A Preliminary Determination of the Second Mellin Moment of the Pion's Distribution Amplitude Using the Heavy Quark Operator Product Expansion

TL;DR

This paper investigates using the heavy quark operator product expansion to estimate the second Mellin moment of the pion's distribution amplitude, demonstrating a preliminary result in the quenched approximation.

Contribution

It introduces a novel application of HOPE for extracting Mellin moments of the pion's distribution amplitude, focusing on the second moment as a proof of concept.

Findings

Preliminary value of the second Mellin moment: 0.19(7)

Method successfully extracts moments at low pion momentum

Results obtained in the continuum limit within the quenched approximation

Abstract

We explore the feasibility of determining Mellin moments of the pion's light cone distribution amplitude using the heavy quark operator product expansion (HOPE) method. As the first step of a proof of principle study we pursue a determination of the second Mellin moment. We discuss our choice of kinematics which allows us to successfully extract the moment at low pion momentum. We describe the numerical simulation, and describe the data analysis, which leads us to a preliminary determination of the second Mellin moment in the continuum limit in the quenched approximation as $\langle\xi^2\rangle=0.19(7)$ in the $\bar{\text{MS}}$ scheme at 2 GeV.