Exploring the hadron resonance gas phase on the QCD phase diagram

Lattice computations of strongly interacting matter at finite temperature $T$ and baryon chemical potential $\mu_B$ suggest that the QCD thermodynamics deep in the hadronic phase can be adequately modeled by an ideal hadron resonance gas (I-HRG). However, it is not clear where on the $(\mu_B, T)$ plane this description breaks down, making it essential to account for hadronic interactions and change in the nature of the degrees of freedom. We have studied several thermodynamic functions within the I-HRG model and try to identify the region of the QCD phase diagram where it becomes essential to include non-ideal effects into the I-HRG model. We work with only those thermodynamic quantities that show a monotonic rise with $T$ and $\mu_B$ in I-HRG. Their high temperature limiting values where QCD becomes simply a Stefan-Boltzmann (SB) gas of massless quarks and gluons is known. The rise of these quantities in I-HRG beyond the corresponding SB limit values indicate the need to include interactions into I-HRG to study QCD thermodynamics. This works as a guiding principle on the QCD phase diagram where interacting HRG can take over from I-HRG. For $\mu_B/T\leq2$, $\chi^Q_2$ shoots the SB limit at the smallest $T$, while for higher values of $\mu_B/T$,$C_{BS}=-3\chi^{BS}_{11}/\chi^S_2$ takes over. We further comment on the relative positions between the freezeout curve obtained by thermal fits to the measured hadron yields and the obtained line where I-HRG overshoots SB limit.