Limit on the pion distribution amplitude

TL;DR

This paper derives an upper theoretical limit on the pion distribution amplitude based on QCD Green's functions and compares the resulting photon-pion transition form factor with experimental data.

Contribution

It introduces a field-theoretical upper limit on the pion distribution amplitude and computes the corresponding transition form factor for comparison with experimental results.

Findings

Derived an upper limit on the pion distribution amplitude.

Calculated the photon-pion transition form factor from the upper limit.

Compared the theoretical upper limit with experimental data from CLEO, BaBar, and Belle.

Abstract

The pion distribution amplitude (DA) can be related to the fundamental QCD Green's functions as a function of the quark self-energy and the quark-pion vertex, which in turn are associated with the pion wave function through the Bethe-Salpeter equation. Considering the extreme hard asymptotic behavior in momentum space allowed for a pseudoscalar wave function, which is limited by its normalization condition, we compute the pion DA and its second moment. From the resulting amplitude, representing the field theoretical upper limit on the DA behavior, we calculate the photon-pion transition form factor $F_{\pi\gamma\gamma^{\ast}}(Q^{2})$. The resulting upper limit on the pion transition form factor is compared with existing data published by CLEO, BaBar and Belle collaborations.