In-medium effect on the thermodynamics and transport coefficients in van der Waals hadron resonance gas

An extension of the van der Waals hadron resonance gas (VDWHRG) model which includes the in-medium thermal modification of hadron masses, the thermal VDWHRG (TVDWHRG) model, is considered in this paper. Based on the $2+1$ flavor Polyakov linear sigma model (PLSM) and the scaling mass rule of hadrons, we obtain the temperature behavior of all hadron masses for different fixed baryon chemical potentials ${\ensuremath{\mu}}_{B}$. We calculate various thermodynamic observables at ${\ensuremath{\mu}}_{B}=0\text{ }\text{ }\mathrm{GeV}$ in the TVDWHRG model. An improved agreement with the lattice data from the TVDWHRG model in the crossover region ($T\ensuremath{\sim}0.16--0.19\text{ }\text{ }\mathrm{GeV}$) is observed as compared to those from the VDWHRG and ideal HRG (IHRG) models. We further discuss the effects of the in-medium modification of hadron masses and VDW interactions between (anti)baryons on the dimensionless transport coefficients, such as the shear viscosity to entropy density ratio ($\ensuremath{\eta}/s$) and scaled thermal ($\ensuremath{\lambda}/{T}^{2}$) and electrical (${\ensuremath{\sigma}}_{\mathrm{el}}/T$) conductivities in the IHRG model at different ${\ensuremath{\mu}}_{B}$ by utilizing quasiparticle kinetic theory with relaxation time approximation. We find in contrast to the IHRG model, the TVDWHRG model leads to a qualitatively and quantitatively different behavior of transport coefficients with $T$ and ${\ensuremath{\mu}}_{B}$.