Are Parton Showers in a Quark-Gluon Plasma Strongly Coupled? A Theorist's Test

We study whether in-medium showers of high-energy quarks and gluons can be treated as a sequence of individual splitting processes or whether there is significant quantum overlap between where one splitting ends and the next begins. Accounting for the Landau-Pomeranchuk-Migdal (LPM) effect, we calculate such overlap effects to leading order in high-energy ${\alpha }_s(\mu )$ for the simplest theoretical situation. We investigate a measure of overlap effects that is independent of physics that can be absorbed into an effective value ${\widehat{q}}_{eff}$ of the jet-quenching parameter $\widehat{q}$.