like MSSM and SUSY GUTs to improve naturalness and accommodate neutrino sectors, drawing on work by King, S.F. and Altarelli, Guido. Variations replace single Clebsch factors with textures emerging from higher-dimensional operators in string theory embeddings studied in contexts like heterotic string model-building and F-theory GUT constructions by researchers including Vafa, Cumrun and Beasley, C.. Modular symmetry approaches and non-Abelian horizontal symmetries have produced alternative derivations consistent with modern fits from Planck-era cosmology and collider bounds from ATLAS and CMS.

Category:Particle physics