Measurement of the Lepton Forward-Backward Asymmetry in $B\to X_s{\ell }^{+}{\ell }^{-}$ Decays with a Sum of Exclusive Modes

Abstract

We report the first measurement of the lepton forward-backward asymmetry ${\mathcal{A}}_{\mathrm{FB}}$ as a function of the squared four-momentum of the dilepton system, $q^2$, for the electroweak penguin process $B\to X_s{\ell }^{+}{\ell }^{-}$ with a sum of exclusive final states, where $\ell$ is an electron or a muon and $X_s$ is a hadronic recoil system with an $s$ quark. The results are based on a data sample containing $772\times 10^6$ $B\bar{B}$ pairs recorded at the $\hat{I}\yen (4S)$ resonance with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. ${\mathcal{A}}_{\mathrm{FB}}$ for the inclusive $B\to X_s{\ell }^{+}{\ell }^{-}$ is extrapolated from the sum of 10 exclusive $X_s$ states whose invariant mass is less than 2 GeV/$c^2$. For $q^2>10.2$ GeV${}^2$/$c^2$, ${\mathcal{A}}_{\mathrm{FB}}<0$ is excluded at the 2.3$\ddot{I}ƒ$ level, where $\ddot{I}ƒ$ is the standard deviation. For $q^2<4.3$ GeV${}^2$/$c^2$, the result is within 1.8$\ddot{I}ƒ$ of the Standard Model theoretical expectation.

13 pages, 23 figures, Belle Preprint 2014-1, KEK preprint 2013-60