Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects

TL;DR

This paper presents a method to extract the pion distribution amplitude from Euclidean correlation functions at large momentum, incorporating higher-twist effects and using stochastic estimators to reduce errors.

Contribution

It introduces a simultaneous analysis of multiple correlation functions and the use of all-to-all propagators for improved accuracy in calculating the pion distribution amplitude.

Findings

Higher-twist parameter $oldsymbol{ ext{delta}_2^ ext{pi}}$ agrees with QCD sum rule estimates.

Simultaneous correlation function analysis enhances extraction robustness.

Stochastic estimators effectively reduce statistical errors.

Abstract

Building upon our recent study arXiv:1709.04325, we investigate the feasibility of calculating the pion distribution amplitude from suitably chosen Euclidean correlation functions at large momentum. We demonstrate in this work the advantage of analyzing several correlation functions simultaneously and extracting the pion distribution amplitude from a global fit. This approach also allows us to study higher-twist corrections, which are a major source of systematic error. Our result for the higher-twist parameter $\delta^\pi_2$ is in good agreement with estimates from QCD sum rules. Another novel element is the use of all-to-all propagators, calculated using stochastic estimators, which enables an additional volume average of the correlation functions, thereby reducing statistical errors.