Intermediate left-right gauge symmetry, unification of couplings and fermion masses in SUSY $SO(10)\times S_4$

TL;DR

This paper demonstrates how spontaneous symmetry breaking in SUSY SO(10)×S_4 can achieve gauge coupling unification with an intermediate left-right scale, fitting fermion masses and predicting neutrino mixing parameters.

Contribution

It introduces a flavor symmetry extension that enables gauge coupling unification with an intermediate scale and fits fermion masses within SUSY SO(10).

Findings

Achieves gauge coupling unification with intermediate scale $M_R \\sim 5 \\times 10^{9}$ to $10^{15}$ GeV.

Fits charged fermion masses at the see-saw scale $M_N \\sim 4 imes 10^{13}$ GeV.

Predicts neutrino mixing angle $\theta_{13} \sim 3^{\circ}-5^{\circ}$ and leptonic CP phase $\delta \sim 2.9-3.1$ radians.

Abstract

If left-right gauge theory occurs as an intermediate symmetry in a GUT then, apart from other advantages, it is possible to obtain the see-saw scale necessary to understand small neutrino masses with Majorana coupling of order unity. Barring threshold or non-renormalizable gravitational effects, or assumed presence of additional light scalar particles of unprescribed origin, all other attempts to achieve manifest one-loop gauge coupling unification in SUSY SO(10) with left-right intermediate symmetry have not been successful so far. Attributing this failure to lack of flavor symmetry in the GUT, we show how the spontaneous symmetry breaking of $SO(10)\times S_4$ leads to such intermediate scale extending over a wide range, $M_R \simeq 5\times 10^{9}$ GeV to $10^{15}$ GeV. All the charged fermion masses are fitted at the see-saw scale, $M_N\simeq M_R \simeq 4 \times 10^{13}$ GeV which is obtained with Majorana coupling $f_0 \simeq 1$. Using a constrained parametrization in which CP-violation originates only from quark sector, besides other predictions made in the neutrino sector, the reactor mixing angle is found to be $\theta_{13} \simeq 3^{\circ} - 5^{\circ}$ which is in the range accessible to ongoing and planned experiments. The leptonic Dirac phase turns out to be $\delta \sim 2.9- 3.1$ radians with Jarlskog invariant $J \sim 2.95 \times 10^{-5} - 10^{-3}$.