Sensitivity bounds on heavy neutrino mixing $|U_{\mu N}|^2$ and $|U_{\tau N}|^2$ from LHCb upgrade

Decays of heavy pseudoscalar mesons $B$, $B_c$, $B_s$ and $D_s$ at LHCb upgrade are considered, which produce either two equal sign muons or taus. In addition, we consider the analogous decays with opposite sign muons or taus. All these decays are considered to be mediated by a heavy on-shell neutrino $N$. Such decays of $B$ mesons, if not detected, will give in general stringent upper bounds on the heavy-light mixing parameter $|U_{\mu N}|^2$ as a function of the neutrino mass $M_N \sim 1$ GeV, principally due to the large expected number of produced mesons $B$. While some of the decays of the other mentioned mesons are attractive due to a weaker CKM-suppression, the expected produced number of such mesons is significantly smaller that that of $B$'s; therefore, the sensitivity bounds from such decays are in general comparable or less restrictive. When $\tau$ pairs are produced, only two types of such decays are significant: $B^{\pm}, B_{c}^{\pm} \to \tau^{\pm} \tau^{\pm} \pi^{\mp}$ (and $\tau^{\pm} \tau^{\mp} \pi^{\pm}$), giving us stringent upper bounds on $|U_{\tau N}|^2$; the other decays with a pair of $\tau$, such as $B^0 \to D^{(*)-} \tau^+ \tau^+ \pi^-$ (and $D^{(*)-} \tau^+ \tau^- \pi^+$), are prohibited or very suppressed by kinematics.