The longitudinal and transverse distributions of the pion wavefunction from the present experimental data on the pion-photon transition form factor

TL;DR

This study analyzes experimental data on the pion-photon transition form factor to determine the pion wavefunction's longitudinal and transverse distributions, revealing consistency among some datasets and differences with others, especially BABAR.

Contribution

It provides a combined analysis of multiple experimental datasets to extract pion wavefunction parameters, offering insights into its longitudinal and transverse behavior and their compatibility with different models.

Findings

BELLE and CLEO data favor asymptotic-like distribution amplitude.

BABAR data suggests a broader, CZ-like distribution amplitude.

Experimental datasets show varying preferences for pion wavefunction models.

Abstract

It is noted that the low-energy behavior of the pion-photon transition form factor $F_{\pi\gamma}(Q^2)$ is sensitive to the transverse distribution of the pion wavefunction, and its high-energy behavior is sensitive to the longitudinal one. Thus a careful study on $F_{\pi\gamma}(Q^2)$ can provide helpful information on the pion wavefunction precisely. In this paper, we present a combined analysis of the data on $F_{\pi\gamma}(Q^2)$ reported by the CELLO, the CLEO, the BABAR and the BELLE collaborations. It is performed by using the method of least squares. By using the combined measurements of BELLE and CLEO Collaborations, the pion wavefunction longitudinal and transverse behavior can be fixed to a certain degree, i.e. we obtain $\beta \in [0.691,0.757] \rm GeV$ and $B \in [0.00,0.235]$ for $P_{\chi^2} \geq 90\%$, where $\beta$ and $B$ are two parameters of a convenient pion wavefunction model whose distribution amplitude can mimic the various longitudinal behavior under proper choice of parameters. We observe that the CELLO, CLEO and BELLE data are consistent with each other, all of which prefers the asymptotic-like distribution amplitude; while the BABAR data prefers a more broad distribution amplitude, such as the CZ-like one.