Perturbative QCD and Power Corrected Hadron Spectra and Spectral Moments in the Decays $B \to X_s \ell^+ \ell^-$

Abstract

Leading order (in $\alpha_s$) perturbative QCD and power ($1/m_b^2)$ corrections to the hadronic invariant mass and hadron energy spectra in the decay $B \to X_s \ell^+ \ell^-$ are reviewed in the standard model using the heavy quark expansion technique (HQET). In particular, the first two hadronic moments $<S_H^n>$ and $<E_H^n>$, $n=1,2$, are presented working out their sensitivity on the HQET parameters $\lambda_1$ and $\bar{\Lambda}$. Data from the forthcoming B facilities can be used to measure the short-distance contribution in $B \to X_s \ell^+ \ell^-$ and determine the HQET parameters from the moments $<S_H^n>$. This could be combined with complementary constraints from the decay $B \to X \ell \nu_\ell$ to determine these parameters precisely.