Revisiting the Pion Leading-Twist Distribution Amplitude within the QCD Background Field Theory

TL;DR

This paper refines the calculation of the pion's leading-twist distribution amplitude using QCD background field theory and sum rules, incorporating higher-dimension operators for improved accuracy and consistency with lattice QCD.

Contribution

It introduces an expanded sum rule approach including dimension-six operators to accurately determine pion DA moments and Gegenbauer coefficients.

Findings

Pion DA moments are quantified with uncertainties.

Dimension-six condensates significantly affect the moments.

The first Gegenbauer moment aligns with lattice QCD but suggests a larger value.

Abstract

We study the pion leading-twist distribution amplitude (DA) within the framework of SVZ sum rules under the background field theory. To improve the accuracy of the sum rules, we expand both the quark propagator and the vertex $(z\cdot \tensor{D})^n$ 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 $\left<\xi^2\right>|_{\rm 1\;GeV} = 0.338 \pm 0.032$, $\left<\xi^4\right>|_{\rm 1\;GeV} = 0.211 \pm 0.030$ and $\left<\xi^6\right>|_{\rm 1\;GeV} = 0.163 \pm 0.030$. 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 $a^\pi_2|_{\rm 1\;GeV} = 0.403 \pm 0.093$, which is consistent with those obtained in the literature within errors but prefers a larger central value as indicated by lattice QCD predictions.