jats:titleAbstract</jats:title>jats:pWe compute the in-medium jet broadening jats:inline-formulajats:alternativesjats:tex-math$$\langle p_\perp ^2\rangle $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mo⟨</mml:mo> mml:msubsup mml:mip</mml:mi> mml:mo⊥</mml:mo> mml:mn2</mml:mn> </mml:msubsup> mml:mo⟩</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> to leading order in energy in the opacity expansion. At leading order in jats:inline-formulajats:alternativesjats:tex-math$$\alpha _s$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:miα</mml:mi> mml:mis</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> the elastic energy loss gives a jet broadening that grows with jats:inline-formulajats:alternativesjats:tex-math$$\ln E$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:moln</mml:mo> mml:miE</mml:mi> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>. The next-to-leading order in jats:inline-formulajats:alternativesjats:tex-math$$\alpha s$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:miα</mml:mi> mml:mis</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> result is a jet narrowing, due to destructive LPM interference effects, that grows with jats:inline-formulajats:alternativesjats:tex-math$$\ln ^2 E$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:msup mml:moln</mml:mo> mml:mn2</mml:mn> </mml:msup> mml:miE</mml:mi> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>. 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 jats:inline-formulajats:alternativesjats:tex-math$$\langle p\perp ^2\rangle $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mo⟨</mml:mo> mml:msubsup mml:mip</mml:mi> mml:mo⊥</mml:mo> mml:mn2</mml:mn> </mml:msubsup> mml:mo⟩</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> 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.</jats:p>