Non-Abelian energy loss in cold nuclear matter

Abstract

We use a formal recurrence relation approach to multiple parton scattering to find the complete solution to the problem of medium-induced gluon emission from partons propagating in cold nuclear matter. The differential bremsstrahlung spectrum, where Landau-Pomeranchuk-Migdal destructive interference effects are fully accounted for, is calculated for three different cases: (i) a generalization of the incoherent Bertsch-Gunion solution for asymptotic on-shell jets, (ii) initial-state energy loss of incoming jets that undergo hard scattering, and (iii) final-state energy loss of jets that emerge out of a hard scatter. Our analytic solutions are given as an infinite opacity series, which represents a cluster expansion of the sequential multiple scattering. These new solutions allow, for the first time, direct comparison between initial- and final-state energy loss in cold nuclei. We demonstrate that, contrary to the naive assumption, energy loss in cold nuclear matter can be large. Numerical results to first order in opacity show that, in the limit of large jet energies, initial- and final-state energy losses exhibit different path length dependences, linear versus quadratic, in contrast to earlier findings. In addition, in this asymptotic limit, initial-state energy loss is considerably larger than final-state energy loss. These new results have significant implications for heavy-ion phenomenology in both $p+A$ and $A+A$ reactions.