Finite T topological Susceptibility with heavy Quarks

TL;DR

This paper estimates the impact of the bottom quark on QCD topological susceptibility relevant for axion cosmology by using a caloron gas approximation and advanced mathematical expansions.

Contribution

It introduces a novel method to estimate heavy quark effects on topological susceptibility using small- and large-mass expansions and Padé approximants.

Findings

Quantifies the bottom quark's effect on susceptibility in the 400-1100 MeV range.

Develops a new computational approach for heavy quark contributions.

Provides data relevant for axion cosmology models.

Abstract

Axion cosmology needs the QCD topological susceptibility between 400 and 1100 MeV. In this range the bottom quark is inconvenient to include in lattice simulations, but not heavy enough to ignore. We estimate its effect on the susceptibility by computing the ratio of the 4-quark susceptibility and the 4+1-quark susceptibility in the caloron gas approximation. We do so by computing small-mass and large-mass expansions of the finite mass and temperature fluctuation determinant and connecting them with a Pad\'e approximant.