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

TL;DR

This study investigates how Hagedorn states influence the isothermal compressibility of hadronic matter across different energies, revealing significant effects at high temperatures and potential incompressibility at low-energy heavy-ion collision facilities.

Contribution

The paper introduces the impact of Hagedorn mass spectrum on isothermal compressibility in hadron resonance gas models, highlighting differences from traditional models and implications for various collider energies.

Findings

Hagedorn states significantly affect compressibility at high temperatures.

Inclusion of Hagedorn spectrum reduces compressibility near the Hagedorn temperature.

Low-energy facilities produce nearly incompressible hadronic matter.

Abstract

In this work, we have studied the isothermal compressibility ($\kappa_T$) as a function of temperature, baryon chemical potential and centre-of-mass energy ($\sqrt{s_{NN}}$) 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 ($>$ 2 GeV) on the isothermal compressibility by considering the Hagedorn mass spectrum, ${\rho}(m)\sim{\exp(bm)}/{(m^2+m_0^2)^{5/4}}$. Here, the parameters, $b$ and $m_0$ 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 a higher temperatures and higher baryochemical potentials. 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 ($T_H$). We show explicitly that at the future low energy accelerator facilities like FAIR (CBM), Darmstadt and NICA, Dubna the created matter would be incompressible compared to the high energy facilities like RHIC and LHC.