No-go theorems for R symmetries in four-dimensional GUTs

103

Abstract:We propose a renormalisable model based on A 4 family symmetry with an SU(5) grand unified theory (GUT) which leads to the minimal supersymmetric standard model (MSSM) with a two right-handed neutrino seesaw mechanism. Discrete Z 9 × Z 6 symmetry provides the fermion mass hierarchy in both the quark and lepton sectors, while Z R 4 symmetry is broken to Z R 2 , identified as usual R-parity. Proton decay is highly suppressed by these symmetries. The strong CP problem is solved in a similar way to the Nelson-Barr mechanism. We discuss both the A 4 and SU(5) symmetry breaking sectors, including doublet-triplet splitting, Higgs mixing and the origin of the µ term. The model provides an excellent fit (better than one sigma) to all quark and lepton (including neutrino) masses and mixing with spontaneous CP violation. With the A 4 vacuum alignments, (0, 1, 1) and (1, 3, 1), the model predicts the entire PMNS mixing matrix with no free parameters, up to a relative phase, selected to be 2π/3 from a choice of the nine complex roots of unity, which is identified as the leptogenesis phase. The model predicts a normal neutrino mass hierarchy with leptonic angles θ l 13 ≈ 8.7 • , θ l 12 ≈ 34 • , θ l 23 ≈ 46 • and an oscillation phase δ l ≈ −87 • .

Section: Fieldmentioning

confidence: 82%

Towards a complete A4 × SU(5) SUSY GUT

Björkeroth

Anda

Varzielas

et al. 2015

103

“…There is a claim [27] that the MSSM with an additional unbroken R-symmetry can not be obtained from the spontaneous breaking of a…”

Section: Jhep09(2014)141mentioning

confidence: 99%

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

Antusch

Varzielas

Maurer

et al. 2014

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.

“…because the saxion expectation value sets the gauge coupling [13,14]. But already in typical string compactifications, there is no sense of unification in a semisimple group.…”

Section: Jhep01(2014)011mentioning

confidence: 99%

Discrete R symmetries and anomalies

Dine

Monteux

2014

Abstract:We comment on aspects of discrete anomaly conditions focussing particularly on R symmetries. We review the Green-Schwarz cancellation of discrete anomalies, providing a heuristic explanation why, in the heterotic string, only the "model-independent dilaton" transforms non-linearly under discrete symmetries; this argument suggests that, in other theories, multiple fields might play a role in anomaly cancellations, further weakening any anomaly constraints at low energies. We provide examples in open string theories of non-universal discrete anomalies at low energies. We then consider the fact that R symmetries are necessarily broken at low energies. We exhibit dynamical models, in which fields charged under the Standard Model gauge group (for example, a doublet and a triplet) gain roughly equal masses, but where the doublet and the triplet possess different discrete charges and the low-energy anomaly conditions fail.