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

Understand

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.