Consequences of high-$x$ proton size fluctuations in small collision systems at RHIC

Recent measurements of jet production rates at large transverse momentum ($p_T$) in the collisions of small projectiles with large nuclei at RHIC and the LHC indicate that they have an unexpected relationship with estimates of the collision centrality. One compelling interpretation of the data is that it captures an $x_p$-dependent decrease in the average interaction strength of the nucleon in the projectile undergoing a hard scattering. A weakly interacting or "shrinking" nucleon in the projectile strikes fewer nucleons in the nucleus, resulting in a particular pattern of centrality-dependent modifications to high-$p_T$ processes. We describe a simple one-parameter geometric implementation of this picture within a modified Monte Carlo Glauber model tuned to $d$$+$Au jet data, and explore two of its major consequences. First, the model predicts a particular projectile-species dependence to the centrality dependence at high-$x_p$, opposite to that expected from an energy loss effect. Second, we find that some of the large centrality dependence observed for forward di-hadron production in $d$$+$Au collisions at RHIC may arise from the physics of the "shrinking" projectile nucleon, in addition to impact parameter-dependent shadowing or saturation effects at low nuclear-$x$. We conclude that analogous measurements in recently collected $p$$+$Au and $^3$He$+$Au collision data at RHIC can provide a unique test of these predictions.