[Paper Review] Calculating hard probe radiative energy loss beyond soft-gluon approximation: how valid is the approximation?

Bojana Ilic, Magdalena Djordjevic+1 more|arXiv (Cornell University)|Apr 20, 2018

High-Energy Particle Collisions Research3 citations

TL;DR

This paper relaxes the soft-gluon approximation in the DGLV formalism for radiative energy loss of high-pT partons in QGP, deriving analytical expressions beyond the assumption that radiated gluons carry negligible energy. Despite significant analytical differences, numerical results show minimal impact on energy loss and gluon multiplicity predictions, indicating the soft-gluon approximation remains surprisingly accurate in practice.

ABSTRACT

The soft-gluon approximation, which implies that radiated gluon carries away a small fraction of initial parton's energy, is a commonly used assumption in calculating radiative energy loss of high momentum partons traversing QGP created at RHIC and LHC. While soft-gluon approximation is convenient, different theoretical approaches reported significant radiative energy loss of high $p_{\perp}$ partons, thereby questioning its validity. To address this issue, we relaxed the soft-gluon approximation within DGLV formalism. The obtained analytical expressions are quite distinct compared to the soft-gluon case. However, numerical results for the first order in opacity fractional energy loss lead to small differences in predictions for the two cases. The difference in the predicted number of radiated gluons is also small. Moreover, the effect on these two variables has an opposite sign, which when combined results in almost overlapping suppression predictions. Therefore, our results imply that, contrary to the commonly held doubts, the soft-gluon approximation in practice works surprisingly well in DGLV formalism. Finally, we also discuss generalizing this relaxation in the dynamical QCD medium, which suggests a more general applicability of the conclusions obtained here.

Motivation & Objective

• To assess the validity of the soft-gluon approximation in calculating radiative energy loss of high-pT partons in QGP.
• To relax the soft-gluon approximation within the DGLV formalism and derive exact analytical expressions for energy loss.
• To compare predictions from the relaxed approximation with those from the standard soft-gluon approach.
• To evaluate the practical impact of the relaxation on observable quantities like energy loss and gluon multiplicity.
• To explore the implications for dynamical QCD media and broader applicability of the findings.

Proposed method

• Relax the soft-gluon approximation by allowing radiated gluons to carry a finite fraction of the initial parton's energy in the DGLV formalism.
• Derive analytical expressions for the first-order opacity energy loss without assuming soft gluon emission.
• Perform numerical comparisons between the relaxed and standard soft-gluon approximations for energy loss and gluon multiplicity.
• Analyze the sign and magnitude of differences in predictions for key observables.
• Extend the analysis to consider implications in a dynamical QCD medium for broader physical relevance.

Experimental results

Research questions

• RQ1 How do the analytical expressions for radiative energy loss change when the soft-gluon approximation is relaxed in the DGLV formalism?
• RQ2 What is the quantitative difference in predicted energy loss between the relaxed and standard soft-gluon approximations?
• RQ3 How does the relaxation affect the predicted number of radiated gluons?
• RQ4 Why do the predictions for parton suppression remain nearly identical despite analytical differences?
• RQ5 Can the conclusions about the soft-gluon approximation's robustness be generalized to dynamical QCD media?

Key findings

• The analytical expressions for energy loss in the relaxed approximation differ significantly from those in the soft-gluon limit.
• Numerical results for first-order opacity energy loss show only small differences between the relaxed and soft-gluon cases.
• The difference in predicted gluon multiplicity is also small and of opposite sign to the energy loss difference.
• The combined effect of opposing sign differences leads to nearly overlapping predictions for parton suppression in both models.
• These results suggest the soft-gluon approximation remains surprisingly accurate in practice, even when its assumptions are relaxed.
• The findings indicate potential broader applicability of the soft-gluon approximation in dynamical QCD media.