Determination of the pion distribution amplitude

Abstract

Currently, not enough is known to determine the hadron distribution amplitudes (DAs)---which are universal physical quantities in the high-energy processes involving hadrons---in order to apply perturbative QCD to exclusive processes. Even for the simplest pion, one cannot discriminate between different DA models. Conversely, one expects that processes involving pions can in principle provide strong constraints on the pion DA. For example, the pion-photon transition form factor (TFF) can get accurate information about the pion wave function or DA due to the single pion in this process. However, the data from Belle and BABAR show a big difference regarding this TFF in high-${Q}^{2}$ regions; at present, they are unable to determine the pion DA. In the present paper, we think it is still possible to determine the pion DA as long as we perform a combined analysis of the existing data of the processes involving pions, such as $\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\mu}\overline{\ensuremath{\nu}}$, ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$, $B\ensuremath{\rightarrow}\ensuremath{\pi}l\ensuremath{\nu}$, $D\ensuremath{\rightarrow}\ensuremath{\pi}l\ensuremath{\nu}$, etc. Based on the revised light-cone harmonic oscillator model, a convenient DA model is suggested, whose parameter $B$---which dominates its longitudinal behavior for ${\ensuremath{\phi}}_{\ensuremath{\pi}}(x,{\ensuremath{\mu}}^{2})$---can be determined in a definite range by these processes. A light-cone sum rule analysis of the semileptonic processes $B\ensuremath{\rightarrow}\ensuremath{\pi}l\ensuremath{\nu}$ and $D\ensuremath{\rightarrow}\ensuremath{\pi}l\ensuremath{\nu}$ leads to a narrow region $B=[0.01,0.14]$, which indicates a slight deviation from the asymptotic DA. Then, one can predict the behavior of the pion-photon TFF in high-${Q}^{2}$ regions which can be tested in future experiments. This method provides the possibility that the pion DA will be finally determined by a global fit.