Asymptotics of Heavy-Meson Form Factors

Abstract

Using methods developed for hard exclusive QCD processes, we calculate the asymptotic behaviour of heavy-meson form factors at large recoil. It is determined by the leading- and subleading-twist meson wave functions. For $1\ll |v\cdot v'|\ll m_Q/\Lambda$, 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 $|v\cdot v'|\gg m_Q/\Lambda$, 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 $|v\cdot v'|\gg 1$. As a consequence, there is an exact zero in the form factor for the scattering of longitudinally polarized $B^*$ mesons at some value $v\cdot v'\sim m_b/\Lambda$, and an approximate zero in the form factor of $B$ mesons in the timelike region ($v\cdot v'\sim -m_b/\Lambda$). 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 $e^+ e^-$ collisions.