Decay of $B^{\pm }\to {\tau }^{\pm }+$ "missing momentum" and direct measurement of the mixing parameter $U_{\tau N}$

We derive the decay widths for the leptonic decays of heavy charged pseudoscalars to massive sterile neutrinos, $M^{\pm }\to {\mathrm{\ell }}^{\pm }+N$, within the frameworks involving the Standard Model and two-Higgs doublets (type II). We then apply the result to $B^{\pm }\to {\tau }^{\pm }+$ “missing momentum” of the Belle/BaBar experimental results, in order to measure directly the relevant parameter space, including the mixing parameter $U_{\tau N}$.