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 ($0\nu \beta \beta$) 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 $|\delta m^{ee}_\nu| < 7.43 \times 10^{-29}~{\rm eV}$ 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 $|\delta m^{ee}_\nu| < 9.7 \times 10^{-18}~{\rm eV}$, $|\delta m^{e\mu}_\nu| < 1.6 \times 10^{-15}~{\rm eV}$ and $|\delta m^{\mu \mu}_\nu| < 1.0 \times 10^{-12}~{\rm eV}$ 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.Comment: 10 pages, 1 figure, clarification added and references updated, Phys. Lett. B in pres

Implication the observed ψ(3770)→ppˉπ0\psi(3770)\to p\bar{p}\pi^0 for studying the ppˉ→ψ(3770)π0p\bar{p}\to \psi(3770)\pi^0 process

We study the charmonium $p \bar{p} \to \psi(3770) \pi^0$ reaction using effective lagrangian approach where the contributions from well established $N^*$ states are considered, and all parameters are fixed in the process of $e^+e^- \to p \bar{p}\pi^0$ at center of mass energy $\sqrt{s} = 3.773$ GeV. The experimental data on the line shape of the mass distribution of the $e^+e^- \to p\bar{p}\pi^0$ can be well reproduced. Based on the studying of $e^+e^- \to p \bar{p}\pi^0$, the total and differential cross sections of the $p \bar{p} \to \psi(3770) \pi^0$ reaction are predicted. At the same time we evaluated also the cross sections of the $p \bar{p} \to \psi(3686) \pi^0$ reaction. It is shown that the contribution of nucleon pole to this reaction is largest close to the reaction threshold. However, the interference between nucleon pole and the other nucleon resonance can still change the angle distributions significantly. Those theoretical results may be test by the future experiments at \overline{\mbox{P}}ANDA.Comment: 8 pages, 10 figures, and 4 tables. More discussions added and typos corrected. Accepted by Eur. Phys. J.