A modified-Boltzmann approach for modeling the hot QCD medium-induce splitting vertices in the deep LPM region

Abstract: Hard probes produced in perturbative processes are excellent probes for the study of the hot and dense QCD matter created in relativistic heavy-ion collisions. Transport theory, allowing for coupling to an evolving medium with fluctuating initial conditions, has become a powerful tool in this endeavor. However, the implementation of the Landau-Pomeranchuk-Migdal (LPM) effect for medium-induced parton bremsstrahlung and pair production, poses a challenge to semi-classical transport models based on Boltzmann-type transport equations. In this work, we investigate a possible solution to approximate the LPM effect in a "modified Boltzmann transport" approach, including a prescription for the running coupling constant. By fixing a numerical parameter, this approach quantitatively reproduces the rates of medium-induced parton splitting predicted by the next-to-lead-log solution of the AMY equation which is valid in the deep-LPM regime of an infinite medium. We also find qualitative agreement of our implementation with calculations in a finite and expanding medium, but future improvements are needed for added precision at small path length. This work benefits transport model-based studies and the usage of these models in the phenomenological extraction of the jet transport coefficient.