Jet broadening in the opacity and twist expansions

Abstract

<jats:title>Abstract</jats:title><jats:p>We compute the in-medium jet broadening <jats:inline-formula><jats:alternatives><jats: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:mi>p</mml:mi> <mml:mo>⊥</mml:mo> <mml:mn>2</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-formula><jats:alternatives><jats:tex-math>$$\alpha _s$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> the elastic energy loss gives a jet broadening that grows with <jats:inline-formula><jats:alternatives><jats:tex-math>$$\ln E$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>ln</mml:mo> <mml:mi>E</mml:mi> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>. The next-to-leading order in <jats:inline-formula><jats:alternatives><jats:tex-math>$$\alpha _s$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</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-formula><jats:alternatives><jats:tex-math>$$\ln ^2 E$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mo>ln</mml:mo> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>E</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-formula><jats:alternatives><jats: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:mi>p</mml:mi> <mml:mo>⊥</mml:mo> <mml:mn>2</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>