Standard Model predictions for B -> Kll with form factors from lattice QCD

Abstract

We calculate, for the first time using unquenched lattice QCD form factors, the Standard Model differential branching fractions $dB/d{q}^2(B\to Kll)$ for $l=e,\mu ,\tau$ and compare with experimental measurements by Belle, BABAR, CDF, and LHCb. We report on $\mathcal{B}(B\to Kll)$ in $q^2$ bins used by experiment and predict $\mathcal{B}(B\to K\tau \tau )=(1.44\pm 0.15)10^{-7}$. We also calculate the ratio of branching fractions $R_e^{\mu }=1.00023(63)$ and predict $R_l^{\tau }=1.159(40)$, for $l=e,\mu$. 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.

Comments: 6 pages, 3 figures; v4 corrected error in evaluation of Wilson coefficient C9eff, resulting in <~ 1\sigma\ shift in observables; v3 matches version published in Phys. Rev. Lett; v2 updated to include comparison with most recent, and significantly more precise, results from LHCb. References updated