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

We report the first measurement of the lepton forward-backward asymmetry ${cal A}_{rm FB}$ as a function of the squared four-momentum of the dilepton system, $q^2$, for the electroweak penguin process $B rightarrow X_s ell^+ ell^-$ 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 $772times10^6$ $Bbar{B}$ pairs recorded at the $Upsilon(4S)$ resonance with the Belle detector at the KEKB $e^+ e^-$ collider. ${cal A}_{rm FB}$ for the inclusive $B rightarrow X_s ell^+ ell^-$ 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$^2$/$c^2$, ${cal A}_{rm FB} < 0$ is excluded at the 2.3$sigma$ level, where $sigma$ is the standard deviation. For $q^2 < 4.3$ GeV$^2$/$c^2$, the result is within 1.8$sigma$ of the Standard Model theoretical expectation.