Majorana neutrino masses from neutrinoless double-beta decays and lepton-number-violating meson decays

The Schechter–Valle theorem states that a positive observation of neutrinoless double-beta (0νββ0νββ) 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 0νββ0νββ-decaying nuclei have placed a restrictive upper bound on the Majorana neutrino mass |δmνee|<7.43×10−29 eV radiatively generated at the four-loop level. Furthermore, we generalize this quantitative analysis of 0νββ0νββ decays to that of the lepton-number-violating (LNV) meson decays M−→M′++ℓα−+ℓβ− (for α,β=eα,β=e or μ  ). Given the present upper limits on these rare LNV decays, we have derived the loop-induced Majorana neutrino masses |δmνee|<9.7×10−18 eV, |δmνeμ|<1.6×10−15 eV and |δmνμμ|<1.0×10−12 eV from K−→π++e−+e−K−→π++e−+e−, K−→π++e−+μ−K−→π++e−+μ− and K−→π++μ−+μ−K−→π++μ−+μ−, respectively. A partial list of radiative neutrino masses from the LNV decays of D  , DsDs and B mesons is also given.