An S4×SU(5)S_4 \times SU(5) SUSY GUT of flavour in 6d

We propose a 6d model with a SUSY $SU(5)$ gauge symmetry. After compactification, it explains the origin of the $S_4$ Family Symmetry with CSD3 vacuum alignment, as well as $SU(5)$ breaking with doublet-triplet splitting. The model naturally accounts for all quark and lepton (including neutrino) masses and mixings, incorporating the highly predictive Littlest Seesaw structure. It spontaneously breaks CP symmetry, resulting in successful CP violation in the quark and lepton sectors, while solving the Strong CP problem. It also explains the Baryon Asymmetry of the Universe (BAU) through leptogenesis, with the leptogenesis phase directly linked to the Dirac and Majorana phases.Comment: 23 pages, 6 figures. v3: Version published in JHE

SO(10)×S4\mathbf{SO(10)}\times \mathbf{S_4} Grand Unified Theory of Flavour and Leptogenesis

We propose a Grand Unified Theory of Flavour, based on $SO(10)$ together with a non-Abelian discrete group $S_4$, under which the unified three quark and lepton 16-plets are unified into a single triplet $3'$. The model involves a further discrete group $\mathbb{Z}_4^R\times \mathbb{Z}_4^3$ which controls the Higgs and flavon symmetry breaking sectors. The CSD2 flavon vacuum alignment is discussed, along with the GUT breaking potential and the doublet-triplet splitting, and proton decay is shown to be under control. The Yukawa matrices are derived in detail, from renormalisable diagrams, and neutrino masses emerge from the type I seesaw mechanism. A full numerical fit is performed with 15 input parameters generating 19 presently constrained observables, taking into account supersymmetry threshold corrections. The model predicts a normal neutrino mass ordering with a CP oscillation phase of $260^{\circ}$, an atmospheric angle in the first octant and neutrinoless double beta decay with $m_{\beta \beta}= 11$ meV. We discuss $N_2$ leptogenesis, which fixes the second right-handed neutrino mass to be $M_2\simeq 2\times 10^{11}$ GeV, in the natural range predicted by the model.Comment: 26 pages, 10 figure

Towards a complete A4×SU(5)A_4 \times SU(5) SUSY GUT

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 $\mathbb{Z}_9\times \mathbb{Z}_6$ symmetry provides the fermion mass hierarchy in both the quark and lepton sectors, while $\mathbb{Z}_4^R$ symmetry is broken to $\mathbb{Z}_2^R$, identified as usual R-parity. Proton decay is highly suppressed by these symmetries. We discuss both the $A_4$ and $SU(5)$ symmetry breaking sectors, including doublet-triplet splitting, Higgs mixing and the origin of the $\mu$ 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 $2\pi/3$ from a choice of the nine complex roots of unity, providing a direct link between neutrino oscillations and leptogenesis.Comment: 30 pages, 17 figures, 7 tables; Minor changes, references added, version accepted in JHE

Leptogenesis in minimal predictive seesaw models

We 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 $(\nu_e, \nu_{\mu}, \nu_{\tau})$ 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 $A_4$ vacuum alignment provides the required Yukawa structures with $n=3$, while a $\mathbb{Z}_9$ symmetry fixes the relatives phase to be a ninth root of unity.Comment: 16 pages, 2 tables. v2: minor changes, references added, version accepted in JHE