Abstract
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.
Highlights
The study of the QCD phase diagram has been a very active area of research for the last few decades
One simple way to go beyond the ideal hadron resonance gas is to use some kind of mean field model for the short range repulsion and the long range attraction between the baryons. Such models were compared to lattice results in Refs. [42,72,73,74]. These works in particular emphasized the importance of the hard core repulsive interactions between hadrons when describing thermodynamics at finite baryon chemical potential
This type of interaction is completely absent in the ideal hadron resonance gas (HRG) model and leads to a sizable negative contribution to the fugacity expansion coefficients with baryon number two
Summary
The study of the QCD phase diagram has been a very active area of research for the last few decades. These works in particular emphasized the importance of the hard core repulsive interactions between hadrons when describing thermodynamics at finite baryon chemical potential This type of interaction is completely absent in the ideal HRG model and leads to a sizable negative contribution to the fugacity expansion coefficients with baryon number two. Since comparisons with the available lattice data suggest that the agreement between full QCD and the ideal hadron resonance gas model gets worse at finite chemical potential, we suspect that nonresonant scattering effects will be even more important at the RHIC Beam Energy Scan and future experiments at lower collision energies, like FAIR and NICA. VI we give a brief summary and outlook for future work
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