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We present the derivation of heavy quark energy loss in a viscous QCD plasmausing kinetic theory. Shear flow changes both boson and fermion distributionfunctions which eventually modify heavy quark energy loss. Due to presence ofnon-zero flow gradient in the medium all the bath particles here are out ofequilibrium. In these types of plasmas we show that without plasma screeningeffects heavy quark energy loss suffers similar type of infrared divergence asone encounters in non-viscous plasma. The screening effects are incorporatedconsistently through Hard Thermal Loop resummation perturbation theory in thesmall-momentum-transfer region to obtain finite leading order result in$\eta/s$. We also quantify the importance of the result and demonstrate thatshear flow has significant effect on the heavy quark energy loss.

Modification of heavy quark energy loss due to shear flow in hot QCD plasma