$B\to K^{\ast }{l}^{+}{l}^{-}$, $K{l}^{+}{l}^{-}$ decays in a family non-universal $Z^{\prime }$ model

Abstract

Motivated by the observed forward-backward asymmetry in $B\to K^{\ast }{l}^{+}{l}^{-}$ decay, we perform a detailed analysis of this decay mode within a family non-universal $Z^{\prime }$ model. With the related coupling $Z^{\prime }-\bar{s}b$ constrained by ${\bar{B}}_s-B_s$ mixing, $B\to \pi K$, and $B\to X_s{\mu }^{+}{\mu }^{-}$ decays, we look for further constraint on the couplings $Z^{\prime }-{\mu }^{+}{\mu }^{-}$ from $A_{FB}(B\to K^{\ast }{\mu }^{+}{\mu }^{-}{)}_{0{\mathrm{GeV}}^2⩽q^2⩽2{\mathrm{GeV}}^2}$ and get numerically $B_{\mu \mu }^{L,R}\sim \mathcal{O}(10^{-2})$. Moreover, we find that the relations, $B_{\mu \mu }^L<B_{\mu \mu }^R$ and $B_{\mu \mu }^L+B_{\mu \mu }^R<0$, with a small negative ${\varphi }_s^L$, are crucial to moderate the discrepancy for $A_{FB}(B\to K^{\ast }{\mu }^{+}{\mu }^{-})$ between the SM prediction and the experimental data. Numerically, comparing with the SM prediction, we find that $A_{FB}(B\to K^{\ast }{\mu }^{+}{\mu }^{-}{)}_{0{\mathrm{GeV}}^2⩽q^2⩽2{\mathrm{GeV}}^2}$ could be enhanced about 80% and 50% by $Z^{\prime }$ contribution at most in scenarios S1 and S2, corresponding to the two fitted results of ${\varphi }_s$ by UTfit collaboration, respectively. However, the results are still about $1.5\sigma$ lower than the experimental measurement.

Comments: 20 pages, 3 figures. To appear in JHEP