Low-scale leptogenesis with flavour and CP symmetries

We consider a type-I seesaw framework with a flavour symmetry from the series of non-abelian groups $\Delta (3 n^2)$ and $\Delta (6 n^2)$ and a CP symmetry. Breaking these symmetries non-trivially results in the right-handed neutrinos being degenerate in mass up to possible (further symmetry-breaking) splittings $\kappa$ and $\lambda$, 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 has five real free parameters. Four of them are set by light neutrino masses and data on lepton mixing, while $\theta_R$ 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 (BAU) through low-scale leptogenesis numerically and analytically. The main results are: a) the possible correlation of the BAU and the Majorana phases of the PMNS mixing matrix in certain instances; b) the possibility to generate the correct amount of BAU for zero $\kappa$ and $\lambda$ as well as for large $\kappa$, depending on the case and choice of group theory parameters; c) the chance to produce sufficient BAU for large active-sterile mixing angles, enabling direct experimental tests at current and future facilities, for $\theta_R$ 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 lepton mixing angles and, possibly, the current hint of the CP phase $\delta$. We identify the CP-violating combinations relevant for low-scale leptogenesis, and show that the parametric dependence of the BAU found numerically can be understood well with their help.