Intermediate left-right gauge symmetry, unification of couplings, and fermion masses in supersymmetric SO(10) S4

Abstract

If left-right gauge theory, SU(2)(L) x SU(2)(R) x U(1)(B-L) x SU(3)(C)(g(L) = g(R))(equivalent to G(2213)), occurs as an intermediate symmetry in a grand unified theory then, apart from other advantages, it is possible to obtain the seesaw scale necessary to understand small neutrino masses with Majorana coupling of order unity. Barring threshold or nonrenormalizable gravitational effects at the GUT scale, or the assumed presence of additional light scalar particles of unprescribed origin, all other attempts to achieve manifest one-loop gauge coupling unification in supersymmetry SO(10) with such intermediate symmetry have not been successful so far. Attributing this failure to lack of flavor symmetry in the grand unified theory, we show how the spontaneous symmetry breaking of SO(10) x S-4 leads to such left- right intermediate breaking scale extending over the range M-R similar or equal to 5 x 10(9) GeV to 10(15) GeV. All the charged fermion masses are fitted at the intermediate seesaw scale, M-N similar or equal to M-R similar or equal to 4 x 10(13) GeV which is obtained with Majorana coupling f(0) similar or equal to 1. Using type-I seesaw and a constrained parametrization in which CP-violation originates only from the quark sector, in addition to other predictions made in the neutrino sector, the reactor mixing angle is found to be theta(13) similar or equal to 3 degrees - 5 degrees which is in the range accessible to ongoing experiments. The leptonic Dirac phase turns out to be delta similar or equal to 2.9 - 3.1 radians with the predicted values of Jarlskog invariant J(CP) similar or equal to 2.95 x 10(-5) - 10(-3).