Towards predictive flavour models in SUSY SU(5) GUTs with doublet-triplet splitting

TL;DR

This paper explores combining the double missing partner mechanism in SUSY SU(5) GUTs with predictive quark-lepton Yukawa models, analyzing constraints from gauge unification and proton decay, and presenting explicit flavor models.

Contribution

It introduces a second adjoint Higgs field to enhance predictive flavor models in SUSY SU(5) GUTs with doublet-triplet splitting, including detailed superpotentials and decay rate calculations.

Findings

Successful gauge coupling unification constraints derived.

Two explicit flavor models with distinct Yukawa predictions.

Calculated Clebsch-Gordan coefficients for proton decay operators.

Abstract

We discuss how the double missing partner mechanism solution to the doublet-triplet splitting problem in four-dimensional supersymmetric SU(5) Grand Unified Theories (GUTs) can be combined with predictive models for the quark-lepton Yukawa coupling ratios at the GUT scale. It is argued that towards this goal a second SU(5) breaking Higgs field in the adjoint representation is very useful and we discuss all possible renormalizable superpotentials with two adjoint Higgs fields and calculate the constraints on the GUT scale and effective triplet mass from a two-loop gauge coupling unification analysis. Two explicit flavour models with different predictions for the GUT scale Yukawa sector are presented, including shaping symmetries and a renormalizable messenger sector. Towards calculating the rates for proton decay induced by the exchange of colour triplets, the required Clebsch-Gordan coefficients for their couplings are calculated for the possible dimension five and six operators. They are provided in detailed tables in the appendix, together with additional helpful material for GUT flavour model building.