Contribution to differential $\pi^0$ and $\gamma_\mathrm{dir}$ modification in small systems from color fluctuation effects

A major complication in the search for jet quenching in proton- or deuteron-nucleus collision systems is the presence of physical effects which influence the experimental determination of collision centrality in the presence of a hard process. For example, in the proton color fluctuation picture, protons with a large Bjorken-$x$ ($x \gtrsim 0.1$) parton interact more weakly with the nucleons in the nucleus, leading to a smaller (larger) than expected yield in large (small) activity events. A recent measurement by PHENIX compared the yield of neutral pion and direct photon production in $d$+Au collisions, under the argument that the photon yields correct for such biases, and the difference between the two species is thus attributable to final-state effects (i.e., jet quenching). The main finding suggests a significant degree of jet quenching for hard processes in small systems. In this paper, I argue that the particular photon and pion events selected by PHENIX arise from proton configurations with significantly different Bjorken-$x$ distributions, and thus are subject to different magnitudes of modification in the color fluctuation model. Using the results of a previous global analysis of RHIC and LHC data, I show that potentially all of the pion-to-photon difference in PHENIX data can be described by a proton color fluctuation picture at a quantitative level before any additional physics from final-state effects is required. This finding reconciles the interpretation of the PHENIX measurement with others at RHIC and LHC, which have found no observable evidence for jet quenching in small systems.