Jet Broadening in the Opacity and Twist Expansions

TL;DR

This paper calculates the in-medium jet broadening at leading order in energy, revealing a sensitivity to finite kinematic effects and a discrepancy with twist-4 predictions, impacting interpretations of jet modification in dense media.

Contribution

It provides a detailed leading-order calculation of jet broadening in the opacity expansion and compares it with twist-4 results, highlighting differences in predicted asymptotic behavior.

Findings

Jet broadening grows with g E at leading order.

Next-to-leading order results show jet narrowing due to interference.

Discrepancy between opacity expansion and twist-4 predictions.

Abstract

We compute the in-medium jet broadening $\langle p_\perp^2\rangle$ 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 $\langle p_\perp^2\rangle$ 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.