Sensitivity limits on heavy-light mixing $|U_{\mu N}{|}^2$ from lepton number violating $B$ meson decays

Abstract

We consider the lepton number violating decays $B\to {\mu }^{\pm }{\mu }^{\pm }{\pi }^{\mp }$ and $B\to D^{(\ast )}{\mu }^{\pm }{\mu }^{\pm }{\pi }^{\mp }$ which may be detected at LHCb and Belle-II experiments; and $B\to {\mu }^{\pm }{\mu }^{\pm }{e}^{\mp }\nu$ and $B\to D^{(\ast )}{\mu }^{\pm }{\mu }^{\pm }{e}^{\mp }\nu$ decays which may be detected at Belle-II experiment. The projected total number of produced $B$ mesons is $4.8\times 10^{12}$ at LHCb upgrade and $5\times 10^{10}$ at Belle-II. For the case that the above decays are not detected, we deduce the new upper bounds (sensitivity limits) for the mixing parameter $|U_{\mu N}{|}^2$ of heavy sterile neutrino with sub-eV light neutrino, as a function of the sterile neutrino mass in the interval $1.75\mathrm{GeV}<M_N<5.0\mathrm{GeV}$. 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 LCHb upgrade and $L=1m$ at Belle-II. In the interval $1.75\mathrm{GeV}<M_N<3\mathrm{GeV}$, the most stringent bounds can be obtained with the decays $B\to {\mu }^{\pm }{\mu }^{\pm }{\pi }^{\mp }$ at LHCb upgrade. The sensitivity limits are expected to be in general more stringent at LHCb upgrade than at Belle-II, principally because the number of produced $B$ mesons in LHCb upgrade is expected to be by about two 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 $|U_{\mu N}{|}^2$, particularly in the mass range $1.75\mathrm{GeV}<M_N<3\mathrm{GeV}$. This work is a continuation and refinement of our previous work [1] on the subject.

Comments: revtex, 20 pages, 6 figures; v4: typos in Eqs.(10), (11) and (17b) corrected; the correct expressions had been used in calculations, results unchanged