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

Corrections to the hadron resonance gas from lattice QCD and their effect on fluctuation-ratios at finite density