The medium-modified $$ g\to c\overline{c} $$ splitting function in the BDMPS-Z formalism
2023; Springer Nature; Volume: 2023; Issue: 1 Linguagem: Inglês
10.1007/jhep01(2023)080
ISSN1127-2236
AutoresMaximilian Attems, Jasmine Brewer, Gian Michele Innocenti, Aleksas Mazeliauskas, Sohyun Park, Wilke van der Schee, Urs Achim Wiedemann,
Tópico(s)Quantum Chromodynamics and Particle Interactions
ResumoThe formalism of Baier-Dokshitzer-Mueller-Peign\'e-Schiff and Zakharov determines the modifications of parton splittings in the QCD plasma that arise from medium-induced gluon radiation. Here, we study medium-modifications of the gluon splitting into a quark--anti-quark pair in this BDMPS-Z formalism. We derive a compact path-integral formulation that resums effects from an arbitrary number of interactions with the medium to leading order in the $1/N_c^2$ expansion. Analyses in the $N=1$ opacity and the saddle point approximations reveal two phenomena: a medium-induced momentum broadening of the relative quark--anti-quark pair momentum that increases the invariant mass of quark--anti-quark pairs, and a medium-enhanced 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 ultra-relativistic heavy-ion 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 light-flavoured quark--anti-quark pairs.
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