Pion distribution amplitude extracted from the experimental data with the local duality sum rule

Abstract

The photon-to-pion transition form factor is investigated using the form of the renormalon-based twist-four pion distribution amplitude (DA) in the framework of the light-cone local-duality QCD sum rule, which, with suitable parameters, is insensitive to the higher-order Gegenbauer coefficients. With a careful determination for the insertion parameters so that the contribution from the higher-order Gegenbauer expansions is suppressed, the best-fit central values of the first two nontrivial Gegenbauer coefficients of the pion distribution amplitude are extracted out from the CLEO data to be ${a}_{2}(1\text{ }\text{ }{\mathrm{GeV}}^{2})=0.145\ifmmode\pm\else\textpm\fi{}0.055$ and ${a}_{4}(1\text{ }\text{ }{\mathrm{GeV}}^{2})=\ensuremath{-}(0.125\ifmmode\pm\else\textpm\fi{}0.085)$, respectively. The rescaled photon-to-pion transition form factor with our best-fit parameters is consistent very well with both the CELLO data and the prediction of the interpolation formula in all the experimental accessible region of the momentum transfer. The shape of the pion distribution amplitude based on the two-parameter model favors the camel-like type, where the near-end-point values are suppressed more than the asymptotic DA, and satisfies the midpoint constraint from light-cone sum rules approximately.