HQET and Form Factor Effects in $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$

Abstract

We examine the rates for the exclusive decays $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$. We use the scaling predictions of the heavy quark effective theory to extract the necessary form factors from fits to various combinations of data. These data include the $D\to K^{(\ast )}\ell \nu$ semileptonic decays, as well as the nonleptonic decays $B\to K^{(\ast )}{\psi }^{(\prime )}$ and the rare decay $B\to K^{\ast }\gamma$. We use different parametrizations of form factors, and find that integrated decay rates are not very sensitive to the forms chosen. However, the decay spectra and the forward-backward asymmetry in $B\to K^{\ast }{\ell }^{+}{\ell }^{-}$ are sensitive to the forms chosen for the form factors, while the lepton polarization asymmetry in ${\bar{B}}^0\to {\bar{K}}^0{\mu }^{+}{\mu }^{-}$ is largely independent of the choice of form factors. Contributions from charmonium resonances dominate the spectra and integrated rates. In our `best' scenario, we find $Br({\bar{B}}^0\to {\bar{K}}^0{\mu }^{+}{\mu }^{-})=2.0\pm 0.3\times 10^{-6}$ and $Br({\bar{B}}^0\to {\bar{K}}^{\ast 0}{\mu }^{+}{\mu }^{-})=8.1\pm 2.0\times 10^{-6}$. We also make predictions for other polarization observables in these decays.

24 pages, RevTeX, epsf, rotating 11 postscript figures appended as uuencoded file (hardcopy can be obtained upon request from [email protected])

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• Probing the sources of CP violation via B -> K^* l^+ l^- decay
• Rare decays B -> (K, K*) (l+ l-, nu bar{nu}) in the quark model
• Light-front quark model analysis of rare $B\to K{\ell }^{+}{\ell }^{-}$ decays
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• The exclusive $B->(K,K^{\ast }){\ell }^{+}{\ell }^{-}$ decays in a CP softly broken two Higgs doublet model
• B--> K^* l^+ l^- decay in the two Higgs doublet model with flavor changing neutral currents
• Exclusive rare $B_s\to (K,\eta ,{\eta }^{\prime }){\ell }^{+}{\ell }^{-}$ decays in the light-front quark model
• Measuring |V_{td} / V_{ub}| through B -> M ν\barν(M=π,K,ρ,K^*) decays
• Lepton polarization asymmetries for FCNC decays of the ${\Lambda }_b$ baryon
• Exclusive B --> M l^+ l^- (M=π, K, ρ, K^*) Decays and Determinations of |V_{ts}| (and |V_{td}/V_{ts}|)
• Standard Model CP violation in Polarised b->d l^+ l^-
• Rare B -> K^* l^+ l^- decay, two Higgs doublet model, and light cone QCD sum rules
• Fourth generation effects on the rare $B\to K^{\ast }\nu \bar{\nu }$ decay
• Inelastic Rescattering and CP Asymmetries in D -> pi+ pi-, pi0 pi0