Angular and polarization observables for Majorana-mediated B decays with effective interactions

We probe the effective field theory extending the Standard Model with a sterile neutrino in B meson decays at B factories and lepton colliders, using angular and polarization observables. We put bounds on different effective operators characterized by their distinct Dirac-Lorentz structure, and probe the $N$-mediated B decays sensitivity to these interactions. We define a Forward-Backward asymmetry $A_{FB}^{\mathrm{\ell }\gamma }$ between the muon and photon directions for the $B\to \mu \nu \gamma$ decay, which allows us to separate the SM contribution from the effective lepton number conserving and violating processes, mediated by a near on-shell $N$. Using the most stringent constraints on the effective parameter space from Belle and BaBar we find that a measurement of the final polarization $P_{\tau }$ in the rare $B^-\rightarrow \ell^-{1}\ell^-{2} \pi^+$ decays can help us infer the scalar or vector interaction content in the $N$ production or decay vertices. We find that the B meson decays are more sensitive to scalar operators.