We revisit the picture of jets propagating in the quark-gluon plasma. In addition to vacuum radiation, partons scatter on the medium constituents resulting in induced emissions. Analytical approaches to including these interactions have traditionally dealt separately with multiple, soft, or rare, hard scatterings. A full description has so far only been available using numerical methods. We achieve full analytical control of the relevant scales and map out the dominant physical processes in the full phase space. To this aim, we extend existing expansion schemes for the medium-induced spectrum to the Bethe-Heitler regime. This covers the whole phase space from early to late times, and from hard splittings to emissions below the thermal scale. Based on the separation of scales, a space-time picture naturally emerges: at early times, induced emissions start to build from rare scatterings with the medium. At a later stage, induced emissions due to multiple soft scatterings result in a turbulent cascade that rapidly degrades energy down to, and including, the Bethe-Heitler regime. We quantify the impact of such an improved picture, compared to the current state-of-the-art factorization that includes only soft scatterings, by both analytical and numerical methods for the medium-induced energy distribution function. Our work serves to improve our understanding of jet quenching from small to large systems and for future upgrades of Monte Carlo generators.

We study hard 1 → 2 final-state parton splittings in the medium, and put special emphasis on calculating the Wilson line correlators that appear in these calculations. As partons go through the medium their color continuously rotates, an effect that is encapsulated in a Wilson line along their trajectory. When calculating observables, one typically has to calculate traces of two or more medium-averaged Wilson lines. These are usually dealt with in the literature by invoking the large-Nc limit, but exact calculations have been lacking in many cases. In our work, we show how correlators of multiple Wilson lines appear, and develop a method to calculate them numerically to all orders in Nc. Initially, we focus on the trace of four Wilson lines, which we develop a differential equation for. We will then generalize this calculation to a product of an arbitrary number of Wilson lines, and show how to do the exact calculation numerically, and even analytically in the large-Nc limit. Color sub-leading corrections, that are suppressed with a factor $$ {N}_c^{-2} $$ N c − 2 relative to the leading scaling, are calculated explicitly for the four-point correlator and we discuss how to extend this method to the general case. These results are relevant for high-pT jet processes and initial stage physics at the LHC.

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