Inconsistencies in, and short pathlength correction to, $R_{AA}(p_T)$ in $\mathrm{A}+\mathrm{A}$ and $\mathrm{p} + \mathrm{A}$ collisions

TL;DR

This paper predicts hadron suppression in heavy-ion and proton-ion collisions using a model that includes short pathlength corrections to energy loss, revealing significant effects on pion suppression and examining the validity of underlying assumptions.

Contribution

It introduces the first leading hadron suppression predictions incorporating short pathlength corrections in a realistic energy loss model for $ ext{Pb}+ ext{Pb}$ and $ ext{p}+ ext{Pb}$ collisions.

Findings

Short pathlength correction minimally affects $D$ and $B$ meson $R_{AA}(p_T)$.

Significant reduction in $ ext{p}+ ext{Pb}$ and $ ext{Pb}+ ext{Pb}$ $ ext{pi}$ meson suppression.

Large formation time approximation breaks down at $p_T ightarrow 30$ GeV.

Abstract

We present the first leading hadron suppression predictions in $\mathrm{Pb}+\mathrm{Pb}$ and $\mathrm{p}+\mathrm{Pb}$ collisions from a convolved radiative and collisional energy loss model in which partons propagate through a realistic background and in which the inelastic energy loss receives a short pathlength correction. We find that the short pathlength correction is small for $D$ and $B$ meson $R_{AA}(p_T)$ in both $\mathrm{Pb}+\mathrm{Pb}$ and $\mathrm{p}+\mathrm{Pb}$ collisions. However the short pathlength correction leads to a surprisingly large reduction in suppression for $\pi$ mesons in $\mathrm{p}+\mathrm{Pb}$ and even $\mathrm{Pb}+\mathrm{Pb}$ collisions. We systematically check the consistency of the assumptions used in the radiative energy loss derivation - such as collinearity, softness, and large formation time - with the final numerical model. While collinearity and softness are self-consistently satisfied in the final numerics, we find that the large formation time approximation breaks down at modest to high momenta $p_T \gtrsim 30$ GeV. We find that both the size of the small pathlength correction to $R_{AA}(p_T)$ and the $p_T$ at which the large formation time assumption breaks down are acutely sensitive to the chosen distribution of scattering centers in the plasma.