Towards finite density QCD with Taylor expansions

TL;DR

This paper investigates the convergence of Taylor expansions for QCD observables at finite chemical potential using a Polyakov-quark-meson model, introducing a new computational technique and exploring resummation methods to improve phase boundary detection.

Contribution

It introduces a novel algorithmic differentiation technique for calculating high-order Taylor coefficients in QCD models and assesses their effectiveness for phase boundary analysis.

Findings

Higher order coefficients up to 24th order improve convergence.

Resummation methods like Pade series enhance the series' reliability.

The approach offers insights into locating the QCD critical endpoint.

Abstract

We analyze general convergence properties of the Taylor expansion of observables to finite chemical potential in the framework of an effective 2+1 flavor Polyakov-quark-meson model. To compute the required higher order coefficients a novel technique based on algorithmic differentiation has been developed. Results for thermodynamic observables as well as the phase structure obtained through the series expansion up to 24th order are compared to the full model solution at finite chemical potential. The available higher order coefficients also allow for resummations, e.g. Pade series, which improve the convergence behavior. In view of our results we discuss the prospects for locating the QCD phase boundary and a possible critical endpoint with the Taylor expansion method.