Littlest Seesaw model from S 4 × U(1)

Abstract

We show how a minimal (littlest) seesaw model involving two right-handed neutrinos and a very constrained Dirac mass matrix, with one texture zero and two independent Dirac masses, may arise from S4 ×U(1) symmetry in a semi-direct supersymmetric model. The resulting CSD3 form of neutrino mass matrix only depends on two real mass parameters plus one undetermined phase. We show how the phase may be fixed to be one of the cube roots of unity by extending the S4 × U(1) symmetry to include a product of Z3 factors together with a CP symmetry, which is spontaneously broken leaving a single residual Z3 in the charged lepton sector and a residual Z2 in the neutrino sector, with suppressed higher order corrections. With the phase chosen from the cube roots of unity to be −2π/3, the model predicts a normal neutrino mass hierarchy with m1 = 0, reactor angle θ13 = 8.7°, solar angle θ12 = 34°, atmospheric angle θ23 = 44°, and CP violating oscillation phase δCP = −93°, depending on the fit of the model to the neutrino masses.