Thermodynamics of two flavor QCD from imaginary chemical potentials

We study QCD thermodynamics in presence of two independent imaginary chemical potentials coupled to two degenerate flavors of staggered quarks. Analytic continuation is used to determine non-linear susceptibilities, to test the Hadron Resonance Gas (HRG) model below the zero density critical temperature, Tc, and to determine the average phase factor of the fermion determinant. Deviations from HRG predictions, of the order of a few percent, are clearly visible for temperatures T > 0.95 Tc. The determination of non-linear susceptibilities, using different interpolating functions for analytic continuation, gives consistent results and in agreement with Taylor expansion computations, apart from some systematic effects at or right above Tc. Results for the average phase factor are compared with the predictions of Chiral Perturbation Theory; below Tc we are able to distinguish the contribution of different hadron states, which is positive (i.e. tends to mitigate the sign problem) in the case of baryons.