Consequences of high-$x$ proton size fluctuations in small collision systems at $\sqrt{s_{{}_{NN}}}=200\mathrm{GeV}$

Recent measurements of jet production rates at large transverse momentum ($p_T$) in the collisions of small projectiles with large nuclei at the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider indicate that they have an unexpected relationship with estimates of the collision centrality. One compelling interpretation of the data is that they capture 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 $d+\mathrm{Au}$ jet data, and explore two of its major consequences. First, the model predicts a particular projectile-species effect on the centrality dependence at high $x_p$, opposite to that expected from a final state energy loss effect. Second, we find that some of the large centrality dependence observed for forward dihadron production in $d+\mathrm{Au}$ 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 $p+\mathrm{Au}$ and ${}^3\mathrm{He}+\mathrm{Au}$ collision data at RHIC can provide a unique test of these predictions.

Figure 1

The calculated $R_{p+A}$ as a function of $x_p$ in each centrality bin for $(p,d,{}^3\mathrm{He})+\mathrm{Au}$ compared to the measured $R_{d+\mathrm{Au}}$ of jets in $d+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ [1].

Figure 2

Schematic picture of a nucleon-nucleon collision for the case of (a) an unmodified projectile nucleon and (b) a projectile nucleon whose radius depends on $x_p$.

Figure 3

Ratio of the modified nucleon-nucleon cross section $\sigma \left(x_p\right)$ to the nominal value ${\sigma }_{NN}$, as a function of the momentum fraction in the projectile nucleon ($x_p$).

Figure 4

The calculated $R_{CP}$ as a function of $x_p$ in each centrality bin compared to the measured $R_{CP}$ of jets in $d+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ [1].

Figure 5

The mean charge in the Au-going BBC for each collision system as a function of $x_p$, normalized to the value at $x_p=0$.

Figure 6

The measured $J_{d+\mathrm{Au}}$ as a function of $x_p$ [21] in each centrality bin compared to the calculated modification due to the shrinking projectile nucleon size in $d+\mathrm{Au}$ collisions.

Figure 7

Distributions of the radial impact position of nucleons ($r_T$) in $d+\mathrm{Au}$ collisions for each of the four PHENIX centrality bins, reproduced from Ref. [34]. Also shown is the nuclear thickness as a function of the impact position, in arbitrary units.