Momentum dependence of the topological susceptibility with overlap fermions

TL;DR

This study examines how the topological susceptibility varies with momentum in lattice QCD using overlap fermions, revealing the significance of low-lying eigenmodes and a negative derivative, impacting theoretical formulas and proton spin understanding.

Contribution

It provides the first detailed analysis of the momentum dependence of topological susceptibility with overlap fermions, highlighting the role of low-lying eigenmodes and the sign of its derivative.

Findings

The derivative of the topological susceptibility at zero momentum is negative.

Low-lying Dirac eigenmodes significantly influence the topological charge density.

Ignoring higher eigenmodes overestimates the susceptibility's derivative.

Abstract

Knowledge of the derivative of the topological susceptibility at zero momentum is important for assessing the validity of the Witten-Veneziano formula for the eta' mass, and likewise for the resolution of the EMC proton spin problem. We investigate the momentum dependence of the topological susceptibility and its derivative at zero momentum using overlap fermions in quenched lattice QCD simulations. We expose the role of the low-lying Dirac eigenmodes for the topological charge density, and find a negative value for the derivative. While the sign of the derivative is consistent with the QCD sum rule for pure Yang-Mills theory, the absolute value is overestimated if the contribution from higher eigenmodes is ignored.