Jet broadening in the opacity and twist expansions

Abstract

We compute the in-medium jet broadening $$\langle p_\perp ^2\rangle $$ ⟨ p ⊥ 2 ⟩ to leading order in energy in the opacity expansion. At leading order in $$\alpha _s$$ α s the elastic energy loss gives a jet broadening that grows with $$\ln E$$ ln E . The next-to-leading order in $$\alpha _s$$ α s result is a jet narrowing, due to destructive LPM interference effects, that grows with $$\ln ^2 E$$ 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 $$\langle p_\perp ^2\rangle $$ ⟨ p ⊥ 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.

Are Jets Narrowed or Broadened in e+A SIDIS?

“…A. Horowitz in exact agreement with the opacity expansion. We show the full numerics of the first order in opacity, and NLO in in our original work [24]. Surprisingly, the numerics clearly show a jet narrowing in nuclear media compared to vacuum.…”

“…However, if one explicitly maintains the kinematic limits while still taking the → ∞ limit, which is highly non-trivial [24], then one finds a jet narrowing:…”

Energy Loss in Small Collision Systems

“…Additional future work in small systems may seek to place energy loss calculations on a more rigorous footing [33] or consider the small system size corrections to thermodynamics [34], the equation of state [35], and the effective coupling [36].…”

Jets in e+A SIDIS and Denominator Regularization

“…in exact agreement with the opacity expansion. We show the full numerics of the first order in opacity, and NLO in α s in our original work [18]. Surprisingly, the numerics clearly show a jet narrowing in nuclear media compared to vacuum.…”

“…However, if one explicitly maintains the kinematic limits while still taking the E → ∞ limit, which is highly non-trivial [18], then one finds a jet narrowing:…”