Arbitrary mass Majorana neutrinos in neutrinoless double beta decay

We revisit the mechanism of neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decay mediated by the exchange with the heavy Majorana neutrino $N$ of arbitrary mass ${m}_{N}$, slightly mixed $\ensuremath{\sim}{U}_{\mathit{eN}}$ with the electron neutrino ${\ensuremath{\nu}}_{e}$. By assuming the dominance of this mechanism, we update the well-known $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay exclusion plot in the ${m}_{N}\ensuremath{-}{U}_{\mathit{eN}}$ plane taking into account recent progress in the calculation of nuclear matrix elements within quasiparticle random phase approximation and improved experimental bounds on the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay half-life of $^{76}\mathrm{Ge}$ and $^{136}\mathrm{Xe}$. We also consider the known formula approximating the ${m}_{N}$ dependence of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay nuclear matrix element in a simple explicit form. We analyze its accuracy and specify the corresponding parameters, allowing one to easily calculate the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay half-life for arbitrary ${m}_{N}$ for all the experimentally interesting isotopes without resorting to real nuclear structure calculations.