Universality (beyond leading log) of soft radiative corrections to hat{q} in p⊥ broadening and energy loss

Abstract

It has been known for many years that soft radiation can give potentially large double-logarithm corrections to p⊥ 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} eff for the medium p⊥-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→gg, where double logarithms can also be absorbed using the same effective hat{q} eff. In this paper, I study whether the same holds true for potentially large, subleading, single-logarthim corrections. The correspondence is more indirect for single logarithms, but I show (in the large-Nc limit) that single logarithms from soft radiation in the case of p⊥ broadening also determine the single logarithms from soft radiative corrections to hard g→gg splitting. Along the way, there is an interesting variation of the original BDMPS-Z calculation of splitting rates in the hat{q} approximation. I also discuss how, for soft-radiative corrections to hard splitting processes, there are two different types of “ hat{q} eff” that come into play, which differ by “iπ” terms that multiply single logarithms.