Abstract
We report the effect of including repulsive interactions on various thermodynamic observables calculated using a S-matrix based Hadron Resonance Gas (HRG) model to already available corresponding results with only attractive interactions [A. Dash, S. Samanta, and B. Mohanty, Phys. Rev. C 97, 055208 (2018)]. The attractive part of the interaction is calculated by parameterizing the two body phase shifts using 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 $\chi^2_Q$, $\chi^2_B-\chi^4_B$ and $C_{BS}$ in the present model. We find a good agreement between lattice QCD simulations and the present model for $C_{BS}$. 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 results from lattice. Additionally, assuming that the value of interacting pressure versus temperature for a gas of hadrons calculated in S-matrix formalism is 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 $a=1.54\pm 0.064$ GeV $\text{fm}^{3}$ and $r=0.81\pm 0.014$ fm.
Highlights
One of the primary goals of observing relativistic heavy ion collisions is the study of the QCD phase diagram [1]
We extend the Kmatrix formalism to include repulsive interactions between the hadrons using the S-matrix formalism
In the S-matrix formalism, the second virial coefficient is related to the scattering amplitude or alternatively to the scattering phase shifts δlI for a given spin l and isospin I channel
Summary
One of the primary goals of observing relativistic heavy ion collisions is the study of the QCD (quantum chromodynamics) phase diagram [1]. [58], we had developed a HRG model with attractive interactions between hadrons using the K-matrix formalism. After constructing the interacting hadron resonance gas model with both attractive and repulsive interactions using phase shift information for various hadronic interactions, we calculate the various thermodynamic observables like pressure, energy density, entropy density, interaction measure, specific heat, speed of sound, and susceptibilities. The temperature dependences of these observables is compared with corresponding results from lattice QCD, IDHRG, and HRG models with attractive interactions using the K-matrix formalism. We discuss the formalism used to introduce repulsive interactions to our HRG model developed earlier using the K-matrix approach with attractive interactions [58].
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