Accessing high-momentum nucleons with dilute stochastic sources

TL;DR

This paper introduces a stochastic technique combining dilute sources and momentum-smearing to improve the study of proton correlation functions at high momenta in lattice QCD, achieving better statistical accuracy.

Contribution

The paper presents a new stochastic method with optimized source placement that enhances high-momentum proton studies in lattice QCD.

Findings

Optimal source separation (4-8 points) reduces statistical errors.

Successful fitting of proton energies at momenta up to 3.75 GeV.

Technique improves signal quality over single point sources.

Abstract

A novel stochastic technique combining a dilute source grid of $\mathbb{Z}_3$ noise with iterative momentum-smearing is used to study the proton correlation function at rest and in boosted frames on two lattice volumes. The technique makes use of the baryonic version of the so-called one-end trick, and the decomposition into signal and noise terms of the resulting stochastic proton correlation function is made explicit. The number and location of the source points in the dilute grid should be chosen so that the benefits of averaging over many locations overcomes the additional statistical error introduced by the noise terms in the desired fitting region. At all nontrivial momentum values considered we find that the choice of $N=4$--$8$ maximally separated source locations is shown to be optimal, providing a reduced statistical error when compared with a single point source. This enables us to successfully fit the proton energy at momentum values as high as $|\vec{p}| \simeq 3.75$ GeV and $|\vec{p}| \simeq 2.82$ GeV on the small and large volume respectively.