Short-path-length corrections to Djordjevic-Gyulassy-Levai-Vitev energy loss

Abstract

We compute the correction to the energy loss of a hard parton due to short separation distances between the creation of the particle and the in-medium scattering center that stimulates bremsstrahlung radiation to first order in opacity. In deriving the result we make full use of the large-formation-time assumption, which results in a significant reduction of the number of diagrams contributing to the small-separation-distance correction. An asymptotic analysis of our small-separation-distance correction term finds that the correction dominates at large ∼100 GeV parent parton energies, scales like L with the size of the system for small L but like L 0 at larger L, and breaks color triviality. An extensive numerical investigation of the correction term confirms the aforementioned analytic findings, reveals that the correction term does not go to zero for large L, finds that the correction is sensitive to the mass of the parent parton, and shows a crucial dependence of the energy loss on a proper treatment of the physics of separation distances on the order of the Debye screening length. However, on examination, we have found the large-formation-time approximation to be invalid for much of the phase space of the emitted radiation, implying a need to investigate the sensitivity of jet quenching results from relaxing this approximation. Our result constitutes an important step toward understanding partonic energy loss in small colliding systems.

Jet broadening in the opacity and twist expansions

“…This convergence appears to be due to an extremely delicate cancellation of competing divergences. (It's perhaps worth noting that even subleading corrections to the radiative energy loss kernel can destroy this delicate cancellation of divergences, changing the leading in E behavior from E ∼ ln E to E ∼ E [79].) Possibly another way of seeing the difficulty of extracting the leading behavior is that we expect the leading contribution to come from k ⊥ ∼ q ⊥ with 4x E/L acting as a regulator; however we must also integrate over x, and, worse, k max ∼ x for small x.…”

Jet Broadening in the Opacity and Twist Expansions

“…This convergence appears to be due to an extremely delicate cancellation of competing divergences. (It's perhaps worth noting that even subleading corrections to the radiative energy loss kernel can destroy this delicate cancellation of divergences, changing the leading in E behavior from ∆E ∼ log E to ∆E ∼ E [72].) Possibly another way of seeing the difficulty of extracting the leading behavior is that we expect the leading contribution to come from k ⊥ ∼ q ⊥ with 4xE/L acting as a regulator; however we must also integrate over x, and, worse, k max ∼ x for small x.…”

“…In order to facilitate comparison between the twist-4 result and the energy loss result, we consider the ratio of the radiative (NLO) component (72) and collisional (LO) component (65) within the twist-4 formalism. Note also that the observable d 2 ⊥ σ /dx B dy is proportional to p 2 T up to a normalization factor which cancels in the ratio.…”

Jets in e+A SIDIS and Denominator Regularization

“…One may then naturally ask: what are the natural next step(s)? Obvious candidates include: computing higher orders in α s [5], considering small system size corrections [6][7][8], sub-eikonal corrections [9], extracting transport coefficients through a systematic analysis [10], etc. In this work we specifically consider placing energy loss on a more rigorous footing; we also consider quantum field theories in small systems.…”