Shear and bulk viscosities of quark matter from quark-meson fluctuations in the Nambu-Jona-Lasinio model

We have calculated the temperature dependence of shear η and bulk ζ viscosities of quark matter due to quark-meson fluctuations. The quark thermal width originating from quantum fluctuations of quark-π and quark-σ loops at finite temperature is calculated with the formalism of real-time thermal field theory. Temperature-dependent constituent-quark and meson masses and quark-meson couplings are obtained in the Nambu-Jona-Lasinio model. We found a nontrivial influence of the temperature-dependent masses and couplings on the Landau-cut structure of the quark self-energy. Our results for the ratios η/s and ζ/s, where s is the entropy density (also determined in the Nambu-Jona-Lasinio model in the quasiparticle approximation), are in fair agreement with results of the literature obtained from different models and techniques. In particular, our result for η/s has a minimum very close to the quantum lower bound, η/s=1/4π.