Plane correlations in small colliding systems

I propose event-plane correlations as a test of collectivity in small colliding systems: In $d$-Au and ${}^3\mathrm{He}$-Au collisions, I predict a strong anticorrelation between elliptic and triangular flow, generated by the geometry of the light projectile. A significant anticorrelation is also predicted in central $p$-Pb collisions at the CERN Large Hadron Collider, which is solely generated by fluctuations. Similar, but stronger correlation patterns are predicted in correlations involving dipolar flow.

Figure 1

Initial state mixing between ${\mathcal{E}}_2$ and ${\mathcal{E}}_3$ as a function of number of participants. Results in (a) are from the PHOBOS Monte Carlo Glauber model with a constant weighting of $C_s$ in Eq. (12). Dashed line is analytical expectation from the independent-source model. Results with an extra NBD weighting is shown in (b). Results from smearing with $\sigma =0.4$ fm are plotted with symbols, while shaded bands correspond to the case with $\sigma =0.8$ fm.

Figure 2

Initial state mixing involving ${\mathcal{E}}_1$ as a function of number of participants, represented by (a) ${\mathcal{P}}_{12}^{\varepsilon \varepsilon }$, (b) $-{\mathcal{P}}_{13}^{\varepsilon \varepsilon }$, and (c) $-{\mathcal{P}}_{123}^{\varepsilon \varepsilon }$. All the results are obtained with an extra NBD weighting for the entropy production. Results with $\sigma =0.4$ fm are plotted with symbols, while shaded bands correspond to $\sigma =0.8$ fm.

Figure 3

Alignment of anisotropies due to fluctuations on top of smooth background (solid blue shape) with a net ellipticity ${\mathcal{E}}_2$ (a) and a net triangularity ${\mathcal{E}}_3$ (b). Green dashed shapes correspond to anisotropies generated by one addition hot spot in the tip area of the background. Dipolar asymmetry is illustrated as green arrows.