Disentangling centrality bias and final-state effects in the production of high-$p_T$ $\pi^0$ using direct $\gamma$ in $d$$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV

PHENIX presents a simultaneous measurement of the production of direct $\gamma$ and $\pi^0$ in $d$$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV over a $p_T$ range of 7.5 to 18 GeV/$c$ for different event samples selected by event activity, i.e. charged-particle multiplicity detected at forward rapidity. Direct-photon yields are used to empirically estimate the contribution of hard-scattering processes in the different event samples. Using this estimate, the average nuclear-modification factor $R_{d\rm Au,EXP}^{\gamma^{\rm dir}}$ is $0.925{\pm}0.023({\rm stat}){\pm}0.15^{\rm (scale)}$, consistent with unity for minimum-bias (MB) $d$$+$Au events. For event classes with moderate event activity, $R_{d\rm Au,EXP}^{\gamma^{\rm dir}}$ is consistent with the MB value within 5\% uncertainty. These results confirm that the previously observed enhancement of high-$p_T$ $\pi^0$ production found in small-system collisions with low event activity is a result of a bias in interpreting event activity within the Glauber framework. In contrast, for the top 5\% of events with the highest event activity, $R_{d\rm Au,EXP}^{\gamma^{\rm dir}}$ is suppressed by 20\% relative to the MB value with a significance of $4.5\sigma$, which may be due to final-state effects.