Thermodynamics of a gas of hadrons with attractive and repulsive interactions within an S -matrix formalism

We report the effect of including repulsive interactions on various thermodynamic observables calculated using an S -matrix based hadron resonance gas (HRG) model applied to already available corresponding results with only attractive interactions [A. Dash, S. Samanta, and B. Mohanty, Phys. Rev. C 97, 055208 (2018), 10.1103/PhysRevC.97.055208]. The attractive part of the interaction is calculated by parametrizing the two-body phase shifts using the K -matrix formalism, while the repulsive part is included by fitting to the experimental phase shifts which carry the information about the nature of the interaction. We find that the bulk thermodynamic variables for a gas of hadrons, such as energy density, pressure, entropy density, speed of sound, and specific heat, are suppressed by the inclusion of repulsive interactions and are more pronounced for second- and higher-order correlations and fluctuations, particularly for the observables χ_Q², χ_B²-χ_B⁴ , and C_{B S} in the present model. We find a good agreement between lattice QCD simulations and the present model for C_{B S}. We have also computed two leading-order Fourier coefficients of the imaginary part of the first-order baryonic susceptibility at imaginary baryon chemical potential within this model and compared them with the corresponding lattice results. Additionally, assuming that the value of interacting pressure versus temperature for a gas of hadrons calculated in the S -matrix formalism is the same as that from a van der Waals HRG (VDWHRG) model, we have quantified the attractive and repulsive interactions in our model in terms of attractive and repulsive parameters used in the VDWHRG model. The values of parameters thus obtained are a =1.54 ±0.064 GeV fm³ and r =0.81 ±0.014 fm.