Francisco J. de Anda

Towards a complete A4 × SU(5) SUSY GUT

A bstractWe propose a renormalisable model based on A4 family symmetry with an SU(5) grand unified theory (GUT) which leads to the minimal supersymmetric standard model (MSSM) with a ℤ9 × ℤ6 symmetry provides the fermion mass hierarchy in both the quark and lepton sectors, while ℤ4R symmetry is broken to ℤ2R, identified as usual R-parity. Proton decay is highly sup-pressed by these symmetries. The strong CP problem is solved in a similar way to the Nelson-Barr mechanism. We discuss both the A4 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 neu-trino) masses and mixing with spontaneous CP violation. With the A4 vacuum alignments, (0, 1, 1) and (1, 3, 1), the model predicts the entire PMNS mixing matrix with no free pa-rameters, 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 θ13ι ≈ 8.7∘, θ12ι ≈ 34∘, θ23ι ≈ 46∘ and an oscillation phase δι ≈ − 87∘.

Leptogenesis in minimal predictive seesaw models

A bstractWe estimate the Baryon Asymmetry of the Universe (BAU) arising from leptogenesis within a class of minimal predictive seesaw models involving two right-handed neutrinos and simple Yukawa structures with one texture zero. The two right-handed neutrinos are dominantly responsible for the “atmospheric” and “solar” neutrino masses with Yukawa couplings to (νe, νμ, ντ) proportional to (0, 1, 1) and (1, n, n − 2), respectively, where n is a positive integer. The neutrino Yukawa matrix is therefore characterised by two proportionality constants with their relative phase providing a leptogenesis-PMNS link, enabling the lightest right-handed neutrino mass to be determined from neutrino data and the observed BAU. We discuss an SU(5) SUSY GUT example, where A4 vacuum alignment provides the required Yukawa structures with n = 3, while a ℤ9

\Delta(27) \times SO(10)

{\mathrm{\mathbb{Z}}}_9

Leptogenesis in a Δ(27) × SO(10) SUSY GUT

symmetry fixes the relatives phase to be a ninth root of unity.

A natural S 4 × SO(10) model of flavour

We propose a renormalizable model based on Δ(27) family symmetry with an SO(10) grand unified theory leading to a novel form of spontaneous geometrical CP violation. The symmetries, including Δ(27) and Z9×Z12×ZR4, are broken close to the grand unified theory breaking scale to yield the minimal supersymmetric standard model with the standard R parity. SO(10) is broken via SU(5) with doublet-triplet splitting achieved by a version of the Dimopoulos-Wilczek (missing vacuum expectation value) mechanism. Low-scale Yukawa structure is dictated by the coupling of matter to Δ(27) antitriplets ¯ϕ of which the vacuum expectation values are aligned in the constrained sequential dominance 3 directions by the superpotential. Light physical Majorana neutrinos masses emerge from a specific implementation of the seesaw mechanism within SO(10). The model predicts a normal neutrino mass hierarchy with the best-fit lightest neutrino mass between 0.32 and 0.38 meV, CP-violating oscillation phase δl≈(275–280)°, and the remaining neutrino parameters all within 1σ of their best-fit experimental values.

Left–right model from gauge-Higgs unification with dark matter

A bstractAlthough SO(10) Supersymmetric (SUSY) Grand Unification Theories (GUTs) are very attractive for neutrino mass and mixing, it is often quite difficult to achieve successful leptogenesis from the lightest right-handed neutrino N1 due to the strong relations between neutrino and up-type quark Yukawa couplings. We show that in a realistic model these constraints are relaxed, making N1 leptogenesis viable. To illustrate this, we calculate the baryon asymmetry of the Universe YB from flavoured N1 leptogenesis in a recently proposed Δ(27) × SO(10) SUSY GUT. The flavoured Boltzmann equations are solved numerically, and comparison with the observed YB places constraints on the allowed values of right-handed neutrino masses and neutrino Yukawa couplings. The flavoured SO(10) SUSY GUT is not only fairly complete and predictive in the lepton sector, but can also explain the BAU through leptogenesis with natural values in the lepton sector albeit with some tuning in the quark sector.

Higgs decay into two photons from a 3HDM with flavor symmetry

A bstractWe propose a natural S4 × SO(10) supersymmetric grand unified theory of flavour with an auxiliary ℤ42×ℤ4R