Low-scale leptogenesis with flavour and CP symmetries

We consider a type-I seesaw framework endowed with a flavour symmetry, belonging to the series of non-abelian groups ∆(3 n$^{2}$) and ∆(6 n$^{2}$), and a CP symmetry. Breaking these symmetries in a non-trivial way results in the right-handed neutrinos being degenerate in mass up to possible (further symmetry-breaking) splittings κ and λ, while the neutrino Yukawa coupling matrix encodes the entire flavour structure in the neutrino sector. For a fixed combination of flavour and CP symmetry and residual groups, this matrix contains five real free parameters. Four of them are determined by the light neutrino mass spectrum and by accommodating experimental data on lepton mixing well, while the angle θ$_{R}$ is related to right-handed neutrinos. We scrutinise for all four lepton mixing patterns, grouped into Case 1) through Case 3 b.1), the potential to generate the baryon asymmetry of the Universe through low-scale leptogenesis numerically and analytically. The main results are: a) the possible correlation of the baryon asymmetry and the Majorana phases, encoded in the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix, in certain instances; b) the possibility to generate the correct amount of baryon asymmetry for vanishing splittings κ and λ among the right-handed neutrinos as well as for large κ, depending on the case and the specific choice of group theory parameters; c) the chance to produce sufficient baryon asymmetry for large active-sterile mixing angles, enabling direct experimental tests at current and future facilities, if θ$_{R}$ is close to a special value, potentially protected by an enhanced residual symmetry. We elucidate these results with representative examples of flavour and CP symmetries, which all lead to a good agreement with the measured values of the lepton mixing angles and, possibly, the current indication of the CP phase δ. We identify the CP-violating combinations relevant for low-scale leptogenesis, and show that the parametric dependence of the baryon asymmetry found in the numerical study can be understood well with their help.