Eccentric Protons? Sensitivity of Flow to System Size and Shape in $p+p$, $p+\mathrm{Pb}$, and $\mathrm{Pb}+\mathrm{Pb}$ Collisions

We determine the transverse system size of the initial nonequilibrium Glasma state and of the hydrodynamically evolving fireball as a function of produced charged particles in $p+p$, $p+\mathrm{Pb}$, and $\mathrm{Pb}+\mathrm{Pb}$ collisions at the Large Hadron Collider. Our results show features similar to those of recent measurements of Hanbury Brown–Twiss (HBT) radii by the ALICE Collaboration. Azimuthal anisotropy coefficients $v_n$ generated by combining the early time Glasma dynamics with viscous fluid dynamics in $\mathrm{Pb}+\mathrm{Pb}$ collisions are in excellent agreement with experimental data for a wide range of centralities. In particular, event-by-event distributions of the $v_n$ values agree with the experimental data out to fairly peripheral centrality bins. In striking contrast, our results for $p+\mathrm{Pb}$ collisions significantly underestimate the magnitude and do not reproduce the centrality dependence of data for $v_2$ and $v_3$ coefficients. We argue that the measured $v_n$ data and HBT radii strongly constrain the shapes of initial parton distributions across system sizes that would be compatible with a flow interpretation in $p+\mathrm{Pb}$ collisions. Alternately, additional sources of correlations may be required to describe the systematics of long-range rapidity correlations in $p+p$ and $p+\mathrm{Pb}$ collisions.

Figure 1

The event-averaged $p_T$-integrated $⟨v_n⟩$ value as a function of centrality compared to experimental data from the ATLAS Collaboration [34].

Figure 2

Data points corresponding to the event-by-event distributions of $v_2$, $v_3$, and $v_4$ in the respective maximal peripheral bin measured by the ATLAS Collaboration [34]. These are compared to the distributions of initial eccentricities in the IP-Glasma model and the distributions of $v_n$ obtained after fluid dynamic evolution.

Figure 3

$r_{\max }$ determined using the IP-Glasma model and fluid dynamic expansion. The lower end of the band indicates the size of the initial state, and the upper end is the maximal value of $r_{\max }$ during the hydrodynamic evolution.

Figure 4

Multiplicity dependence of the root-mean-square elliptic flow coefficient $v_2$ in $\mathrm{Pb}+\mathrm{Pb}$ (open symbols) and $p+\mathrm{Pb}$ collisions (filled symbols) from the IP-$\text{Glasma}\hspace{0.17em}+$music model (connected triangles) compared to experimental data by the CMS Collaboration [39].

Figure 5

Multiplicity dependence of the root-mean-square triangular flow coefficient $v_3$ in $\mathrm{Pb}+\mathrm{Pb}$ (open symbols) and $p+\mathrm{Pb}$ collisions (filled symbols) from the IP-$\text{Glasma}\hspace{0.17em}+$music model (connected triangles) compared to experimental data by the CMS Collaboration [39].