Exclusive production of pions and the pion distribution amplitude

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.