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

Abstract

We reconsider the calculation of $\mathcal{O}({\Lambda }_{QCD}^2/m_b^2)$ nonperturbative corrections to $\bar{B}\to X_s{l}^{+}{l}^{-}$ 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 $\mathcal{O}({\Lambda }_{QCD}^2/m_b^2)$ 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 $\bar{B}\to \bar{K}{l}^{+}{l}^{-}$ 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 $\bar{B}\to X_s{l}^{+}{l}^{-}$.

18 pages, LaTeX, 1 figure

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