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

Abstract

We compute the 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 $B\to X_s{\ell }^{+}{\ell }^{-}$ in standard model. This is done both by using the heavy quark expansion technique (HQET) and a perturbative-QCD improved Fermi motion (FM) model which takes into account $B$-meson wave-function effects. The corrections in the hadron energy ($E_H$) spectrum are found to be small over a good part of this spectrum in both the methods. However, the expansion in $1/m_b$ in HQET fails near the lower kinematic end-point and at the $c\bar{c}$ threshold. The hadronic invariant mass ($S_H$) spectrum is calculable only over a limited range $S_H>\bar{\Lambda }{m}_B$ in the heavy quark expansion, where $\bar{\Lambda }\simeq m_B-m_b$. We also present results for the first two hadronic moments $<S_H^n>$ and $<E_H^n>$, $n=1,2$, working out their sensitivity on the HQET and FM model parameters. For equivalent values of these parameters, the moments in these methods are remarkably close to each other. Using the FM model, we study the effect of the experimental cuts, used recently by the CLEO collaboration in searching for the decay $B\to X_s{\ell }^{+}{\ell }^{-}$, on the hadron spectra and hadronic invariant mass moments. The constraints following from assumed values of $<S_H^n>$ on the HQET parameters ${\lambda }_1$ and $\bar{\Lambda }$ are worked out. Data from the forthcoming B facilities could be used to measure the short-distance contribution in $B\to X_s{\ell }^{+}{\ell }^{-}$ and determine the HQET parameters ${\lambda }_1$ and $\bar{\Lambda }$. This could be combined with complementary constrains in $B\to X\ell {\nu }_{\ell }$ to determine them precisely.

44 pages, 15 figure (require epsf.sty);, March 1998; Several typos and composition errors corrected; four references added; no change in formulae or results

References in corpus (10)

• Corrections of Order ${\Lambda }_{QCD}^2/m_c^2$ to Inclusive Rare B Decays
• QCD estimate of the long-distance effect in $B\to K^{\ast }\gamma$
• Comment on nonperturbative effects in $B\to X_s\gamma$
• V_{ub} from the Hadronic Invariant Mass Spectrum in Semileptonic B Decay
• Comment On Nonperturbative O(1/m_c^2) Corrections to B -> X_s gamma
• Hadronic Spectral Moments in Semileptonic B Decays With a Lepton Energy Cut
• Corrections to Moments of the Photon Spectrum in the Inclusive Decay B \to X_s γ
• Search for Inclusive $b\to sl^{+]l^{-}$
• Non-1/m_b^n Power Suppressed Contributions to Inclusive b->s l+ l- Decays
• Key Distributions for Charmless Semileptonic B Decay

Cited by in corpus (12)

• Photonic penguins at two loops and m_t-dependence of BR[ B -> X_s l^+ l^-]
• Flavor Physics in the Quark Sector
• B -> Xs l+ l- decays in supersymmetry
• B decay shape variables and the precision determination of |Vcb| and mb
• Probe R-parity Violating Supersymmetry Effects in $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$ and $B_s\to {\ell }^{+}{\ell }^{-}$ Decays
• The rare decays $B_u^{+}\to {\pi }^{+}{\ell }^{+}{\ell }^{-}$, ${\rho }^{+}{\ell }^{+}{\ell }^{-}$ and $B_d^0\to {\ell }^{+}{\ell }^{-}$ in the R-parity violating supersymmetry
• Nonperturbative corrections to moments of the decay B -> X_s l^+ l^-
• Shape-Function Effects and Split Matching in B-> Xs l+ l-
• Nonperturbative corrections to B -> X_s l^+ l^- with phase space restrictions
• CP Violation in rare semileptonic B decays and supersymmetry
• Phenomenological Profiles of the Inclusive Hadron Spectra in the Decay $B\to X_s{\ell }^{+}{\ell }^{-}$
• Next-to-leading Order Calculations of the Radiative and Semileptonic Rare B Decays in the Standard Model and Comparison with Data