Deviations to cobimaximal mixing in a 3+1 neutrino scenario
Cobimaximal mixing remains a viable approximate pattern since the predicted atmospheric angle ($π/4$) and Dirac CP phase ($-π/2$) are compatible with current experimental data at the $3σ$ level. In this work, we investigate how an additional sterile neutrino state breaks the cobimaximal mixing and the underlying $μ-τ$ reflection symmetry in a $3+1$ neutrino scenario. Given the strong constraints already imposed on active-sterile mixings, we examine the resulting restrictions on the model parameter space, assuming a small symmetry breaking induced by the sterile state. We derive predictions for the relevant model parameters, active-sterile mixing angles, and Dirac CP-violating phases, by considering small deviations from the symmetric limit. We also analyze the allowed combinations of Majorana phases through their impact on the effective Majorana mass governing neutrinoless double beta decay. Current experimental limits on this process impose severe constraints on the inverted ordering realization of the $3+1$ scenario, excluding the small breaking regime within the parameter ranges considered. In contrast, the normal ordering case remains viable and predicts values of the effective Majorana mass that lie within the sensitivity reach of upcoming neutrinoless double beta decay experiments.