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