Medium-modifications of $g\to c \bar{c}$ splitting

We study medium-modifications of the gluon splitting into a quark and anti-quark pair. Applying the Baier-Dokshitzer-Mueller-Peign\'e-Schiff and Zakharov (BDMPS-Z) formalism, we derive a path-integral formula for the in-medium $g\to q \bar{q}$ splitting function in the close-to-eikonal limit. Our analysis shows that there are two qualitatively different medium effects: transverse momentum broadening of $q \bar{q}$ pairs and enhanced production of such pairs. We note that both effects are numerically sizeable if the average momentum transfer from the medium to the parton is at the quark mass scale. In ultra-relativistic heavy-ion collisions, this condition is realized by charm quarks, therefore we focus our numerical analysis on the medium-modifications of $g\to c \bar{c}$ splitting.
Comment: 4 pages, 1 figure, contribution to the proceedings of the 20th International Conference on Strangeness in Quark Matter (SQM 2022)