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We present a new expansion scheme to compute the rate for parton splittings in dense and finite QCD media. In contrast to the standard opacity expansion, our expansion is performed around the harmonic oscillator whose characteristic frequency depends on the typical transverse momentum scale generated in the splitting. The first two orders account for the high frequency regime that is dominated by single hard scatterings together with the regime of multiple soft scatterings at low frequency. This work generalizes the findings of Ref. cite{Mehtar-Tani:2019tvy} beyond the leading logarithmic approximation allowing to account also for the Bethe-Heitler regime and compare to the full numerical results from Ref. cite{CaronHuot:2010bp}. We investigate the sensitivity of our results to varying the separation scale that defines the leading order. Finally, the application to Monte Carlo event generators is discussed.
We revisit the calculation of the medium-induced gluon radiative spectrum and propose a novel expansion scheme that encompasses the two known analytic limits: i) the high frequency regime dominated by a single hard scattering that corresponds to the
When an energetic parton propagates in a hot and dense QCD medium it loses energy by elastic scatterings or by medium-induced gluon radiation. The gluon radiation spectrum is suppressed at high frequency due to the LPM effect and encompasses two regi
We calculate the fully differential medium-induced radiative spectrum at next-to-leading order (NLO) accuracy within the Improved Opacity Expansion (IOE) framework. This scheme allows us to gain analytical control of the radiative spectrum at low and
We investigate the radiative break-up of a highly energetic quark or gluon in a high-temperature QCD plasma. Within an inertial range of momenta $T ll omega ll E$, where $E$ denotes the energy of the original hard parton (jet) and $T$ the temperature
We map the spectrum of $1to 2$ 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 i