The mediummodified $g\to c\bar{c}$ splitting function in the BDMPSZ formalism
Abstract
The formalism of BaierDokshitzerMuellerPeignéSchiff and Zakharov determines the modifications of parton splittings in the QCD plasma that arise from mediuminduced gluon radiation. Here, we study mediummodifications of the gluon splitting into a quarkantiquark pair in this BDMPSZ formalism. We derive a compact pathintegral formulation that resums effects from an arbitrary number of interactions with the medium to leading $\mathcal{O}(1/N_c^2)$. Analyses in the $N=1$ opacity and the saddle point approximations reveal two phenomena: a mediuminduced momentum broadening that increases the invariant mass of quarkantiquark pairs, and a mediumenhanced production of such pairs. We note that both effects are numerically sizeable if the average momentum transfer from the medium is comparable to the quark mass. In ultrarelativistic heavyion collisions, this condition is satisfied for charm quarks. We therefore focus our numerical analysis on the medium modification of $g\to c\bar{c}$, although our derivation applies equally well to $g\to b\bar{b}$ and to gluons splitting into lightflavoured quarkantiquark pairs.
 Publication:

arXiv eprints
 Pub Date:
 March 2022
 arXiv:
 arXiv:2203.11241
 Bibcode:
 2022arXiv220311241A
 Keywords:

 High Energy Physics  Phenomenology;
 High Energy Physics  Theory;
 Nuclear Experiment;
 Nuclear Theory
 EPrint:
 58 pages, 12 figures