On analytic continuation from imaginary to real chemical potential in Lattice QCD

TL;DR

This paper explores methods for analytically continuing lattice QCD results from imaginary to real chemical potential, comparing Padé approximants with a novel Cauchy integral approach to improve finite density QCD studies.

Contribution

It introduces and compares a Padé-based method and a new Cauchy integral approach for analytic continuation in lattice QCD at finite density.

Findings

Padé method effectively identifies Lee-Yang singularities.

The Cauchy integral approach offers a promising alternative for analytic continuation.

Comparison highlights strengths and limitations of both methods.

Abstract

Imaginary baryon number chemical potential simulations are a popular workaround for the (in)famous sign problem plaguing finite density QCD studies on the lattice. One is necessarily left with the problem of analytically continuing results to real values of $\mu_B$. In the framework of the Bielefeld Parma Collaboration, we have in recent years studied a multi-point Pad\'e description of the net baryon number density computed as a function of imaginary baryon number chemical potential. While our main emphasis has till now been on the determination of Lee-Yang singularities, the method is per se a natural tool to analytically continue results. We report on the status of our projects with this respect, comparing the Pad\'e approach to analytic continuation to another, new strategy, which is an application of the Cauchy integral formula in the sense of an inverse problem.