CP violation in lepton number violating semihadronic decays of K,D,Ds,B,Bc

We study the CP violation in lepton-number-violating meson decays M±→1±2±M′, where M and M′ are pseudoscalar mesons, M=K,D,Ds,B,Bc and M′=π,K,D,Ds, and the charged leptons are 1,2=e,μ. It turns out that the CP-violating difference S-(M) ≡[Γ(M-→1-2-M′+)-Γ(M+→1+2+M′-)] can become appreciable when two intermediate on-shell Majorana neutrinos Nj (j=1,2) participate in these decays. Our calculations show that the asymmetry becomes largest when the masses of N1 and N2 are almost degenerate, i.e., when the mass difference ΔMN becomes comparable with the (small) decay widths ΓN of these neutrinos: ΔMNΓN. We show that in such a case, the CP ratio ACP(M)≡[Γ(M-→1-2-M′+)-Γ(M+→1+2+M′-)]/ [Γ(M-→1-2-M′+)+Γ(M+→1+2+M′-)] becomes a quantity ∼1. The observation of CP violation in these decays would be consistent with the existence of the well-motivated νMSM model with two almost degenerate heavy neutrinos in the mass range MN∼0.1-101GeV.