Assumption Breakdown in Radiative Energy Loss

We show that an integral assumption in DGLV radiative energy loss - the large formation time assumption - is violated at high-$p_T$ for phenomenologically relevant parameters. We further investigate the phenomenological impact of placing a new kinematic bound on the radiated gluon transverse momentum, which ensures that there are no contributions to the energy loss from regions of parameter space that violate the large formation time assumption. We find that this places a large sensitivity on the exact kinematic cutoff used, similar to the known collinear cutoff sensitivity, indicating the theoretical need for a rederivation of DGLV radiative energy with the large formation time assumption relaxed in order to make rigorous predictions. We additionally find that this large formation time cutoff dramatically reduces the size of a short pathlength correction to the DGLV radiative energy loss, which is of phenomenological interest in predicting suppression in small $p +A$ systems. We compute the phenomenological predictions utilizing this large formation time cutoff in both $p+A$ and $A+A$ collisions at the LHC, in a convolved radiative and elastic energy loss model.