Heavy quark dynamics for charm and bottom flavor on Fermi surface at zero temperature

We discuss the dynamics in finite density medium including a heavy impurity particle (hadron or quark) with a heavy flavor, charm and bottom, at zero temperature. As a system, we consider a $\bar{D}$ ($B$) meson embedded in nuclear matter as a heavy impurity boson with SU(2) isospin symmetry. As another system, we also consider a charm (bottom) quark embedded in quark matter as a heavy impurity fermion with SU(3) color symmetry. We suppose a vector current interaction with SU($n$) symmetry ($n \ge 2$) for the fermion composing the Fermi surface and the embedded heavy impurity particle, and calculate the scattering amplitude perturbatively for the small coupling constant up to one-loop level. We obtain that the scattering amplitude has a logarithmic enhancement in the large mass limit of the heavy impurity particle, and show that the perturbative calculation breaks down for any small coupling constant in this limit.