Probing eV-scale sterile neutrinos with neutrinoless double-beta decay and beta decay

An eV-scale sterile Majorana neutrino can suppress neutrinoless double-beta decay through destructive interference with the active-neutrino contribution, weakening the resulting constraints on sterile-neutrino parameters. We investigate how complementary beta-decay information restricts this cancellation in the 3+1 framework. Using updated oscillation parameters that include the first JUNO results, we determine the allowed sterile-neutrino mass and mixing regions for both normal and inverted ordering. We show that an upper limit on the effective beta-decay mass $m_{\beta }$ of the three light neutrinos strengthens the constraints from neutrinoless double-beta decay alone. The beta-decay bound restricts the light-neutrino masses and hence the cancellation between the active and sterile contributions to $m_{\beta \beta }$. We derive analytic expressions for the resulting boundaries and use complex-plane geometry to explain the allowed values of the sterile Majorana phase ${\alpha }_4$ for a finite $\mathrm{\mid }{m}_{\beta \beta }\mathrm{\mid }$ limit. For the mixing considered, normal ordering allows a broad range of ${\alpha }_4$ at small sterile masses, whereas inverted ordering favors values near $\pi$. The allowed phase range narrows as the sterile mass approaches its upper bound or the limit on $\mathrm{\mid }{m}_{\beta \beta }\mathrm{\mid }$ becomes more stringent.