  The hadron resonance gas (HRG) model is often believed to correctly describe
the confined phase of QCD. This assumption is the basis of many
phenomenological works on QCD thermodynamics and of the analysis of hadron
yields in relativistic heavy ion collisions. We use first-principle lattice
simulations to calculate corrections to the ideal HRG. Namely, we determine the
sub-leading fugacity expansion coefficients of the grand canonical free energy,
receiving contributions from processes like kaon-kaon or baryon-baryon
scattering. We achieve this goal by performing a two dimensional scan on the
imaginary baryon number chemical potential ($\mu_B$) - strangeness chemical
potential ($\mu_S$) plane, where the fugacity expansion coefficients become
Fourier coefficients. We carry out a continuum limit estimation of these
coefficients by performing lattice simulations with temporal extents of
$N_\tau=8,10,12$ using the 4stout-improved staggered action. We then use the
truncated fugacity expansion to extrapolate ratios of baryon number and
strangeness fluctuations and correlations to finite chemical potentials.
Evaluating the fugacity expansion along the crossover line, we reproduce the
trend seen in the experimental data on net-proton fluctuations by the STAR
collaboration.
