All-path-length and sub-eikonal corrections to momentum broadening in the opacity expansion approach

TL;DR

This paper extends the GLV formalism for momentum broadening of high-energy partons in QGP by including all-path-length and sub-eikonal corrections, providing analytic expressions and numerical insights into their effects.

Contribution

It introduces all-path-length and sub-eikonal corrections to the GLV formalism, improving accuracy for small systems like pp and p/dA.

Findings

APL reduces low-momentum broadening

Sub-eikonal correction increases high-momentum broadening

Combined corrections mitigate each other's effects

Abstract

We present a detailed study of momentum broadening for high-energy partons traversing the Quark-Gluon Plasma (QGP), extending the Gyulassy-Levai-Vitev (GLV) formalism to include both all-path-length (APL) and sub-eikonal corrections. Traditional GLV calculations rely on the large separation distance and large formation time approximations, which are valid for large systems, but whose applicability in small systems such as pp and p/dA may fail. We derive analytic expressions for the momentum broadening distributions to first order in the opacity expansion, and perform a numerical investigation to quantify their impact. Our results show that the APL result reduces the low-momentum broadening and the sub-eikonal correction enhances the high-momentum broadening. The combined APL and sub eikonal correction show that the sub-eikonal correction mitigates the effect of the APL correction.