An Implication on the Pion Distribution Amplitude from the Pion-Photon Transition Form Factor with the New BABAR Data

TL;DR

This paper analyzes the pion-photon transition form factor data from BABAR to infer that a broader pion distribution amplitude, similar to the Chernyak-Zhitnitsky form, better explains the experimental results across energy regions.

Contribution

It introduces a phenomenological model considering both valence and non-valence quark contributions to determine the pion distribution amplitude consistent with new BABAR data.

Findings

A broader pion distribution amplitude explains the data better.

Parameter B around 0.60 fits the data well.

Pion distribution amplitude resembles Chernyak-Zhitnitsky form.

Abstract

The new BABAR data on the pion-photon transition form factor arouses people's new interests on the determination of pion distribution amplitude. To explain the data, we take both the leading valence quark state's and the non-valence quark states' contributions into consideration, where the valence quark part up to next-to-leading order is presented and the non-valence quark part is estimated by a phenomenological model based on its limiting behavior at both $Q^2\to 0$ and $Q^2\to\infty$. Our results show that to be consistent with the new BABAR data at large $Q^2$ region, a broader other than the asymptotic-like pion distribution amplitude should be adopted. The broadness of the pion distribution amplitude is controlled by a parameter $B$. It has been found that the new BABAR data at low and high energy regions can be explained simultaneously by setting $B$ to be around 0.60, in which the pion distribution amplitude is closed to the Chernyak-Zhitnitsky form.