Medium-induced radiative kernel with the Improved Opacity Expansion

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 high gluon frequencies simultaneously. The high frequency regime can be obtained in the standard opacity expansion framework in which the resulting power series diverges at the characteristic frequency omega(c) similar to (q) over capL(2). In the IOE, all orders in opacity are resumed systematically below omega(c) yielding an asymptotic series controlled by logarithmically suppressed remainders down to the thermal scale T << omega(c), while matching the opacity expansion at high frequency. Furthermore, we demonstrate that the IOE at NLO accuracy reproduces the characteristic Coulomb tail of the single hard scattering contribution as well as the Gaussian distribution resulting from multiple soft momentum exchanges. Finally, we compare our analytic scheme with a recent numerical solution, that includes a full resummation of multiple scatterings, for LHC-inspired medium parameters. We find a very good agreement both at low and high frequencies showcasing the performance of the IOE which provides for the first time accurate analytic formulas for radiative energy loss in the relevant perturbative kinematic regimes for dense media.

Automated summary

The study calculates the medium-induced radiative spectrum within the Improved Opacity Expansion (IOE) framework at next-to-leading order (NLO) accuracy, providing analytical control at low and high gluon frequencies simultaneously. The IOE scheme systematically resums all orders in opacity below a certain characteristic frequency, yielding an asymptotic series controlled by logarithmically suppressed remainders. Comparing the analytic scheme with a recent numerical solution for LHC-inspired medium parameters, a very good agreement is found at both low and high frequencies, demonstrating the performance of IOE for accurate analytic formulas in perturbative kinematic regimes for dense media.