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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 (0νββ0\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 0νββ0\nu \beta \beta-decaying nuclei have placed a restrictive upper bound on the Majorana neutrino mass δmνee<7.43×1029 eV|\delta m^{ee}_\nu| < 7.43 \times 10^{-29}~{\rm eV} radiatively generated at the four-loop level. Furthermore, we generalize this quantitative analysis of 0νββ0\nu \beta \beta decays to that of the lepton-number-violating (LNV) meson decays MM++α+βM^- \to {M^\prime}^+ + \ell^-_\alpha + \ell^-_\beta (for α\alpha, β\beta = ee or μ\mu). Given the present upper limits on these rare LNV decays, we have derived the loop-induced Majorana neutrino masses δmνee<9.7×1018 eV|\delta m^{ee}_\nu| < 9.7 \times 10^{-18}~{\rm eV}, δmνeμ<1.6×1015 eV|\delta m^{e\mu}_\nu| < 1.6 \times 10^{-15}~{\rm eV} and δmνμμ<1.0×1012 eV|\delta m^{\mu \mu}_\nu| < 1.0 \times 10^{-12}~{\rm eV} from Kπ++e+eK^- \to \pi^+ + e^- + e^-, Kπ++e+μK^- \to \pi^+ + e^- + \mu^- and Kπ++μ+μK^- \to \pi^+ + \mu^- + \mu^-, respectively. A partial list of radiative neutrino masses from the LNV decays of DD, DsD_s^{} and BB mesons is also given.Comment: 10 pages, 1 figure, clarification added and references updated, Phys. Lett. B in pres

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