Revisiting the pion leading-twist distribution amplitude within the QCD background field theory

We study the pion leading-twist distribution amplitude (DA) within the framework of Shifman-Vainshtein-Zakharov sum rules under the background field theory. To improve the accuracy of the sum rules, we expand both the quark propagator and the vertex (z·↔D)ⁿ of the correlator up to dimension-six operators in the background field theory. The sum rules for the pion DA moments are obtained, in which all condensates up to dimension-six have been taken into consideration. Using the sum rules, we obtain ⟨ξ²⟩|1 GeV=0.338±0ex0ex0.032, ⟨ξ⁴⟩|1 GeV=0.211±0.030 and ⟨ξ⁶⟩|1 GeV=0.163±0.030. It is shown that the dimension-six condensates shall provide sizable contributions to the pion DA moments. We show that the first Gegenbauer moment of the pion leading-twist DA is a₂^π|1 GeV=0.403±0.093, which is consistent with those obtained in the literature within errors but prefers a larger central value as indicated by lattice QCD predictions.