The LPM effect in sequential bremsstrahlung: analytic results for sub-leading (single) logarithms

Abstract

Consider the in-medium splitting $g\to gg$ of a very high-energy gluon traversing a QCD medium, accounting for the Landau-Pomeranchuk-Migdal (LPM) effect. It has been known for some time that soft radiative corrections to that splitting generate a double-log correction to the splitting rate, whose effects can be absorbed into running of the medium parameter $\hat{q}$ describing the rate of transverse momentum kicks to high-energy particles due to small-angle scattering from the medium. Less has been known about sub-leading, single logarithms in this context. In this paper, we find analytic formulas for those single logs (with various caveats and clarifications).

Comments: 54 pages, 20 figures. Chages from v1 are superficial -- mostly a slight expansion of the introduction and conclusion