Taylor expansions and Padé approximants for cumulants of conserved charge fluctuations at nonvanishing chemical potentials
Dennis Bollweg, Jishnu Goswami, Olaf Kaczmarek, F. Karsch, Swagato Mukherjee, Péter Petreczky, Christian Schmidt, Philipp Scior
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 nonzero values of the baryon chemical potential. We calculate Taylor expansions for the pressure (zeroth-order cumulant), the 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 ${\ensuremath{\mu}}_{B}/T\ensuremath{\le}2.5$, 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 pseudocritical temperature ${T}_{pc}\ensuremath{\simeq}156.5\text{ }\text{ }\mathrm{MeV}$, we find ${\ensuremath{\mu}}_{B}/T\ensuremath{\gtrsim}2.9$ at vanishing strangeness chemical potential and somewhat larger values for strangeness neutral matter. These estimates are temperature dependent and range from ${\ensuremath{\mu}}_{B}/T\ensuremath{\gtrsim}2.2$ at $T=135\text{ }\text{ }\mathrm{MeV}$ to ${\ensuremath{\mu}}_{B}/T\ensuremath{\gtrsim}3.2$ at $T=165\text{ }\text{ }\mathrm{MeV}$. The estimated radius of convergences is the same for any higher-order cumulant.