Asymptotics of Heavy-Meson Form Factors

TL;DR

This work analyzes heavy-meson form factors at large recoil within HQET, showing that the asymptotics are governed by light-cone heavy-meson wave functions. The leading Isgur–Wise function dominates in an intermediate recoil regime, while at still larger recoil the 1/m_Q–suppressed contributions, ξ_3 and χ_2, take over, determined by the leading-twist wave function. The authors derive evolution equations for the wave functions, construct QCD sum rules to estimate nonperturbative parameters λ_E^2 and λ_H^2, and provide model wave functions, obtaining predictions such as zeros in certain form factors in the spacelike region and implications for heavy-meson pair production in $e^+e^-$ collisions. They also discuss Sudakov suppression and the matching of HQET results to full QCD at large recoil, connecting hard-exclusive QCD methods with heavy-quark symmetry. Overall, the paper presents a coherent, model-independent framework for the asymptotics of heavy-meson form factors across large recoil, with concrete predictions for observables in $e^+e^-$ processes.

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 $1\ll |v\cdot v'|\ll m_Q/Λ$, 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 $|v\cdot v'|\gg m_Q/Λ$, 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 $v\cdot v'\sim m_b/Λ$, and an approximate zero in the form factor of $B$ mesons in the timelike region ($v\cdot v'\sim -m_b/Λ$). 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.

Figures (11)

• Figure 1: Hard-gluon exchange contributions to heavy-meson form factors. The external current is presented by the wave line; the heavy antiquark is represented by a double line.
• Figure 2: One-loop diagrams contributing to the matrix elements $\langle\,0\,|O^{\text{bare}}_\pm(\omega)|\omega'\rangle$. The bare current operators are represented by a circle.
• Figure 3: Feynman rules for vertices involving $O_\pm(\omega)$.
• Figure 4: Non-vanishing diagrams for the correlators $\Pi_E$ and $\Pi_H$. The higher-dimensional current operators $O_E$ and $O_H$ are represented by a gray circle; the interpolating current is represented by a white circle.
• Figure 5: Sum-rule results for $\lambda_E^2$ (upper plot) and $\lambda_H^2$ (lower plot) as a function of $1/\tau$, for three values of the continuum threshold $\varepsilon_c$. The stability window lies in between the dashed lines.