Effect of Hagedorn States on Isothermal Compressibility of Hadronic Matter formed in Heavy-Ion Collisions: From NICA to LHC Energies

In this work, we have studied the isothermal compressibility (κT) as a function of temperature, baryon chemical potential, and center-of-mass energy (sNN) using hadron resonance gas (HRG) and excluded-volume hadron resonance gas (EV-HRG) models. A mass cut-off dependence of isothermal compressibility has been studied for a physical resonance gas. Further, we study the effect of heavier resonances (>2GeV) on the isothermal compressibility by considering the Hagedorn mass spectrum, ρ(m)∼exp(bm)/(m2+m02)5/4. Here the parameters b and m0 are extracted after comparing the results of recent lattice QCD simulations at finite baryonic chemical potential. We find a significant difference between the results obtained in EV-HRG and HRG models at higher temperatures. The inclusion of the Hagedorn mass spectrum in the partition function for hadron gas has a large effect at a higher temperature. A higher mass cut-off in the Hagedorn mass spectrum takes the isothermal compressibility to a minimum value, which occurs near the Hagedorn temperature (TH). We show explicitly that at the future low-energy accelerator facilities like FAIR (CBM), Darmstadt, and NICA, Dubna, the created matter would have higher compressibility compared to the high-energy facilities like the Relativistic Heavy Ion Collider and Large Hadron Collider.