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The possible existence of an eV-mass sterile neutrino, slightly mixing withordinary active neutrinos, is not yet excluded by neutrino oscillationexperiments. Assuming neutrinos to be Majorana particles, we explore the impactof such a sterile neutrino on the effective neutrino mass of neutrinolessdouble-beta decays $\langle m \rangle^\prime_{ee} \equiv m^{}_1 |V^{}_{e1}|^2e^{{\rm i}\rho} + m^{}_2 |V^{}_{e2}|^2 + m^{}_3 |V^{}_{e3}|^2 e^{{\rm i}\sigma}+ m^{}_4 |V^{}_{e4}|^2 e^{{\rm i}\omega}$, where $m^{}_i$ and $V^{}_{ei}$ (for$i = 1, 2, 3, 4$) denote respectively the absolute masses and the first-rowelements of the 4$\times$4 neutrino flavor mixing matrix $V$, for which a fullparametrization involves three Majorana-type CP-violating phases $\{\rho,\sigma, \omega\}$. A zero effective neutrino mass $|\langle m\rangle^\prime_{ee}| = 0$ is possible no matter whether three active neutrinostake the normal or inverted mass ordering, and its implications for theparameter space are examined in great detail. In particular, given the best-fitvalues of $m^{}_4 \approx 1.3~{\rm eV}$ and $|V^{}_{e4}|^2 \approx 0.019$ fromthe latest global analysis of neutrino oscillation data, a three-dimensionalview of $|\langle m \rangle^\prime_{ee}|$ in the $(m^{}_1, \rho)$-plane ispresented and further compared with that of the counterpart $|\langle m\rangle^{}_{ee}|$ in the absence of any sterile neutrino.

Another look at the impact of an eV-mass sterile neutrino on the effective neutrino mass of neutrinoless double-beta decays