We calculate, for the first time using unquenched lattice QCD form factors, the standard model differential branching fractions $d\mathcal{B}/d{q}^2(B\to K{\ell }^{+}{\ell }^{-})$ for $\ell =e$, $\mu$, $\tau$ and compare with experimental measurements by Belle, BABAR, CDF, and LHCb. We report on $\mathcal{B}(B\to K{\ell }^{+}{\ell }^{-})$ in $q^2$ bins used by experiment and predict $\mathcal{B}(B\to K{\tau }^{+}{\tau }^{-})=(1.41\pm 0.15)\times {10}^{-7}$. We also calculate the ratio of branching fractions $R_e^{\mu }=1.00029(69)$ and predict $R_{\ell }^{\tau }=1.176(40)$, for $\ell =e$, $\mu$. Finally, we calculate the “flat term” in the angular distribution of the differential decay rate $F_H^{e,\mu ,\tau }$ in experimentally motivated $q^2$ bins.

• Received 12 June 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.162002