Medium-induced radiative kernel with the Improved Opacity Expansion

TL;DR

This paper develops an analytical framework called the Improved Opacity Expansion (IOE) to accurately compute medium-induced radiative spectra at NLO, effectively covering both low and high gluon frequencies in dense media.

Contribution

The paper introduces the IOE scheme that systematically resums all orders in opacity, providing accurate analytic formulas for radiative spectra across different frequency regimes at NLO.

Findings

IOE reproduces Coulomb tail and Gaussian distribution features.

Good agreement with numerical solutions at LHC-inspired parameters.

Provides the first accurate analytic formulas for radiative energy loss in dense media.

Abstract

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 $\omega_c\sim \hat q L^2$. 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 $T \ll \omega_c$, 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.