One Phase to Rule Them All: Spontaneous CP Violation and Leptogenesis in SO(10)

TL;DR

This paper introduces a minimal renormalizable SO(10) GUT model with spontaneous CP violation that successfully explains fermion masses, mixings, neutrino oscillations, and baryon asymmetry via leptogenesis, all from a single complex parameter.

Contribution

It proposes a minimal SO(10) model with spontaneous CP violation capable of reproducing observed fermion data and baryon asymmetry with only 19 real parameters.

Findings

Predicts normal neutrino mass ordering and specific mixing angles.

Achieves successful N2-dominated leptogenesis consistent with cosmological data.

Fermion mass spectrum and CP phases arise from a single complex Higgs parameter.

Abstract

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. All $CP$-violating phases, including the Dirac phases $\delta_\mathrm{CKM}$ and $\delta_\mathrm{PMNS}$, the neutrino Majorana phases, as well as those responsible for leptogenesis, arise solely from a single complex parameter in the Higgs potential. The proposed minimal setup predicts a normal ordering of neutrino masses, with the atmospheric mixing angle $\theta_{23}$ preferred in the first octant and the leptonic $\delta_{\mathrm{PMNS}}$ lying in the range $(-38^\circ,\, +31^\circ)$. The fermion fits in our scenario further yield a strongly hierarchical mass spectrum for the three right-handed neutrinos, $(M_1,\,M_2,\,M_3) \sim \left(10^{5},\, 10^{12},\, 5\cdot 10^{14}\right)~\mathrm{GeV}$, which is shown to result in successful $N_2$-dominated leptogenesis, consistent with current cosmological data.