The LPM effect in sequential bremsstrahlung: incorporation of “instantaneous” interactions for QCD
Peter Arnold (Department of Physics, University of Virginia, Charlottesville, VA, 22904, U.S.A.); Tyler Gorda (Technische Universität Darmstadt, Department of Physics, Darmstadt, 64289, Germany, ExtreMe Matter Institute EMMI and Helmholtz Research Academy for FAIR, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, 64291, Germany); Shahin Iqbal (Institute of Particle Physics, Central China Normal University, Wuhan, 430079, China, National Centre for Physics, Quaid-i-Azam University Campus, Islamabad, 45320, Pakistan)
The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We continue study of the case when the coherence lengths (formation lengths) of two consecutive splitting processes overlap, avoiding soft-emission approximations. Previous work made a “nearly-complete” calculation of the effect of overlapping formation times on gluonic splittings such as g → gg → ggg (with simplifying assumptions such as an infinite QCD medium and the large-N c limit). In this paper, we extend those previous rate calculations from nearly-complete to complete by including processes involving the exchange of longitudinally-polarized gluons. In the context of Lightcone Pertubation Theory, used earlier for the “nearly-complete” calculation, such exchanges are instantaneous in lightcone time and have their own diagrammatic representation.