Measurement of the Differential Branching Fraction and Forward-Backward Asymmetry for $B\to K^{(*)}{l}^{+}{l}^{-}$

We study $B\to K^{(*)}{\ell }^{+}{\ell }^{-}$ decays ($\ell =e$, $\mu$) based on a data sample of $657\times {10}^6$ $B\overline{B}$ pairs collected with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. We report the differential branching fraction, isospin asymmetry, $K^{*}$ polarization, and the forward-backward asymmetry ($A_{\mathrm{FB}}$) as functions of $q^2=M_{\ell \ell }^2{c}^2$. The fitted $A_{\mathrm{FB}}$ spectrum exceeds the standard model expectation by 2.7 standard deviations. The measured branching fractions are $\mathcal{B}(B\to K^{*}{\ell }^{+}{\ell }^{-})=({10.7}_{-1.0}^{+1.1}\pm 0.9)\times {10}^{-7}$ and $\mathcal{B}(B\to K{\ell }^{+}{\ell }^{-})=({4.8}_{-0.4}^{+0.5}\pm 0.3)\times {10}^{-7}$, where the first errors are statistical and the second are systematic, with the muon to electron ratios $R_{K^{*}}=0.83\pm 0.17\pm 0.08$ and $R_K=1.03\pm 0.19\pm 0.06$.

Figure 1

Differential branching fractions for the (a) $K^{*}{\ell }^{+}{\ell }^{-}$ and (b) $K{\ell }^{+}{\ell }^{-}$ modes as a function of $q^2$. The two shaded regions are veto windows to reject $J/\psi ({\psi }^{\prime })X$ events. The solid curves show the SM theoretical predictions with the minimum and maximum allowed form factors [16]. (c) and (d) show the fit results for $F_L$ and $A_{\mathrm{FB}}$ in $K^{*}{\ell }^{+}{\ell }^{-}$ as a function of $q^2$, together with the solid (dotted) curve representing the SM ($C_7=-C_7^{\mathrm{SM}}$) prediction [16]. (e) is the $A_I$ asymmetry as a function of $q^2$ for the $K^{*}{\ell }^{+}{\ell }^{-}$ (filled circles) and $K{\ell }^{+}{\ell }^{-}$ (open circles) modes.