Spontaneous CP violation and leptogenesis in SO(10)

A bstract We present a renormalizable SO(10) grand unified theory with a minimal Yukawa sector consisting of a 126 H , a real 10 H and a real 120 H , where CP violation has a spontaneous origin. We show that the Yukawa sector in this setup, which consists of only 19 real parameters, is capable of simultaneously reproducing the observed fermion masses and mixings, including neutrino oscillations, as well as the baryon asymmetry of the Universe via thermal leptogenesis. In this framework, CP is spontaneously broken when a CP -odd Higgs field 54 H , used for GUT symmetry breaking, acquires a non-zero vacuum expectation value. The Yukawa sector of the model contains four independent phases which determine the Dirac phases δ CKM and δ PMNS , the neutrino Majorana phases, as well as those responsible for leptogenesis. We show that these four phases can arise from a single complex parameter in the Higgs potential involving the CP -odd Higgs field 54 H . The proposed minimal setup predicts a normal ordering of neutrino masses, with the atmospheric mixing angle θ 23 preferred in the first octant and the δ PMNS lying in the range (–37°, +31°). The fermion fits in our scenario further yield a strongly hierarchical mass spectrum for the three right-handed neutrinos, ( M 1 , M 2 , M 3 ) ∼ (10 5 , 10 12 , 5 · 10 14 ) GeV, which is shown to result in successful N 2 -dominated leptogenesis, consistent with current cosmological data.