Comparing conserved charge fluctuations from lattice QCD to HRG model calculations

We present results from lattice QCD calculations for $2^{nd}$ and $4^{th}$ order cumulants of conserved charge fluctuations and correlations, and compare these with various HRG model calculations. We show that differences between HRG and QCD calculations already show up in the second order cumulants close to the pseudo-critical temperature for the chiral transition in (2+1)-flavor QCD and quickly grow large at higher temperatures. We also show that QCD results for strangeness fluctuations are enhanced over HRG model calculations which are based only on particles listed in the Particle Data Group tables as 3-star resonances. This suggests the importance of contributions from additional strange hadron resonances. We furthermore argue that additional (repulsive) interactions, introduced either through excluded volume (mean field) HRG models or the S-matrix approach, do not improve the quantitative agreement with $2^{nd}$ and $4^{th}$ order cumulants calculated in lattice QCD. HRG based approaches fail to describe the thermodynamics of strongly interacting matter at or shortly above the pseudo-critical temperature of QCD.