Unraveling the collisional energy loss of a heavy quark in a quark-gluon plasma

Abstract

At leading order in the QCD coupling constant, we compute the energy loss per traveling distance of a heavy quark dE/dz from elastic scattering off thermal quarks and gluons at a temperature T, including the thermal perturbative description of soft scatterings (−t<−t*) and a perturbative QCD-based calculation for hard collisions (−t>−t*). Within this soft-hard factorization model, we find that the full results of dE/dz behaves a mild sensitivity to the intermediate cutoff t*, supporting the validity of the soft-hard approach within the temperature region of interest. We rederive the analytic formula for dE/dz in the high-energy approximation, E1≫m12/T, where E1 is the injected heavy quark energy and m1 is its mass. It is realized that the soft logarithmic contribution, dE/dz∝ln(−t*/mD2), arises from the t-channel scattering off thermal partons, while the hard logarithmic term, dE/dz∝ln[E1T/(−t*)], stems from the t-channel scattering off thermal partons, and the one dE/dz∝ln(E1T/m12) comes from the s- and u-channel scattering off gluons. The sum of these contributions cancels the t*-dependence as observed in the full result. The mass hierarchy is observed dE/dz(charm)>dE/dz(bottom). Our full results are crucial for a better description of heavy quark transport in QCD medium, in particular at low and moderate energy. We also calculate the energy loss by imposing the Einstein’s relationship. The related results appear to be systematically larger than that without imposing the Einstein’s relationship. Published by the American Physical Society 2024