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: $B\to (D^{(\ast )}){\ell }_1^{\pm }N$, then $N\to {\ell }_1^{\pm }{\ell }_2^{\mp }\nu$ or $N\to {\ell }^{\pm }{\pi }^{\mp }$. Here, ${\ell }_1\ne {\ell }_2$ 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 ($D^{(\ast )}$) 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 $D^{(\ast )}$ 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.

Comments: 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)