Flavour in $SU(5)$ Finite Grand Unified Models

Abstract

Four $SU(5)$ $N=1$ supersymmetric models which exhibit $S_3$ and/or $Z_N$ symmetries are studied, that are finite to two or all loops, and their corresponding mass matrices. The first is an all-loop finite model based on an $S_3\times Z_3\times Z_2$ flavour symmetry, which leads to phenomenologically nonviable mass matrices. The remaining models, based on cyclic symmetries, show various mass textures, some of which are phenomenologically promising. For the two-loop finite models, the parametric solutions to the finiteness conditions determine completely some of the Yukawa couplings, and lead to a restricted range of values for other ones at the GUT scale, with a considerable reduction in the number of free parameters. One particular solution of the two-loop models shows an enhanced symmetry, leading to an all-loop finite model, which has a significant parameter reduction and could in principle reproduce the observed quark masses and mixing pattern. In this case the finiteness conditions determine the absolute value of all the Yukawa couplings at the unification scale. Finally, the minimum number of phases in the mass matrices and their position are determined, a task not previously done in Finite Unified Theories, which contributes towards the reduction of parameters and a better understanding of the Yukawa couplings. the Yukawa couplings.

42 pages, no figures. Modified abstract, extended introduction and conclusions, added references, and corrected typos. This version corresponds to the published paper in Fortschr. Phys

References in corpus (41)

• Non-Abelian Discrete Symmetries in Particle Physics
• Proton stability in grand unified theories, in strings, and in branes
• Updated Values of Running Quark and Lepton Masses
• Neutrino Masses and Mixings from Supersymmetry with Bilinear R--Parity Violation: A Theory for Solar and Atmospheric Neutrino Oscillations
• Flavor structures of charged fermions and massive neutrinos
• Soft supersymmetry breaking and finiteness
• Neutrino Masses and Mixing Angles in SUSY-GUT Theories with explicit R-Parity Breaking
• The Flavor Symmetry
• Unification and Fermion Mass Structure
• The Gaugino β-Function
• Lepton masses, mixings and FCNC in a minimal S_3-invariant extension of the Standard Model
• Renormalisation Invariance and the Soft $\beta$-Functions
• Further all-loop results in softly-broken supersymmetric gauge theories
• Quark sector of S3 models: classification and comparison with experimental data
• Constraints on Finite Soft Supersymmetry-Breaking Terms
• Constraints on Finite Soft Supersymmetry Breaking Terms
• RG invariant solutions for the soft supersymmetry breaking parameters
• The $S_3$ flavour symmetry: Neutrino masses and mixings
• Perturbative Unification of Soft Supersymmetry--Breaking Terms
• Gauge-Yukawa Unification in Asymptotically Non-free Theories
• All-order Finiteness in N=1 SYM Theories: Criteria and Applications
• Testing Supergravity Grand Unification at Future Accelerator and Underground Experiments
• Finiteness of Soft Terms in Finite N=1 SUSY Gauge Theories
• Finite Grand Unified Theories and the Quark Mixing Matrix
• Exploring Softly Broken SUSY Theories via Grassmannian Taylor Expansion
• Softly Broken Finite Supersymmetric Grand Unified Theory
• Confronting Finite Unified Theories with Low-Energy Phenomenology
• Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory
• Can Supersymmetric Loops Correct the Fermion Mass Relations in SU(5)?
• Finite Theories and the SUSY Flavor Problem
• Reduction of Couplings and its application in Particle Physics
• Resurrecting the minimal renormalizable supersymmetric SU(5) model
• Suppression of Higgsino mediated proton decay by cancellations in GUTs and strings
• Finding a unique texture for quark mass matrices
• Bilinear R-parity violating supersymmetry under the light of neutrino oscillation, higgs and flavor data
• Finite Theories Before and After the Discovery of a Higgs Boson at the LHC
• Updates and New Results in Models with Reduced Couplings
• Probing Unified Theories with Reduced Couplings at Future Hadron Colliders
• Transports of Disordered Carbon Nanotubes with Long Range Coulomb Interaction
• Effects of Supersymmetric Threshold Corrections on High-Scale Flavor Textures
• From Veltman's conditions to Finite Unification

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