Sensitivity limits on heavy-light mixing |UμN |2 from lepton number violating B meson decays

We consider the lepton number violating decays B→μ±μ±π and B→D(∗)μ±μ±π which may be detected at the LHCb and Belle-II experiments and B→μ±μ±eν and B→D(∗)μ±μ±eν decays which may be detected at the Belle-II experiment. The projected total number of produced B mesons is 4.8×1012 at the LHCb upgrade and 5×1010 at Belle-II. For the case in which the above decays are not detected, we deduce the new upper bounds (sensitivity limits) for the mixing parameter |UμN|2 of heavy sterile neutrino with sub-eV light neutrino, as a function of the sterile neutrino mass in the interval 1.75 GeV<MN<5.0 GeV. We take into account the probability of decay of the sterile neutrino N within the detector, taking as the effective detector length L=2.3m at the LCHb upgrade and L=1m at Belle-II. In the interval 1.75 GeV<MN<3 GeV, the most stringent bounds can be obtained with the decays B→μ±μ±π at the LHCb upgrade. The sensitivity limits are expected to be, in general, more stringent at the LHCb upgrade than at Belle-II, principally because the number of produced B mesons in the LHCb upgrade is expected to be about 2 orders of magnitude larger than at Belle-II. We conclude that the LHCb upgrade and Belle-II experiments have the potential to either find a new heavy Majorana neutrino N or to improve significantly the sensitivity limits (upper bounds) on the heavy-light mixing parameter |UμN|2, particularly in the mass range 1.75 GeV<MN<3 GeV. This work is a continuation and refinement of our previous work [Phys. Rev. D 94, 053001 (2016); PRVDAQ2470-001010.1103/PhysRevD.94.053001Phys. Rev. D 95, 039901(E) (2017)PRVDAQ2470-0010] on the subject.