The LPM effect in sequential bremsstrahlung: analytic results for sub-leading (single) logarithms
Peter Arnold (Department of Physics, University of Virginia, P.O. Box 400714, Charlottesville, VA, 22904, USA); Tyler Gorda (Technische Universität Darmstadt, Department of Physics, Darmstadt, D-64289, Germany, Helmholtz Research Academy for FAIR, Darmstadt, D-64289, Germany); Shahin Iqbal (Institute of Particle Physics, Central China Normal University, Wuhan, 430079, China, National Centre for Physics, Quaid-i-Azam University, Islamabad, Pakistan)
Consider the in-medium splitting g → 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).
