Rare decays of B mesons via on-shell sterile neutrinos

Abstract

In view of the projected high number of produced $B$ mesons in Belle II experiment ($\sim 10^{10}$ per year), in addition to the presently ongoing LHC-b, we calculate the rate of decay for the rare decays of $B$ mesons via a sterile on-shell neutrino $N$, which subsequently may decay leptonically or semileptonically within the detector: $B \to (D^{(*)}) \ell_1^{\pm} N$, then $N \to \ell_1^{\pm} \ell_2^{\mp} ν$ or $N \to \ell^{\pm} π^\mp$. Here, $\ell_1 \not= \ell_2$ in order to avoid serious QED background. We account for the possible effects of the strong neutrino lifetime on the observability of the rare decays. If no charmed mesons ($D^{(*)}$) are produced at the first vertex of the sterile neutrino, a strong CKM-suppression becomes effective; this is not true if we consider instead the decays of $B_c$ mesons which can be produced copiously in LHC-b. The production of charmed mesons $D^{(*)}$ at the first vertex offers an attractive possibility because it avoids strong CKM-suppression. Such rare decays of $B$ mesons could be detected at Belle II experiment, with $N$ neutrino either decaying within the detector or manifesting itself as a massive missing momentum.

32 pages, 22 figures, v4: in Fig.4(b) the lower curve [for (B -> D* tau N) decay] is now correct (in v3 an obsolete version of the curve was inadvertently included); a typo in Eq.(C15a) is corrected; as published in Phys.\ Rev.\ D94, 053001 (2016) and Phys.\ Rev.\ D95, 039901(E) (2017)