Mapping collinear in-medium parton splittings

We map the spectrum of 1→2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\rightarrow 2$$\end{document} parton splittings inside a medium characterized by a transport coefficient q^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{q}}$$\end{document} onto the kinematical Lund plane, taking into account the finite formation time of the process. We discuss the distinct regimes arising in this map for in-medium splittings, pointing out the close correspondence to a semi-classical description in the limit of hard, collinear radiation with short formation times. Although we disregard any modifications of the original parton kinematics in course of the propagation through the medium, subtle modifications to the radiation pattern compared to the vacuum baseline can be traced back to the physics of color decoherence and accumulated interactions in the medium. We provide theoretical support to vacuum-like emissions inside the medium by delimiting the regions of phase space where it is dominant, identifying also the relevant time-scales involved. The observed modifications are shown to be quite general for any dipole created in the medium.