Higher order quark number fluctuations via imaginary chemical potentials in $N_f=2+1$ QCD

TL;DR

This paper develops a method using analytic continuation from imaginary chemical potentials to compute higher-order quark number fluctuations in lattice QCD, providing insights into the QCD phase diagram.

Contribution

The study introduces a global fit approach to extract cumulants from lattice QCD at imaginary chemical potentials, extending the analysis up to eighth order and assessing the critical point.

Findings

Cumulants up to eighth order are computed.

The method is particularly effective for higher-order and mixed susceptibilities.

No evidence of a second order critical point is found within the explored parameter range.

Abstract

We discuss analytic continuation as a tool to extract the cumulants of the quark number fluctuations in the strongly interacting medium from lattice QCD simulations at imaginary chemical potentials. The method is applied to $N_f = 2+1$ QCD, discretized with stout improved staggered fermions, physical quark masses and the tree level Symanzik gauge action, exploring temperatures ranging from 135 up to 350 MeV and adopting mostly lattices with $N_t = 8$ sites in the temporal direction. The method is based on a global fit of various cumulants as a function of the imaginary chemical potentials. We show that it is particularly convenient to consider cumulants up to order two, and that below $T_c$ the method can be advantageous, with respect to a direct Montecarlo sampling at $\mu = 0$, for the determination of generalized susceptibilities of order four or higher, and especially for mixed susceptibilities, for which the gain is well above one order of magnitude. We provide cumulants up to order eight, which are then used to discuss the radius of convergence of the Taylor expansion and the possible location of the second order critical point at real $\mu$: no evidence for such a point is found in the explored range of $T$ and for chemical potentials within present determinations of the pseudo-critical line.