Phenomenological Profiles of the Inclusive Hadron Spectra in the Decay $B \to X_s \ell^+ \ell^-$

Hadron spectra and hadronic moments in the decay $B \to X_s \ell^+ \ell^-$ are calculated taking into account both the short-distance and long-distance contributions in the decay amplitude using a Fermi motion (FM) model to incorporate the $B$-meson wave-function effects. The measured branching ratios for the inclusive decays $B \to X_s+ (J/\psi,\psi^\prime,...)\to X_s \ell^+ \ell^-$ are used to fix the normalization of the long-distance contribution. The momentum distribution of the $J/\psi$ measured by the CLEO collaboration is fitted in the FM model which is then used to calculate the hadronic spectra from the resonant contribution also away from the $J/\psi$-resonance. We also study the effect of various descriptions of the resonant and non-resonant $c\bar{c}$ contributions in $B \to X_s \ell^+ \ell^-$ existing in the literature on the hadron energy and invariant mass spectra, and in the Forward-Backward asymmetry. Selective cuts on the hadron and dilepton invariant masses can be used to reduce the $B\bar{B}$ background and resonant contribution and, as an example, we work out the hadron spectra with the experimental cuts used by the CLEO collaboration in searching for the decay $B \to X_s \ell^+ \ell^-$. We show that data from the forthcoming B facilities could be used effectively to measure the short-distance contribution in $B \to X_s \ell^+ \ell^-$, enabling precise determination of the FM model and heavy quark effective theory parameters $\lambda_1$ and $\bar{\Lambda}$.