Branching ratios, forward-backward asymmetries and angular distributions of $B\to K_2^{\ast }{l}^{+}{l}^{-}$ in the standard model and new physics scenarios

Abstract

We analyze the $B\to K_2^{\ast }(\to K\ddot{I}€)l^{+}{l}^{-}$ (with $l=e,\hat{I}¼,\ddot{I}„$) decay in the standard model and two new physics scenarios: vector-like quark model and family non-universal $Z^{\prime }$ model. We derive its differential angular distributions, using the recently calculated form factors in the perturbative QCD approach. Branching ratios, polarizations, forward-backward asymmetries and transversity amplitudes are predicted, from which we find a promising prospective to observe this channel on the future experiment. We also update the constraints on effective Wilson coefficients and/or free parameters in these two new physics scenarios by making use of the experimental data of $B\to K^{\ast }{l}^{+}{l}^{-}$ and $b\to s{l}^{+}{l}^{-}$. Their impact on $B\to K_2^{\ast }{l}^{+}{l}^{-}$ is subsequently explored and in particular the zero-crossing point for the forward-backward asymmetry in these new physics scenarios can sizably deviate from the SM scenario. In addition we also generalize the analysis to a similar mode $B_s\to f_2^{\prime }(1525)(\to K^{+}{K}^{-})l^{+}{l}^{-}$.

21 pages, 9 figures, accepted for publication in Phys. Rev. D