Medium-induced radiative kernel with the Improved Opacity Expansion

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 ωc ∼ $$ \hat{q} $$ q ̂ L2. In the IOE, all orders in opacity are resumed systematically below ωc yielding an asymptotic series controlled by logarithmically suppressed remainders down to the thermal scale T « ωc, 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.

Medium induced gluon spectrum in the Improved Opacity Expansion

“…To introduce the IOE formalism [1][2][3][4][5] we consider first the simplest possible observable: single particle momentum broadening. At eikonal accuracy, momentum broadening can be fully characterized by an associated broadening distribution P ( 𝒌, 𝑡) which gives the probability for a parton to acquire transverse momentum 𝒌 in the medium as a result of its propagation for a time 𝑡.…”

“…Medium induced gluon spectrum in the Improved Opacity Expansion João Barata Comparison between the broadening probability distribution in the IOE at LO (dashed, green), at LO+NLO (solid, red) and the exact Gyulassy-Wang modelresult (solid, navy).The medium parameters used in this proceedings are q0 = 0.16 GeV 3 , 𝐿 = 6 fm and 𝜇 * = 0.355 GeV. See [5] for more details.…”

“…Medium induced gluon spectrum in the Improved Opacity Expansion João Barata transverse momentum 𝒌. In general, this can be written as [5]…”

“…(8) has a term related to modification of the emission kernel (followed by the usual Gaussian broadening), and a term describing the production of a gluon in the MS approximation followed by broadening dominated by single hard scattering contribution. Performing a slightly evolved calculation, it results that (see details in [5])…”

Revisiting transverse momentum broadening in dense QCD media

“…In the present manuscript we study the single particle momentum broadening distribution for the case of an energetic parton propagating through a homogeneous plasma brick of length L. A complementary study of the medium induced radiation mechanism, following a similar scheme to the one present in this paper, is discussed in [20][21][22] for the transverse momentum integrated gluon spectrum and in [23,24] for the transverse momentum dependent distribution.…”