Accessing high-momentum nucleons with dilute stochastic sources

Abstract

A novel stochastic technique combining a dilute source grid of Z3 noise with iterative momentumsmearing 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 | p| 3.75 GeV and | p| 2.82 GeV on the small and large volume respectively.I.

Finite size effect on vector meson and baryon sectors in 2+1 flavor QCD at the physical point

“…As an alternative way to reduce the statistical error of correlator, we develop a variation of the Z 3 grid source method [12][13][14]. We first divide the three-dimensional source space into cubic cells with a crystal structure such as simple-cubic (SC) or body-centered-cubic (BCC) or face-centered-cubic (FCC), whose edge length is b cell = L/n div ∈ Q with n div ∈ N in the lattice unit a.…”

“…In this paper we investigate the finite size effect for the vector meson and the baryon sectors on the same gauge configurations in Ref. [1] employing the all-modeaveraging (AMA) technique [10,11] and the "crystal" source method, which is a sort of Z 3 grid source method [12][13][14], to obtain hadron propagators with high precision. With the use of m π , m K and m Ξ as the physical inputs, we determine the physical point together with the lattice cutoff.…”

Large-Momentum Effective Theory

“…In this way, the overlap with high momentum state is vastly increased after Euclidean time evolution. Although there are other proposed method to generate large momentum [416], the momentum smearing has become a standard technique in LaMET applications. Second, the proton size is frame-dependent and changes with its momentum.…”

Lattice QCD Calculations of Parton Physics

“…Momentum smearing has been widely used to create large-momentum hadron states up to 3 GeV [38], and with sufficient statistics it may be possible to reach 5 GeV for nucleons. A large-momentum method has also been suggested for dilute stochastic sources [39]. To reach very small or large-x partons, new methods are perhaps needed to create even larger momentum states.…”