B -> K1 l^+l^- Decays in a Family Non-universal Z' Model

The implications of the family non-universal $Z^\prime$ model in the $B\to K_{1}(1270,1400)\ell^{+}\ell^{-}(\ell=e\,,\mu\,,\tau)$ decays are explored, where the mass eigenstates $K_{1}(1270,1400)$ are the mixtures of $^{1}{P}_{1}$ and $^{3}{P}_{1}$ states with the mixing angle $\theta$. In this work, considering the $Z^\prime$ boson and setting the mixing angle $\theta=(-34\pm13)^{\circ}$, we analyze the branching ratio, the dilepton invariant mass spectrum, the normalized forward-backward asymmetry and lepton polarization asymmetries of each decay mode. We find that all observables of $B\to K_{1}(1270)\mu^{+}\mu^{-}$ are sensitive to the $Z^{\prime}$ contribution. Moreover, the observables of $B\to K_{1}(1400)\mu^{+}\mu^{-}$ are relatively strong $\theta$-dependence; thus, the $Z^{\prime}$ contribution will be buried by the uncertainty of the mixing angle $\theta$. Furthermore, the zero crossing position in the FBA spectrum of $B\to K_{1}(1270)\mu^{+}\mu^{-}$ at low dilepton mass will move to the positive direction with $Z^\prime$ contribution. For the tau modes, the effects of $Z^\prime$ are not remarkable due to the small phase space. These results could be tested in the running LHC-b experiment and Super-B factory.