Importance of higher orders in opacity in QGP tomography

TL;DR

This paper derives explicit formulas for higher-order opacity effects in QGP energy loss, implementing them into a framework to evaluate their impact, and finds these effects are small for RHIC and LHC conditions.

Contribution

The authors derived the first explicit analytical expressions for dynamical energy loss up to the 4th order in opacity and integrated them into a generalized framework for QGP tomography.

Findings

Higher-order effects are small at RHIC and LHC.

Single scattering center approximation is sufficient for practical purposes.

New analytical expressions for energy loss up to 4th order in opacity.

Abstract

We consider the problem of including a finite number of scattering centers in dynamical energy loss and classical DGLV formalism. Previously, either one or an infinite number of scattering centers were considered in energy loss calculations, while attempts to relax such approximations were largely inconclusive or incomplete. In reality, however, the number of scattering centers is generally estimated to be 4-5 at RHIC and the LHC, making the above approximations (a priori) inadequate and this theoretical problem significant for QGP tomography. We derived explicit analytical expressions for dynamical energy loss and DGLV up to the $4^{th}$ order in opacity, resulting in complex mathematical expressions that were, to our knowledge, obtained for the first time. These expressions were then implemented into an appropriately generalized DREENA framework to calculate the effects of higher orders in opacity on a wide range of high-$p_\perp$ light and heavy flavor predictions. Results of extensive numerical analysis, together with interpretations of nonintuitive results, are presented. We find that, for both RHIC and the LHC, higher-order effects on high-$p_\perp$ observables are small, and the approximation of a single scattering center is adequate for dynamical energy loss and DGLV formalisms.