# Mapping collinear in-medium parton splittings

## TL;DR

This paper maps in-medium 1-to-2 parton splittings onto the Lund plane, analyzing different regimes and the effects of medium interactions on radiation patterns, with implications for understanding jet quenching.

## Contribution

It introduces a mapping of in-medium parton splittings onto the Lund plane considering finite formation times, highlighting regimes and the physics of color decoherence.

## Key findings

- Vacuum-like emissions dominate in specific phase space regions.
- Modifications to radiation patterns are linked to color decoherence.
- The approach applies generally to any dipole in the medium.

## Abstract

We map the spectrum of $1\to 2$ parton splittings inside a medium characterized by a transport coefficient $\hat q$ 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.