Lattice-Constrained Unitarity Bounds for ${\bar{B}}^0\to {\pi }^{+}{l}^{-}{\bar{\nu }}_l$ Decays

Abstract

Lattice results, kinematical constraints and QCD dispersion relations are combined for the first time to derive model-independent bounds for QCD form factors and corresponding rates. To take into account the error bars on the lattice results we develop a general formalism which ascribes well-defined statistical properties to these bounds. We concentrate on ${\bar{B}}^0\to {\pi }^{+}{l}^{-}{\bar{\nu }}_l$ decays because of the relative simplicity of the analytical behavior of the relevant polarization functions and because of their immediate phenomenological relevance. To determine the range of applicability of the dispersive matching required to obtain the bounds, we have evaluated the leading perturbative and non-perturbative QCD corrections to the relevant polarization functions. Despite the lattice results' large error bars and limited kinematical range, the bounds we obtain appear to favor certain parametrizations for the form factors over others. The bounds also enable the determination of $|V_{ub}|$ from the total experimental rate with a theoretical error ranging from 27% to 37%, depending on the assumptions made. The techniques developed here are, in fact, quite general and are not limited to use with lattice results nor to semileptonic ${\bar{B}}^0\to {\pi }^{+}{l}^{-}{\bar{\nu }}_l$ decays.

LaTeX, 34 pages, and 6 PostScript figures. Version to appear in Nuclear Physics B. Small changes in the numerical results as well as a few other minor changes

References in corpus (24)

• Semileptonic Meson Decays in the Quark Model: An Update
• $D^{\ast }D\pi$ and $B^{\ast }B\pi$ couplings in QCD
• Constraints on Form Factors For Exclusive Semileptonic Heavy to Light Meson Decays
• QCD Calculation of the $B\to \pi ,K$ Form Factors
• The Semileptonic Decays $D\to \pi (\rho )e\nu$ and $B\to \pi (\rho )e\nu$ from QCD Sum Rules
• Semi-leptonic Decays of Heavy Flavours on a Fine Grained Lattice
• Lattice Calculation of D- and B-meson Semileptonic Decays, using the Clover Action at beta=6.0 on APE
• The Decay $B\to \pi \ell \nu$ in Heavy Quark Effective Theory
• Form Factors for B -> pi l nu-bar_l and B -> K* gamma Decays on the Lattice
• $D^{\ast }$ Radiative Decays and Strong Coupling of Heavy Mesons with Soft Pions in a QCD Relativistic Potential Model
• Lattice Study of the Decay B^0-bar -> rho^+ l^- nu_l-bar: Model-Independent Determination of |V_{ub}|
• Quenched Heavy-Light Decay Constants
• The Light Hadron Spectrum and Decay Constants in Quenched Lattice QCD
• $B^{\ast }B\pi (\gamma )$ couplings and $D^*\rar Dπ(γ) $-decays within a $1/M$-expansion in $full$ QCD
• Quenched Light Hadron Mass Spectrum and Decay Constants: the effects of $O(a)$-Improvement at $\beta =6.2$
• Analyticity Properties and Unitarity Constraints of Heavy Meson Form Factors
• An ``Improved" Lattice Study of Semi-leptonic Decays of D-Mesons
• Lattice Study of Semi-Leptonic $B$ Decays: I. $\bar{B}\to D\ell \bar{\nu }$ Decays
• {$SU(3)$} breaking in {$\bar{B}/D\rar Kl\bar ν$} decays and value of {$V_{cd}/V_{cs}$}}
• Weak Decays in the light--front Quark Model
• Dominance of the light-quark condensate in the heavy-to-light exclusive decays
• Form Factors in the Heavy Quark and Chiral Limit: Pole dominance in $\bar{B}\to \pi e{\bar{\nu }}_e$
• Probing with Penguins: A lattice calculation of the branching ratio for some of the exclusive modes of $b\to s\gamma$
• The Rate for $e^{+}{e}^{-}\to B{B}^{\pm }{\pi }^{\mp }$ and its Implications for the Study of CP Violation, $B_s$ Identification, and the Study of $B$ Meson Chiral Perturbation Theory

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