Matrix Elements of the Singlet Axial Current in the Proton

TL;DR

This paper introduces a lattice QCD method to estimate the singlet axial current matrix element in the proton, highlighting its limitations in the quenched approximation and presenting preliminary numerical results.

Contribution

The paper proposes a novel lattice QCD approach using the Adler-Bell-Jackiw anomaly to compute the singlet axial current matrix element in the proton, emphasizing its failure in the quenched approximation.

Findings

Method relies on the Adler-Bell-Jackiw anomaly in the chiral limit.

Fails in the quenched approximation due to poor statistical signals.

Preliminary data from quenched configurations show limited success.

Abstract

We present a method to estimate the matrix element of the singlet axial current within a polarized proton state using lattice QCD. The method relies on using the Adler-Bell-Jackiw anomaly and gives the desired result in the chiral limit. We show that this method fails in the quenched approximation. For heavy quarks one does not expect much difference between simulations including dynamical quarks and those done in the quenched approximation. For that reason we explore numerical methods on an existing set of quenched configurations. The data obtained in this exploratory study show a poor statistical signal.