Non-perturbative Pion Matrix Element of a twist-2 operator from the Lattice

TL;DR

This paper presents a non-perturbative lattice calculation of the pion's twist-2 operator matrix element, providing continuum limit values and addressing systematic errors, with the main limitation being the quenched approximation.

Contribution

It offers the first continuum limit value of the pion's twist-2 matrix element from non-perturbative lattice calculations, controlling key systematic errors.

Findings

RGI matrix element <x>_{RGI} = 0.179(11)

MSbar scheme value <x>^{MSbar}(2 GeV) = 0.246(15)

Controlled systematic errors in non-perturbative renormalization and finite size effects

Abstract

We give a continuum limit value of the lowest moment of a twist-2 operator in pion states from non-perturbative lattice calculations. We find that the non-perturbatively obtained renormalization group invariant matrix element is <x>_{RGI} = 0.179(11), which corresponds to <x>^{MSbar}(2 GeV) = 0.246(15). In obtaining the renormalization group invariant matrix element, we have controlled important systematic errors that appear in typical lattice simulations, such as non-perturbative renormalization, finite size effects and effects of a non-vanishing lattice spacing. The crucial limitation of our calculation is the use of the quenched approximation. Another question that remains not fully clarified is the chiral extrapolation of the numerical data.