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 ${x}^{2}\ensuremath{\ne}0$ have the same order in the $1/{m}_{Q}$ expansion. The light-cone correlator, corresponding to ${x}^{2}=0$, is shown to systematically overestimate the full correlator, the difference being $\ensuremath{\sim}{\ensuremath{\Lambda}}_{\mathrm{QCD}}/\ensuremath{\delta}$, with $\ensuremath{\delta}$ the continuum subtraction parameter of order 1 GeV. Numerically, this difference is found to be $10\textdiv{}20%$.