Running quark and lepton parameters at various scales

In light of the latest neutrino oscillation data, we examine whether the leptonic flavor mixing matrix can take on an exact form of tri-bimaximal (TBM), golden-ratio (GR) or bimaximal (BM) mixing pattern at a superhigh-energy scale, where such a mixing pattern could be realized by a flavor symmetry, and become compatible with experimental data at the low-energy scale. Within the framework of the Minimal Supersymmetric Standard Model (MSSM), the only hope for realizing such a possibility is to count on the corrections from the renomalization-group (RG) running. In this work we focus on these radiative corrections, and fully explore the allowed parameter space for each of these mixing patterns. We find that when the upper bound on the sum of neutrino masses Σ ν ≡ m 1 + m 2 + m 3 < 0.23 eV at the 95% confidence level from Planck 2015 is taken into account, none of these mixing patterns can be identified as the leptonic mixing matrix below the seesaw threshold. If this cosmological upper bound on the sum of neutrino masses were relaxed, the TBM and GR mixing patterns would still be compatible with the latest neutrino oscillation data at the 3σ level, but not at the 1σ level. Even in this case, no such a possibility exists for the BM mixing.

Section: General Approachmentioning

confidence: 99%

Viability of exact tri-bimaximal, golden-ratio and bimaximal mixing patterns and renormalization-group running effects

Zhang

Zhou

2016

“…Since the effective triplet mass M dim=5 T receives significant two-loop contributions (cf., for instance, [6]), we have also implemented a numerical two-loop RGE analysis using the following procedure. We start with SM values for the gauge and Yukawa couplings [25] at M Z , run up to to a scale of 1 TeV with the full two-loop SM RGEs and match the SM to the MSSM (including MS to DR scheme conversion). From there we run and match using full two-loop MSSM RGEs and one-loop gauge coupling threshold corrections 5 while step-by-step including all additional multiplets at their mass scale via their contributions to the one-and two-loop gauge coupling RGEs, see appendix B.…”

Section: Jhep09(2014)141mentioning

confidence: 99%

“…which can be checked directly at the GUT scale [25]. In our models we will use the CG factors yτ y b = − 3 2 , yµ ys = 6 and ye…”

Section: Flavour Models With Dmpmmentioning

confidence: 99%

See 1 more Smart Citation

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

Antusch

Varzielas

Maurer

et al. 2014

Self Cite

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.

“…The viablity of the GJ relations is discussed in [33]. The smallness of the down quark mass compared to the bottom quark mass is ascribed to the different couplings and VEVs involved in the ratio y d /y b , for example by assuming a small ratio Σ / Σ 15 1.…”

Section: The Down Sectormentioning

confidence: 99%

A model of quark and lepton mixing

King

2014

We propose a model of quark and lepton mixing based on the tetrahedral A 4 family symmetry with quark-lepton unification via the tetra-colour Pati-Salam gauge group SU(4) P S , together with SU(2) L × U(1) R . The "tetra-model" solves many of the flavour puzzles and remarkably gives ten predictions at leading order, including all six PMNS parameters. The Cabibbo angle is approximately given by θ C ≈ 1/4, due to the tetravacuum alignment (1, 4, 2), providing the Cabibbo connection between quark and lepton mixing. Higher order corrections are responsible for the smaller quark mixing angles and CP violation and provide corrections to the Cabibbo and lepton mixing angles and phases. The tetra-model involves an SO(10)-like pattern of Dirac and heavy right-handed neutrino masses, with the strong up-type quark mass hierarchy cancelling in the see-saw mechanism, leading to a normal hierarchy of neutrino masses with an atmospheric angle in the first octant, θ l 23 = 40 • ± 1 • , a solar angle θ l 12 = 34 • ± 1 • , a reactor angle θ l 13 = 9.0 • ± 0.5 • , depending on the ratio of neutrino masses m 2 /m 3 , and a Dirac CP violating oscillation phase δ l = 260 • ± 5 • .