Restricting Sterile Neutrinos by Neutrinoless Double Beta Decay

The bounds on parameters of the eV and higher scale sterile neutrinos from the $0\nu \beta \beta$ decay have been refined and updated. We present a simple and compact analytic expression for the bound in the $\Delta m^2_{41} - \sin^2 2\theta_{14}$ plane, which includes all relevant parameters. Dependencies of the bound on unknown CP-phases and the type of mass spectrum of light neutrinos (mass ordering and level of degeneracy) are studied in detail. We have computed the bounds using the latest and most stringent data from KamLAND-Zen. The projected constraints from future experiments are estimated. The obtained bounds are confronted with positive indications of the presence of sterile neutrinos as well as with the other existing bounds. The $0\nu \beta \beta$ decay results exclude the regions of parameters implied by BEST and Neutrino-4, and the regions indicated by LSND and MiniBooNE are in conflict with $0\nu \beta \beta$ results combined with $\nu_\mu-$ disappearance bounds.