Accessing High Momentum States In Lattice QCD

TL;DR

This paper introduces measures to evaluate and improve the overlap of smeared operators with high-momentum hadronic states in lattice QCD, highlighting the importance of operator shape tuning for accurate high-momentum studies.

Contribution

It proposes a novel operator shaping technique matching Lorentz contraction to enhance high-momentum state overlap in lattice QCD.

Findings

Enhanced overlap with high-momentum states using shape-matched operators

Reduction in error of two-point functions at high momenta

Overlap sharpness increases, requiring fine tuning of smearing parameters

Abstract

Two measures are defined to evaluate the coupling strength of smeared interpolating operators to hadronic states at a variety of momenta. Of particular interest is the extent to which strong overlap can be obtained with individual high-momentum states. This is vital to exploring hadronic structure at high momentum transfers on the lattice and addressing interesting phenomena observed experimentally. We consider a novel idea of altering the shape of the smeared operator to match the Lorentz contraction of the probability distribution of the high-momentum state, and show a reduction in the relative error of the two-point function by employing this technique. Our most important finding is that the overlap of the states becomes very sharp in the smearing parameters at high momenta and fine tuning is required to ensure strong overlap with these states.