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 ${\omega }_c\sim \hat{q}{L}^2$. 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.

54 pages, 5 figures. Typos fixed. Matches published version

References in corpus (13)

• Measurements of the Nuclear Modification Factor for Jets in Pb+Pb Collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV with the ATLAS Detector
• Measurement of jet suppression in central Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV
• Q-PYTHIA: a medium-modified implementation of final state radiation
• A Monte Carlo Model for 'Jet Quenching'
• Finite-size effects on the radiative energy loss of a fast parton in hot and dense strongly interacting matter
• Simple Formula for High-Energy Gluon Bremsstrahlung in a Finite, Expanding Medium
• Multistage Monte-Carlo simulation of jet modification in a static medium
• QCD Splitting/Joining Functions at Finite Temperature in the Deep LPM Regime
• Cone size dependence of jet suppression in heavy-ion collisions
• Quenching effects in the cumulative jet spectrum
• From soft to hard radiation: the role of multiple scatterings in medium-induced gluon emissions
• The JETSCAPE framework
• Jet evolution in a dense QCD medium

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• The medium-modified $g\to c\bar{c}$ splitting function in the BDMPS-Z formalism
• System of evolution equations for quark and gluon jet quenching with broadening
• Studying the QGP with Jets at the LHC and RHIC