Asymptotics of heavy-meson form factors

Abstract

Using methods developed for hard exclusive QCD processes, we calculate the asymptotic behavior of heavy-meson form factors at large recoil. It is determined by the leading- and subleading-twist meson wave functions. For $1\ensuremath{\ll}|v\ensuremath{\cdot}{v}^{\ensuremath{'}}|\ensuremath{\ll}{m}_{Q}/\ensuremath{\Lambda}$, the form factors are dominated by the Isgur-Wise function, which is determined by the interference between the wave functions of leading and subleading twist. At $|v\ensuremath{\cdot}{v}^{\ensuremath{'}}|\ensuremath{\gg}{m}_{Q}/\ensuremath{\Lambda}$, they are dominated by two functions arising at order ${1/m}_{Q}$ in the heavy-quark expansion, which are determined by the leading-twist wave function alone. The sum of these contributions describes the form factors in the whole region $|v\ensuremath{\cdot}{v}^{\ensuremath{'}}|\ensuremath{\gg}1$. As a consequence, there is an exact zero in the form factor for the scattering of longitudinally polarized ${B}^{*}$ mesons at some value $v\ensuremath{\cdot}{v}^{\ensuremath{'}}\ensuremath{\sim}{m}_{b}/\ensuremath{\Lambda}$, and an approximate zero in the form factor of $B$ mesons in the timelike region $(v\ensuremath{\cdot}{v}^{\ensuremath{'}}\ensuremath{\sim}\ensuremath{-}{m}_{b}/\ensuremath{\Lambda})$. We obtain the evolution equations and sum rules for the wave functions of leading and subleading twist as well as for their moments. We briefly discuss applications to heavy-meson pair production in ${e}^{+}{e}^{\ensuremath{-}}$ collisions.