Collision term dependence of the hadronic shear viscosity and diffusion coefficients

Background: The value of the shear viscosity $\ensuremath{\eta}$ and the diffusion coefficients of conserved charges ${\ensuremath{\kappa}}_{ij}$ with $i,j\ensuremath{\in}{B,Q,S}$ strongly depend on the microscopic interactions of the constituents.Purpose: Study the effects of multiparticle reactions, angular distributions, and additional elastic cross sections via the additive quark model description, the numbers of degrees of freedom, and the baryon density on the transport coefficients.Method: $\ensuremath{\eta}$ and ${\ensuremath{\kappa}}_{ij}$ are extracted from infinite matter simulations of the hadronic transport model SMASH using the Green-Kubo formalism. The transport coefficients are then obtained by integrating the correlation functions which have been thoroughly checked and compared to kinetic theory calculations. We then systematically study the collision term dependence of $\ensuremath{\eta}$ and ${\ensuremath{\kappa}}_{ij}$ by switching the respective cross sections on and off. With this method we are able to extract the relevant interactions and dependencies for $\ensuremath{\eta}$ and ${\ensuremath{\kappa}}_{ij}$.Results: We find that multiparticle reactions decrease the shear viscosity in a simplified hadron gas whereas the electric charge diffusion coefficient is not modified. Furthermore, additional elastic cross sections have a strong impact on both $\ensuremath{\eta}$ and ${\ensuremath{\kappa}}_{ij}$, whereas anisotropic scatterings enhance the shear viscosity in the full hadron gas. When the number of degrees of freedom is increased, the shear viscosity is only slightly modified in comparison to the diffusion coefficients. Finally, the calculation at a finite baryon chemical potential reveals that the shear viscosity itself does not depend on ${\ensuremath{\mu}}_{B}$ but on the ratio $\ensuremath{\eta}/s$. The diffusion coefficients show a strong dependency which we compare to Chapman-Enskog calculations.Conclusions: We conclude that the behavior of the shear viscosity is highly sensitive to the individual treatment of the cross sections. The diffusion coefficients of conserved charges are affected by the averaged cross sections and the charge densities. These results help understand observables when modeling heavy-ion collisions as well as open the opportunity for a better understanding when comparing to first-principles calculations.