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

TL;DR

This paper derives a path-integral formula for medium-modified gluon to charm quark-antiquark splitting, highlighting significant effects like transverse momentum broadening and increased pair production relevant in heavy-ion collisions.

Contribution

It introduces a new path-integral approach to quantify medium effects on gluon splitting into charm pairs, extending the BDMPS-Z formalism.

Findings

Medium effects cause transverse momentum broadening of $car{c}$ pairs.

Enhanced production of $car{c}$ pairs in medium conditions.

Effects are significant at the charm quark mass scale.

Abstract

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.