Nonperturbative Effects in $\bar B\to X_s l^+l^-$ for Large Dilepton Invariant Mass

Abstract

We reconsider the calculation of ${\cal O}(\Lambda^2_{QCD}/m^2_b)$ nonperturbative corrections to $\bar B\to X_sl^+l^-$ decay. Our analysis confirms the results of Ali et al. for the dilepton invariant mass spectrum, which were in disagreement with an earlier publication, and for the lepton forward-backward asymmetry. We also give expressions for the ${\cal O}(\Lambda^2_{QCD}/m^2_b)$ corrections to the left-right asymmetry. In addition we discuss the breakdown of the heavy quark expansion near the point of maximal dilepton invariant mass $q^2$ and consider a model independent approach to this region using heavy hadron chiral perturbation theory. The modes $\bar B\to\bar Kl^+l^-$ and $\bar B\to\bar K\pi l^+l^-$, which determine the endpoint region of the inclusive decay, are analyzed within this framework. An interpolation is suggested between the region of moderately high $q^2$, where the heavy quark expansion is still valid, and the vicinity of the endpoint described by chiral perturbation theory. We also comment on further nonperturbative effects in $\bar B\to X_sl^+l^-$.