Medium-induced radiative kernel with the Improved Opacity Expansion

A bstract We calculate the fully differential medium-induced radiative spectrum at next-to-leading order (NLO) accuracy within Improved Opacity Expansion (IOE) framework. This scheme allows us to gain analytical control of low and high gluon frequencies simultaneously. The frequency regime can be obtained in standard opacity expansion framework which resulting power series diverges characteristic ω c ∼ $$ \hat{q} q ̂ L 2 . In IOE, all orders are resumed systematically below yielding an asymptotic controlled by logarithmically suppressed remainders down thermal scale T « , while matching frequency. Furthermore, we demonstrate that IOE NLO reproduces Coulomb tail single hard scattering contribution as well Gaussian distribution from multiple soft momentum exchanges. Finally, compare our analytic with a recent numerical solution, includes full resummation scatterings, for LHC-inspired medium parameters. find very good agreement both showcasing performance provides first time accurate formulas energy loss relevant perturbative kinematic regimes dense media.