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

Abstract

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 $\bar{\Lambda }$.

24 pages, 21 figures (require epsf.sty)

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• Exclusive semileptonic rare decays $B-{>}_{(}$K,K^*) \ell^+ \ell^- in supersymmetric theories
• Quarkonium momentum distributions in photoproduction and B decay
• Looking for Novel CP-Violating Effects in B->K^*l^+l^-
• SUSY breaking mediation mechanisms and (g-2)_μ, B -> X_s γ, B -> X_{s} l^+ l^- and B_s -> μ^+ μ^-
• Shape-Function Effects and Split Matching in B-> Xs l+ l-
• Flavour-Conserving CP Phases in Supersymmetry and Implications for Exclusive B Decays
• Universality and m_X cut effects in B -> Xs l+ l-
• Rate difference between b $\to$ s mu^+ mu^- and b $\to$ s e^+e^- in SUSY with large tan$\beta$