Lepton Flavor Violating $B\to K_2^{\ast }(1430){\mu }^{\pm }{\tau }^{\mp }$ Decays

A number of measurements in decays induced by the semileptonic $b\to s$ and $b\to c$ transitions hint towards a possible role of new physics in both sectors. Motivated by these anomalies, we investigate the lepton flavor violating $B\to K_2^{\ast }(1430){\mu }^{\pm }{\tau }^{\mp }$ decays. We calculate the two-fold angular distribution of $B\to K_2^{\ast }{\mathrm{\ell }}_1{\mathrm{\ell }}_2$ decay in presence of vector, axial-vector, scalar and pseudo-scalar new physics interactions. We then compute the branching fraction and lepton forward-backward asymmetry in the framework of $U_1^{2\mathrm{/}3}$ vector leptoquark which is a viable solution to the current $B$ anomalies. We find that the upper limits are $\mathcal{B}(B\to K_2^{\ast }{\mu }^{-}{\tau }^{+})\le 1.64\times {10}^{-7}$ and $\mathcal{B}(B\to K_2^{\ast }{\mu }^{+}{\tau }^{-})\le 0.60\times {10}^{-7}$ at $90\mathrm{\%}$ C.L.