Phenomenological profiles of the inclusive hadron spectra in the decayB→Xsl+l−

Abstract

Hadron spectra and hadronic moments in the decay $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{s}{l}^{+}{l}^{\ensuremath{-}}$ 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 $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{s}+(J/\ensuremath{\psi},{\ensuremath{\psi}}^{\ensuremath{'}},\dots{})\ensuremath{\rightarrow}{X}_{s}{l}^{+}{l}^{\ensuremath{-}}$ are used to fix the normalization of the long-distance contribution. Assuming factorization, the momentum distribution of the $J/\ensuremath{\psi}$ 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 $J/\ensuremath{\psi}$ resonance. We also study the effect of various descriptions of the resonant and nonresonant $c\overline{c}$ contributions in $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{s}{l}^{+}{l}^{\ensuremath{-}}$ 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 $B\overline{B}$ 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 $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{s}{l}^{+}{l}^{\ensuremath{-}}$. We show that data from the forthcoming B facilities could be used effectively to measure the short-distance contribution in $\stackrel{\ensuremath{\rightarrow}}{B}{X}_{s}{l}^{+}{l}^{\ensuremath{-}},$ enabling precise determination of the FM model parameters as well as the heavy quark effective theory parameters ${\ensuremath{\lambda}}_{1}$ and $\overline{\ensuremath{\Lambda}}.$