Leptogenesis and residual CP symmetry

TL;DR

This paper explores how residual CP symmetries in neutrino models influence leptogenesis, linking high-energy flavor symmetries with low-energy neutrino parameters and identifying conditions for successful leptogenesis.

Contribution

It systematically classifies residual CP symmetries in neutrino models and demonstrates their impact on leptogenesis and PMNS matrix predictions, providing a general formalism applicable to various flavor symmetries.

Findings

R-matrix is tightly constrained by residual CP symmetries.

Certain residual CP symmetries allow successful leptogenesis.

Application to S4 flavor symmetry yields new insights into leptogenesis.

Abstract

We discuss flavour dependent leptogenesis in the framework of lepton flavour models based on discrete flavour and CP symmetries applied to the type-I seesaw model. Working in the flavour basis, we analyse the case of two general residual CP symmetries in the neutrino sector, which corresponds to all possible semi-direct models based on a preserved $Z_2$ in the neutrino sector, together with a CP symmetry, which constrains the PMNS matrix up to a single free parameter which may be fixed by the reactor angle. We systematically study and classify this case for all possible residual CP symmetries, and show that the $R$-matrix is tightly constrained up to a single free parameter, with only certain forms being consistent with successful leptogenesis, leading to possible connections between leptogenesis and PMNS parameters. The formalism is completely general in the sense that the two residual CP symmetries could result from any high energy discrete flavour theory which respects any CP symmetry. As a simple example, we apply the formalism to a high energy $S_4$ flavour symmetry with a generalized CP symmetry, broken to two residual CP symmetries in the neutrino sector, recovering familiar results for PMNS predictions, together with new results for flavour dependent leptogenesis.