CP violation in lepton number violating semihadronic decays of $K,D,D_s,B,B_c$

Abstract

We study the CP violation in lepton number violating meson decays $M^{\pm }\to {\ell }_1^{\pm }{\ell }_2^{\pm }{M}^{{}^{\prime }\mp }$, where $M$ and $M^{{}^{\prime }}$ are pseudoscalar mesons, $M=K,D,D_s,B,B_c$ and $M^{{}^{\prime }}=\pi ,K,D,D_s$, and the charged leptons are ${\ell }_1,{\ell }_2=e,\mu$. It turns out that the CP-violating difference $S_{-}(M)\equiv [\Gamma (M^{-}\to {\ell }_1^{-}{\ell }_2^{-}{M}^{{}^{\prime }+})-\Gamma (M^{+}\to {\ell }_1^{+}{\ell }_2^{+}{M}^{{}^{\prime }-})]$ can become appreciable when two intermediate on-shell Majorana neutrinos $N_j$ ($j=1,2$) participate in these decays. Our calculations show that the asymmetry becomes largest when the masses of $N_1$ and $N_2$ are almost degenerate, i.e., when the mass difference $\Delta M_N$ becomes comparable with the (small) decay widths ${\Gamma }_N$ of these neutrinos: $\Delta M_N/\gg {\Gamma }_N$. We show that in such a case, the CP ratio ${\mathcal{A}}_{CP}(M)\equiv [\Gamma (M^{-}\to {\ell }_1^{-}{\ell }_2^{-}{M}^{{}^{\prime }+})-\Gamma (M^{+}\to {\ell }_1^{+}{\ell }_2^{+}{M}^{{}^{\prime }-})]/[\Gamma (M^{-}\to {\ell }_1^{-}{\ell }_2^{-}{M}^{{}^{\prime }+})+\Gamma (M^{+}\to {\ell }_1^{+}{\ell }_2^{+}{M}^{{}^{\prime }-})]$ becomes a quantity $\sim 1$. The observation of CP violation in these decays would be consistent with the existence of the well-motivated $\nu$MSM model with two almost degenerate heavy neutrinos in the mass range between $M_N\sim 0.1$-$10^1$ GeV.

19 pages, 8 figures; v2: a new Table (I); minor changes in the text; new references [5,31,32]; ref.[19] extended; to appear in Phys.Rev.D

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