Collisional and radiative energy loss in small systems

We present an energy-loss model which includes small system size corrections to both the radiative and elastic energy loss. Our model is used to compute the nuclear modification factor ${R}_{AB}$ of light and heavy flavor hadrons averaged over realistic collision geometries for central and peripheral $A+A$ and central $p/d/^{3}\mathrm{He}+A$ collisions at the CERN Large Hadron Collider and the BNL Relativistic Heavy Ion Collider. We find that the predicted suppression in small systems is almost entirely due to elastic energy loss. Our results are keenly sensitive to the crossover between elastic energy loss calculated with hard thermal loop propagators and vacuum propagators, respectively, which leads to a large theoretical uncertainty. We find that the ${R}_{AB}$ is largely insensitive to the form of the elastic energy-loss distribution---Gaussian or Poisson---surprisingly so in small systems where the central limit theorem is inapplicable. We present an expansion of the ${R}_{AB}$ in terms of the moments of the energy loss probability distribution, which allows for a rigorous understanding of the dependence of the ${R}_{AB}$ on the underlying energy-loss distribution.