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.
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Arnold, P. Universality (beyond leading log) of soft radiative corrections to \( \hat{q} \) in p⊥ broadening and energy loss. J. High Energ. Phys. 2022, 134 (2022). https://doi.org/10.1007/JHEP03(2022)134
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DOI: https://doi.org/10.1007/JHEP03(2022)134