Reliability of Taylor expansions in QCD

TL;DR

This paper assesses the accuracy and convergence of Taylor series expansions in QCD with isospin chemical potentials using lattice simulations, helping quantify uncertainties in related calculations.

Contribution

It introduces a method to evaluate the validity and convergence of Taylor expansions in QCD, specifically relating to isospin chemical potentials, through lattice simulation comparisons.

Findings

The range of validity for leading and next-to-leading order expansions is established.

The convergence properties are analyzed by comparing the radius of convergence to the pion condensation point.

Quantifies uncertainties in Taylor expansion methods for baryon chemical potentials.

Abstract

We investigate the reliability of the Taylor expansion method in QCD with isospin chemical potentials using lattice simulations. By comparing the expansion of the number density to direct results, the range of validity of the leading- and next-to-leading order expansions is determined. We also elaborate on the convergence properties of the Taylor series by comparing the leading estimate for the radius of convergence to the position of the nearest singularity, i.e. the onset of pion condensation. Our results provide a handle for quantifying the uncertainties of Taylor expansions in baryon chemical potentials.