We present precision corrections to dispersion relation bounds on form factors in bottom hadron semileptonic decays and analyze their effects on parameterizations derived from these bounds. We incorporate QCD two-loop and nonperturbative corrections to the two-point correlator, consider form factors whose contribution to decay rates is suppressed by lepton mass, and implement more realistic estimates of truncation errors associated with the parameterizations. We include higher resonances in the hadronic sum that, * boyd@fermi.phys.cmu.edu † bgrinstein@ucsd.edu ‡ rlebed@ucsd.edu 1 together with heavy quark symmetry relations near zero recoil, further tighten the sum rule bounds. Utilizing all these improvements, we show that each of the six form factors inB → Dℓν andB → D * ℓν can be described with 3% or smaller precision using only the overall normalization and one unknown parameter. A similar one-coefficient parameterization of one of the Λ b → Λ c ℓν form factors, together with heavy quark symmetry relations valid to order 1/m 2 , describes the differential baryon decay rate in terms of one unknown parameter and the phenomenologically interesting quantityΛWe discuss the validity of slope-curvature relations derived by Caprini and Neubert, and present weaker, corrected relations. Finally, we present sample fits of current experimentalB → D * ℓν andB → Dℓν data to the improved one-parameter expansion.

We use rigorous QCD dispersion relations to derive model-independent bounds on the B → πlν, D → πlν and D → K lν form factors. These bounds are particularly restrictive when the value of the observable form factor at one or more kinematic points is assumed.With reasonable assumptions we find f B ≤ 195 MeV and that the shape of the form factor becomes severely constrained. These constraints are useful both for model discrimination and for model-insensitive extraction of CKM mixing parameters.

We present a method for parametrizing heavy meson semileptonic form factors using dispersion relations, and from it produce a two-parameter description of the B → B elastic form factor. We use heavy quark symmetry to relate this function toB → D * lν form factors, and extract |V cb | = 0.037−0.002 from experimental data with a least squares fit. Our method eliminates model-dependent uncertainties inherent in choosing a parametrization for the extrapolation of the differential decay rate to threshold. The method also allows a description ofB → Dlν form factors accurate to 1% in terms of two parameters.April 1995 *

The implications of chiral SU (3) L ×SU (3) R symmetry and heavy quark symmetry for the radiative decays D * 0 → D 0 γ, D * + → D + γ, and D * s → D s γ are discussed. Particular attention is paid to SU (3) violating contributions of order m 1/2 q . Experimental data on these radiative decays provide constraints on the D * Dπ coupling.