Arbitrary mass Majorana neutrinos in neutrinoless double beta decay

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