O(α_s) Corrections to B to X_s e^+ e^- Decay in the 2HDM

$O(\alpha_s)$ QCD corrections to the inclusive $B \to X_s e^+ e^-$ decay are investigated within the two - Higgs doublet extension of the standard model (2HDM). The analysis is performed in the so - called off-resonance region; the dependence of the obtained results on the choice of the renormalization scale is examined in details. It is shown that $O(\alpha_s)$ corrections can suppress the $B \to X_s e^+ e^-$ decay width up to $1.5 \div 3$ times (depending on the choice of the dilepton invariant mass $s$ and the low - energy scale $\mu$). As a result, in the experimentally allowed range of the parameters space, the relations between the $B \to X_s e^+ e^-$ branching ratio and the new physics parameters are strongly affected. It is found also that though the renormalization scale dependence of the $B \to X_s e^+ e^-$ branching is significantly reduced, higher order effects in the perturbation theory can still be nonnegligible.