Corrections of Order ∧_QCD^2/m_c^2 to Inclusive Rare B Decays

We calculate nonperturbative O(∧_QCD^2/m_c^2) corrections to the dilepton invariant mass spectrum and the forward-backwarda charge asymmetry in B->X_s e^+e^- decay using a heavy quark expansion approach. The method has recently been used to estimate long-distance effects in B->X_sγ. We generalize this analysis to the case of non-vanishing photon invariant mass, q^2≠0, relevant for the rare decay mode B->X_s e^+e^-. In the phenomenologically interesting q2 region away from the c`c resonances, the heavy quark expansion approach should provide a reasonable descrption of possible non-perturbative corrections. In particular this picture is preferable to the model-dependent approach relying on the tails of Breit-Wigner resonances, Which has been employed so far in the literature to account for these effects. We find that the O(∧_QCD^2/m_c^2) corrections to the dilepton invariant mass spectrum and to the forward-backward asymmetry in B->X_s e^+e^- amount to several percent at most for q^2/m_b^2≲0.3 and q^2/m_b^2≳0.6 respectively. The O(∧_QCD^2/m_c^2) correction to the B->X_sγ decay rate is also computed and found to be +3%, which agrees in magnitude with previous calculations. Finally, we comment on long-distance effects in B->X_svv, which in this case are extremely suppressed due to the absence of virtual photon contributions.