Universality (beyond leading log) of soft radiative corrections to $\hat q$ in $p_\perp$ broadening and energy loss

Understand

It has been known for many years that soft radiation can give potentially large double-logarithm corrections to $p_\perp$ broadening of a high-energy particle traveling through QCD matter, but that this soft radiation correction can be absorbed into an effective value $\hat q_{\rm eff}$ for the medium $p_\perp$-broadening parameter $\hat q$.

• Here "soft" means high energy compared to medium scales but soft compared to the original high-energy particle traveling through the medium.
• A similar situation arises in the case of soft corrections to hard splitting of a high-energy particle, such as hard $g{\to}gg$, where double logarithms can also be absorbed using the same effective $\hat q_{\rm eff}$.
• In this paper, I study whether the same holds true for potentially large, subleading, *single*-logarthim corrections.