Exclusive production of pions and the pion distribution amplitude

TL;DR

This paper investigates the exclusive production of pions using a flat pion distribution amplitude derived from the Bethe-Salpeter equation, calculating relevant form factors and photoproduction processes within perturbative QCD.

Contribution

It introduces a flat pion distribution amplitude from the Bethe-Salpeter equation and applies it to compute form factors and pion photoproduction, aligning with experimental data.

Findings

Flat distribution amplitude describes data well

Computed pion transition and form factors at LO and NLO

Perturbative QCD effectively models high-energy pion production

Abstract

Considering, as a limit case, an approximately flat pion distribution amplitude, which is determined from the hardest, in momentum space, solution of the Bethe-Salpeter equation for the pion wave function, we compute the pion transition form factor $F_{\pi\gamma\gamma^{*}}(Q^{2})$ and the pion form factor $F_{\pi}(Q^2)$, taking into account the LO as well as NLO form of the hard coefficient function entering the leading-twist factorization formula. We also compute the exclusive photoproduction of pions pairs at high energies, $\gamma \gamma \to \pi^{+}\pi^{-}$, where perturbative QCD can be used to compute the hard scattering matrix elements. We verify that the existent data for exclusive pion production can be reasonably described as a function of such flat distribution amplitude.