Phenomenology of Vanishing Effective Majorana Mass with a Sterile Neutrino under Cosmological and JUNO Constraints

In the present work we investigate the phenomenological implications of a vanishing effective Majorana neutrino mass within a $3+1$ neutrino framework adding a eV-scale sterile neutrino beside three active neutrino states in light of latest cosmology driven bounds on sum of neutrino masses (${\sum }_i{m}_i$). We explore the parameter space where the destructive interference between active and sterile states leads to vanishing amplitude, $M_{ee}$, of neutrinoless double beta ($0\nu \beta \beta$) decay. The allowed parameter space has been identified and predictions have been obtained taking into account the latest Planck and DESI+CMB bound on ${\sum }_i{m}_i$. We find that these bounds restrict the sterile mixing angle ${\theta }_{14}$ and the lightest active neutrino mass. Furthermore, we incorporate the refined precision data from JUNO experiment regarding solar oscillation parameters (${\theta }_{12},\mathrm{\Delta }{m}_{21}^2$). We find that the sterile neutrino parameters like ${\theta }_{14}$ may not be sensitive to the JUNO precision measurements as the constraint imposed by precise ${\theta }_{12}$ is washed out by new cancellations driven through additional CP violating phases leading to vanishing $\mathrm{\mid }{M}_{ee}\mathrm{\mid }$.