Transverse momentum broadening and collinear radiation at NLO in the $\mathcal{N}=4$ SYM plasma

TL;DR

This paper calculates next-to-leading order corrections to transverse momentum broadening and collinear radiation in the weakly-coupled $ ext{N}=4$ SYM plasma, revealing theory-specific behaviors and comparisons with QCD and strong coupling results.

Contribution

It provides the first NLO corrections to $ ext{N}=4$ SYM transverse scattering kernel and $ ext{qhat}$, and analyzes their implications for theory-specific jet quenching phenomena.

Findings

NLO/LO ratio of $ ext{qhat}$ similar to QCD with large corrections

Collinear splitting rate shows better convergence in SYM than in QCD

Comparison of $ ext{qhat}$ ratios with strong coupling expectations

Abstract

We compute O(g) NLO corrections to the transverse scattering kernel and transverse momentum broadening coefficient $\hat{q}$ of weakly-coupled $\mathcal{N}=4$ SYM. Based on this, we also compute NLO correction to the collinear splitting rates. For $\hat{q}$ we find that the NLO/LO ratio is similar to the QCD one, with large NLO corrections. This is contrasted by our findings for the collinear splitting rate, which show a much better convergence in SYM than in QCD, providing further support to earlier expectations that NLO corrections have signs and relative magnitudes controlled by the specifics of the theory. We also compare the ratio of $\hat{q}$ in QCD and in $\mathcal{N}=4$ theory to strong coupling expectations.