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

TL;DR

This paper calculates the first-order correction to parton energy loss due to short separation distances in a medium, revealing significant effects at high energies and emphasizing the importance of formation time assumptions.

Contribution

It provides a detailed analysis of short separation distance corrections to parton energy loss, highlighting their dominance at high energies and the limitations of the large formation time approximation.

Findings

Correction dominates at ~100 GeV energies

Correction scales with system size L for small L, constant for large L

Correction depends on parent parton mass and separation distance physics

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 $\sim 100$ 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, an examination of the large formation time approximation shows that it is violated 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.