Taylor expansions and Pad\'e approximants for cumulants of conserved charge fluctuations at non-vanishing chemical potentials

TL;DR

This study uses high-statistics lattice QCD data to analyze low-order cumulants of net baryon-number fluctuations at finite chemical potential, employing Taylor expansions and Padé approximants to determine their reliability range and convergence properties.

Contribution

It introduces a detailed comparison of Taylor series and Padé approximants for cumulants in (2+1)-flavor QCD at finite chemical potential, estimating their convergence limits.

Findings

Taylor expansions are reliable up to rac{b}{2.5} for rac{b}{T} at low orders.

Pade9 approximants extend the applicability of series expansions.

Estimated radius of convergence varies with temperature, indicating the limits of series-based methods.

Abstract

Using high statistics datasets generated in (2+1)-flavor QCD calculations at finite temperature we present results for low order cumulants of net baryon-number fluctuations at non-zero values of the baryon chemical potential. We calculate Taylor expansions for the pressure (zeroth order cumulant), net baryon-number density (first order cumulant) and the variance of the distribution on net-baryon number fluctuations (second order cumulant). We obtain series expansions from an eighth order expansion of the pressure and compare these to diagonal Pad\'e approximants. This allows us to estimate the range of values for the baryon chemical potential in which these expansions are reliable. We find $\mu_B/T\le 2.5$, $2.0$ and $1.5$ for the zeroth, first and second order cumulants, respectively. We furthermore, construct estimators for the radius of convergence of the Taylor series of the pressure. In the vicinity of the pseudo-critical temperature, $T_{pc}\simeq 156.5$ MeV, we find $\mu_B/T \gtrsim\ 2.9$ at vanishing strangeness chemical potential and somewhat larger values for strangeness neutral matter. These estimates are temperature dependent and range from $\mu_B/T \gtrsim\ 2.2$ at $T=135$ MeV to $\mu_B/T\ \gtrsim\ 3.2$ at $T=165$ MeV. The estimated radius of convergences is the same for any higher order cumulant.