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

TL;DR

This paper investigates the behavior of heavy quarks and mesons in dense nuclear and quark matter at zero temperature, revealing a logarithmic enhancement in scattering amplitude that challenges perturbative approaches at large masses.

Contribution

It introduces a perturbative calculation of heavy impurity dynamics in dense matter, showing the breakdown of perturbation theory due to logarithmic enhancements at large impurity masses.

Findings

Logarithmic enhancement in scattering amplitude for large heavy impurity mass

Perturbative calculation breaks down in the large mass limit

Analysis applies to both mesonic and quark impurities in dense matter

Abstract

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.