Heavy-to-light form factors: Sum rules on the light cone and beyond

Abstract

We report the first systematic analysis of the off-light-cone effects in sum rules for heavy-to-light form factors. These effects are investigated in a model based on scalar constituents, which allows a technically rather simple analysis but has the essential features of the analogous QCD calculation. The correlator relevant for the extraction of the heavy-to-light form factor is calculated in two different ways: first, by adopting the full Bethe-Salpeter amplitude of the light meson and, second, by performing the expansion of this amplitude near the light cone x 2 = 0. We demonstrate that the contributions to the correlator from the light-cone term x 2 = 0 and the off-light-cone terms x 2 = 0 have the same order in the 1/mQ expansion. The light-cone correlator, corresponding to x 2 = 0, is shown to systematically overestimate the full correlator, the difference being ∼ ΛQCD/δ, with δ the continuum subtraction parameter of order 1 GeV. Numerically, this difference is found to be 10 ÷ 20%.

Form factors for $B\to j_1j_2$ decays into two currents in QCD

“…x k q qx =o For the sake of argument, we omit here the Lorentz and the spinor indices and consider field theory with scalar partciles. Such an approach allows us to avoid techncal complications and to concentrate on the conceptual aspects [23][24][25]. Still, we keep the QCD notations of the quark fields b and s and denote b and s the complex conjugate fields.…”

Bound-state parameters from dispersive sum rules for vacuum-to-vacuum correlators

“…The method of sum rules in QCD contains a set of prescriptions (see e.g. [3,4]) which are believed to provide such a systematic error. In QCD this, however, always remains a conjecture-it is impossible to prove that the range provided by the standard sum-rule procedures indeed contains the actual value of the bound-state parameter.…”