CP violation in Bs decays mediated by two nearly-degenerate Majorana neutrinos

Abstract

We study the $CP$ violation in the lepton-number-violating process ${B}_{s}^{0}\ensuremath{\rightarrow}{D}_{s}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and its $CP$-conjugate process $\overline{{B}_{s}^{0}}\ensuremath{\rightarrow}{D}_{s}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{\ensuremath{\mu}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ that are induced by two GeV-scale Majorana neutrinos with nearly-degenerate masses. Our result shows that the size of the $CP$ violation could become considerable if the mass difference between the two Majorana neutrinos is around the decay width of the neutrinos. We perform experimental analysis on the $CP$-violating processes at LHCb within its upgrade II. The analysis shows that under current constraint on the heavy-light neutrino mixing parameter, it is possible that such $CP$ violation is observed with the LHCb experimental ability. We also give the upper bound on the heavy-light mixing parameter $|{U}_{\ensuremath{\mu}N}{|}^{2}$ under the assumption that no positive signal of the process is observed. The result shows that such modes can give complementary constraint compared with previous experiments such as NuTeV, BEBC, etc., in the mass region $1\text{ }\text{ }\mathrm{GeV}<{m}_{N}<3\text{ }\text{ }\mathrm{GeV}$.