Bulk and shear viscosities of hot and dense hadron gas

We estimate the bulk and the shear viscosity at finite temperature and baryon densities of hadronic matter within a hadron resonance gas model which includes a Hagedorn spectrum. The parameters of the Hagedorn spectrum are adjusted to fit recent lattice QCD simulations at finite chemical potential. For the estimation of the bulk viscosity we use low energy theorems of QCD for the energy momentum tensor correlators. For the shear viscosity coefficient, we estimate the same using molecular kinetic theory to relate the shear viscosity coefficient to average momentum of the hadrons in the hot and dense hadron gas. The bulk viscosity to entropy ratio increases with chemical potential and is related to the reduction of velocity of sound at nonzero chemical potential. The shear viscosity to entropy ratio on the other hand, shows a nontrivial behavior with the ratio decreasing with chemical potential for small temperatures but increasing with chemical potential at high temperatures and is related to decrease of entropy density with chemical potential at high temperature due to finite volume of the hadrons.