Lattice-Constrained Unitarity Bounds for $\bar B^0 \to π^+ l^- \bar ν_l$ Decays

Details Lattice-Constrained Unitarity Bounds for $\bar B^0 \to π^+ l^- \bar ν_l$ Decays Lattice-Constrained Unitarity Bounds for $\bar B^0 \to π^+ l^- \bar ν_l$ Decays

1995-09-22

arxiv.org/abs/hep-ph/9509358v6

Nucl.Phys.B479:353-391,1996

Physics

High Energy Physics

High Energy Physics - Phenomenology

LaTeX, 34 pages, and 6 PostScript figures. Version to appear in Nuclear Physics B. Small changes in the numerical results as w

Scientific paper

10.1016/0550-3213(96)00443-9

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.

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