Taylor expansion and the Cauchy Residue Theorem for finite-density QCD

TL;DR

This paper explores using the Cauchy Residue Theorem to compute Taylor coefficients of the pressure expansion in finite-density QCD, offering a potential alternative to existing methods.

Contribution

It introduces a novel approach employing the Cauchy Residue Theorem with discretized contours to determine spectral moments in QCD at zero chemical potential.

Findings

Successful application of the Cauchy Residue Theorem to spectral moments

Potential for improved accuracy in Taylor coefficient calculations

New method complements existing techniques in finite-density QCD

Abstract

We present an update on our efforts to determine the Taylor coefficients of the $\mu/T$ expansion of the pressure for finite-density QCD. Here, we explore alternatives based on the Cauchy Residue Theorem, which allows us to use a discretized contour to determine the desired spectral moments occurring in the Taylor expansion of QCD at zero chemical potential.