Jet broadening in the opacity and twist expansions

We compute the in-medium jet broadening $⟨$p${}_{\perp }^2⟩$ to leading order in energy in the opacity expansion. At leading order in ${\alpha }_s$ the elastic energy loss gives a jet broadening that grows with ln E. The next-to-leading order in ${\alpha }_s$ result is a jet narrowing, due to destructive LPM interference effects, that grows with ln${}^2$ E. We find that in the opacity expansion the jet broadening asymptotics are - unlike for the mean energy loss - extremely sensitive to the correct treatment of the finite kinematics of the problem; integrating over all emitted gluon transverse momenta leads to a prediction of jet broadening rather than narrowing. We compare the asymptotics from the opacity expansion to a recent twist-4 derivation of $⟨$p${}_{\perp }^2⟩$ and find a qualitative disagreement: the twist-4 derivation predicts a jet broadening rather than a narrowing. Comparison with current jet measurements cannot distinguish between the broadening or narrowing predictions. We comment on the origin of the difference between the opacity expansion and twist-4 results.