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We report the effect of including repulsive interactions on variousthermodynamic observables calculated using a S-matrix based Hadron ResonanceGas (HRG) model to already available corresponding results with only attractiveinteractions [A. Dash, S. Samanta, and B. Mohanty, Phys. Rev. C 97, 055208(2018)]. The attractive part of the interaction is calculated by parameterizingthe two body phase shifts using K-matrix formalism while the repulsive part isincluded by fitting to the experimental phase shifts which carry theinformation about the nature of the interaction. We find that the bulkthermodynamic variables for a gas of hadrons such as energy density, pressure,entropy density, speed of sound and specific heat are suppressed by theinclusion of repulsive interactions and are more pronounced for second andhigher 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 agood agreement between lattice QCD simulations and the present model for$C_{BS}$. We have also computed two leading order Fourier coefficients of theimaginary part of the first order baryonic susceptibility at imaginary baryonchemical potential within this model and compared them with the correspondingresults from lattice. Additionally, assuming that the value of interactingpressure versus temperature for a gas of hadrons calculated in S-matrixformalism is same as that from a van der Waals HRG (VDWHRG) model, we havequantified the attractive and repulsive interactions in our model in terms ofattractive and repulsive parameters used in the VDWHRG model. The values ofparameters thus obtained are $a=1.54\pm 0.064$ GeV $\text{fm}^{3}$ and$r=0.81\pm 0.014$ fm.

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