Revisiting $\mathrm{SU}(5)$ Yukawa Sectors Through Quantum Corrections

Abstract

This article revisits the validity of tree-level statements regarding the Yukawa sector of various minimal-renormalisable \(SU(5)\) frameworks at the loop level. It is well-known that an \(SU(5)\) model with only the \(45_{\mathrm{H}}\) dimensional irreducible representation~(irrep) contributing to the Yukawa sector is highly incompatible in yielding the low-energy observables. However, this study shows that when one-loop corrections from heavy degrees of freedom are included in the various Yukawa vertices, the model can reproduce the charged fermion mass spectrum and mixing angles within the assumed experimental uncertainty. The fitted Yukawa couplings remain within the perturbative range. The scenario also necessitates mass splitting among various scalars of $45_{\mathrm{H}}$ dimensional irrep, with some of the scalars' mass deviating significantly from the matching scale \((M_{GUT})\), collectively providing substantial threshold corrections. The effect of the lightest scalar on the RGE evolution of the SM parameters has also been considered. It is shown that this scenario reproduces the SM spectrum at low energy. As an extension, the minimal \(SU(5)\) model with only the \(45_{\mathrm{H}}\) irrep is augmented with the \(15_{\mathrm{H}}\)-dimensional irrep, which also successfully reproduces the observed charged and neutral fermion mass spectra. Finally, the study considers an alternative \(SU(5)\) model incorporating both \(5_{\mathrm{H}}\) and \(15_{\mathrm{H}}\) irreps, which also yields the desired fermion mass spectra and mixing angles. This work demonstrates the viability of a minimal \(SU(5)\) Yukawa sector in different setups when quantum corrections are considered.

Version published in Physical Review D. 34 pages with references, 5 tables, and 6 captioned figures. The revised version includes new plots illustrating the RGE effects of the lightest scalar, updated numerical fits, and expanded proton-decay constraints. Conclusions unchanged, textually and presentationally revised

References in corpus (37)

• Physics of leptoquarks in precision experiments and at particle colliders
• Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry
• Proton stability in grand unified theories, in strings, and in branes
• Running Neutrino Mass Parameters in See-Saw Scenarios
• NuFit-6.0: Updated global analysis of three-flavor neutrino oscillations
• Scalar leptoquarks from GUT to accommodate the $B$-physics anomalies
• Search for Proton Decay via $p\to \nu K^{+}$ using 260 kiloton$\cdot$year data of Super-Kamiokande
• Fermion Masses in SO(10) Models
• Renormalizable Adjoint SU(5)
• From Minimal to Realistic Supersymmetric SU(5) Grand Unification
• Fits to SO(10) Grand Unified Models
• Proton Decay in a Consistent Supersymmetric SU(5) GUT Model
• Running Neutrino Masses, Leptonic Mixing Angles and CP-Violating Phases: From $M_{\mathrm{Z}}$ to ${\Lambda }_{\mathrm{GUT}}$
• Leptoquark mechanism of neutrino masses within the grand unification framework
• A Search for Nucleon Decay via $n\to \bar{\nu }{\pi }^0$ and $p\to \bar{\nu }{\pi }^{+}$ in Super-Kamiokande
• Neutrino Mixings and Fermion Masses in Supersymmetric SU(5)
• Yukawa Sector of Minimal SO(10) Unification
• PyR@TE 3
• Predictions from type II see-saw mechanism in SU(5)
• Fermion Masses and the UV Cutoff of the Minimal Realistic SU(5)
• Unification versus proton decay in SU(5)
• SU(5) Unification with TeV-scale Leptoquarks
• Light vector-like fermions in a minimal SU(5) setup
• Leptogenesis and fermion mass fit in a renormalizable $SO(10)$ model
• Renormalizable SU(5) Unification
• Realistic Fermion Masses and Nucleon Decay Rates in SUSY SU(5) with Vector-Like Matter
• Scalar leptoquark in SU(5)
• Viable quark-lepton Yukawa ratios and nucleon decay predictions in $SU(5)$ GUTs with type-II seesaw
• Realistic model for SU(5) grand unification
• Seesaw Scale, Unification, and Proton Decay
• Nucleon decay in a minimal non-SUSY GUT with predicted quark-lepton Yukawa ratios
• Quark-lepton Yukawa ratios and nucleon decay in SU(5) GUTs with type-III seesaw
• Explaining Why the u and d Quark Masses are Similar
• Flavor physics in SU(5) GUT with scalar fields in the 45 representation
• Gauge coupling unification and proton decay via 45 Higgs boson in SU(5) GUT
• Quantum corrections and the minimal Yukawa sector of $SU(5)$
• Exploring flavour space of an economical SU(5) GUT in future proton decay measurements