Short path length pQCD corrections to energy loss in the quark gluon plasma

TL;DR

This paper investigates short path length corrections to pQCD energy loss in the quark-gluon plasma, revealing that under certain assumptions, these corrections cancel out, but relaxing these assumptions leads to significant modifications.

Contribution

It provides a detailed calculation of short separation distance corrections to the DGLV energy loss formula, highlighting the impact of formation time assumptions on energy loss predictions.

Findings

Short path length corrections cancel under large formation time assumptions.

Relaxing formation time assumptions results in over 100% correction to energy loss.

The study clarifies the role of separation distance in QGP energy dissipation.

Abstract

Recent surprising discoveries of collective behaviour of low-$p_T$ particles in $pA$ collisions at LHC hint at the creation of a hot, fluid-like QGP medium. The seemingly conflicting measurements of non-zero particle correlations and $R_{pA}$ that appears to be consistent with unity demand a more careful analysis of the mechanisms at work in such ostensibly minuscule systems. We study the way in which energy is dissipated in the QGP created in $pA$ collisions by calculating, in pQCD, the short separation distance corrections to the well-known DGLV energy loss formulae that have produced excellent predictions for $AA$ collisions. We find that, shockingly, due to the large formation time (compared to the $1/\mu$ Debye screening length) assumption that was used in the original DGLV calculation, a highly non-trivial cancellation of correction terms results in a null short path length correction to the DGLV energy loss formula. We investigate the effect of relaxing the large formation time assumption in the final stages of the calculation -- doing so throughout the calculation adds immense calculational complexity -- and find, since the separation distance between production and scattering centre is integrated over from $0$ to $\infty$, $\gtrsim 100\%$ corrections, even in the large path length approximation employed by DGLV.