Majorana Neutrino Masses from Neutrinoless Double-Beta Decays and Lepton-Number-Violating Meson Decays

Abstract

The Schechter-Valle theorem states that a positive observation of neutrinoless double-beta ($0\nu \beta \beta$) decays implies a finite Majorana mass term for neutrinos when any unlikely fine-tuning or cancellation is absent. In this note, we reexamine the quantitative impact of the Schechter-Valle theorem, and find that current experimental lower limits on the half-lives of $0\nu \beta \beta$-decaying nuclei have placed a restrictive upper bound on the Majorana neutrino mass $|\delta m_{\nu }^{ee}|<7.43\times 10^{-29}\mathrm{eV}$ radiatively generated at the four-loop level. Furthermore, we generalize this quantitative analysis of $0\nu \beta \beta$ decays to that of the lepton-number-violating (LNV) meson decays $M^{-}\to {M^{\prime }}^{+}+{\ell }_{\alpha }^{-}+{\ell }_{\beta }^{-}$ (for $\alpha$, $\beta$ = $e$ or $\mu$). Given the present upper limits on these rare LNV decays, we have derived the loop-induced Majorana neutrino masses $|\delta m_{\nu }^{ee}|<9.7\times 10^{-18}\mathrm{eV}$, $|\delta m_{\nu }^{e\mu }|<1.6\times 10^{-15}\mathrm{eV}$ and $|\delta m_{\nu }^{\mu \mu }|<1.0\times 10^{-12}\mathrm{eV}$ from $K^{-}\to {\pi }^{+}+e^{-}+e^{-}$, $K^{-}\to {\pi }^{+}+e^{-}+{\mu }^{-}$ and $K^{-}\to {\pi }^{+}+{\mu }^{-}+{\mu }^{-}$, respectively. A partial list of radiative neutrino masses from the LNV decays of $D$, $D_s^{}$ and $B$ mesons is also given.

Comments: 10 pages, 1 figure, clarification added and references updated, Phys. Lett. B in press