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

Abstract

We discuss how the double missing partner mechanism solution to the doublettriplet 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 ClebschGordan 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.

Towards a complete A4 × SU(5) SUSY GUT

“…Such a spontaneous CP violating scenario had been proposed previously in order to account for the smallness of CP violation in the soft SUSY sector [19,20]. We also employ a Z R 4 discrete R-symmetry (as the origin of MSSM R-parity, as in [21]) and a missing partner (MP) mechanism [22,23] for doublet-triplet splitting as recently advocated for flavoured GUTs in [24]. The model predicts very sparse lepton and down-type quark Yukawa matrices, with five texture zeroes, and Yukawa elements involving simple SU(5) Clebsch-Gordan (CG) ratios of 4/9 and 9/2 for the first and second families, with m τ /m b = 1 for the third family, all in excellent agreement with their experimental values run up to the GUT scale [25,26].…”

“…The resulting effective Yukawa matrices are, schematically: Furthermore, because the underlying renormalisable theory is known, the diagrams in figure 2 are the only contributions for each family. The SU(5) contractions and associated CG coefficients appearing for each family are unique [24][25][26]. With the GUT scale symmetry breaking as discussed in section 4, each of the scalars here get a VEV with the group JHEP06(2015)141 structure:…”

“…Although one could alternatively introduce the double MP mechanism [63] as demonstrated in [24], here we limit ourselves to describing how the MP mechanism is implemented with the fields listed in table 6. We have a superpotential…”

“…The most dangerous processes come from the "dimension 5" operators T T T F (for a discussion of dimension 6 operators we refer the reader to [24]). The "dimension 5" operators are forbidden by the symmetries of the model, but related higher order operators of the following form are allowed: 10) where the extra superfields shown are needed for such terms to be invariant under the symmetries.…”

Predictions from a flavour GUT model combined with a SUSY breaking sector

“…It has recently been demonstrated that such models can be combined with suitable GUT symmetry breaking sectors in predictive theory frameworks [2] which can also resolve the doublet-triplet (DT) splitting challenge in GUTs. Since models for W mat and W fl often rely on R symmetry, it has also been discussed in [2] how spontaneous GUT and R symmetry breaking can be realized with discrete R symmetries Z R n . In this work, we investigate how to combine W mat and W fl with a superpotential W SUSY for SUSY breaking in the framework of supergravity.…”