Quark scattering off quarks and hadrons

The in-medium elastic scattering $qq\to qq, q\bar{q}\to q\bar{q}$ and $\bar{q}\bar{q}\to \bar{q}\bar{q}$ is calculated within the two-flavor Polyakov-loop-extended Nambu-Jona-Lasinio model. The integral and differential quark-quark scattering, its energy and temperature dependence are considered and their flavor dependence is emphasized. The comparison with results of other approaches is presented. The consideration is implemented to the case of quark-pion scattering characterizing the interaction between quarks and hadrons in a kinetic multiphase treatment, and the first estimate of the quark-pion cross sections is given. A possible application of the obtained results to heavy ion collisions is shortly discussed.