Correlated wounded hot spots in proton-proton interactions

We investigate the effect of nontrivial spatial correlations between proton constituents, considered in this work to be gluonic hot spots, on the initial conditions of proton-proton collisions from ISR to Large Hadron Collider energies, i.e., $\sqrt{s}=52.6$, 7000, and 13 000 GeV. The inclusion of these correlations is motivated by their fundamental role in the description of a recently observed new feature of $pp$ scattering at $\sqrt{s}=7$ TeV, the hollowness effect. Our analysis relies on a Monte Carlo Glauber approach including fluctuations in the hot spot positions and their entropy deposition in the transverse plane. We explore both the energy dependence and the effect of spatial correlations on the number of wounded hot spots, their spatial distribution, and the eccentricities, ${\varepsilon }_n$, of the initial state geometry of the collision. In minimum bias collisions we find that the inclusion of short-range repulsive correlations between the hot spots reduces the value of the eccentricity (${\varepsilon }_2$) and the triangularity (${\varepsilon }_3$). In turn, upon considering only the events with the highest entropy deposition, i.e., the ultracentral ones, the probability of having larger ${\varepsilon }_{2,3}$ increases significantly in the correlated scenario. Finally, the eccentricities show a quite mild energy dependence.

Figure 1

Fit to the charged particle multiplicity distributions for different collision energies in the wounded hot spot model, Eqs. (7) and (8). The experimental data from top to bottom are taken from the ATLAS Collaboration [43], the ALICE Collaboration [44], and ISR [45]. Note that each experiment has a different rapidity acceptance window, $\eta$, that influences the shape of the data. Also, the ALICE (red) and ISR (blue) curves are multiplied by 0.1 and 0.01, respectively.

Figure 2

The histogram of the integrated entropy deposition for the $r_c=0.4$ fm case at $\sqrt{s}=7$ TeV. Vertical red lines labeled by black numbers define centrality classes as fractions of the total number of events.

Figure 3

Average number of wounded hot spots for different impact parameter bins of the collision. The horizontal lines indicate the width of the bins.

Figure 4

Normalized radial distribution of the wounded hot spots before shifting and rotating to the participant plane.

Figure 5

Probability distribution of the eccentricity, ${\varepsilon }_2$, for $r_c=0$ (short-dashed blue line), $r_c=0.4$ fm (long-dashed red line), $r_c=0,nc$ (dotted grey line), and $\langle s_1\rangle$ fixed (solid purple line).

Figure 6

Probability distribution of the triangularity, ${\varepsilon }_3$, for $r_c=0$ (short-dashed blue line), $r_c=0.4$ fm (long-dashed red line), $r_c=0,nc$ (dotted grey line), and $\langle s_1\rangle$ fixed (solid purple line).

Figure 7

Probability distribution of the eccentricity, ${\varepsilon }_2$, for $r_c=0$ (short-dashed blue line), $r_c=0.4$ fm (long-dashed red line), $r_c=0,nc$ (dotted grey line), and $\langle s_1\rangle$ fixed (solid purple line) after selecting the 1% most entropic events.

Figure 8

Probability distribution of the triangularity, ${\varepsilon }_3$, for $r_c=0$ (short-dashed blue line), $r_c=0.4$ fm (long-dashed red line), $r_c=0,nc$ (dotted grey line), and $\langle s_1\rangle$ fixed (solid purple line) after selecting the 1% most entropic events.

Figure 9

Average values of the eccentricity, ${\varepsilon }_2$, for $r_c=0$ (open blue circle), $r_c=0.4$ fm (open red square), $r_c=0,nc$ (solid grey triangle), and $\langle s_1\rangle$ fixed (solid purple circle) as a function of the centrality range.

Figure 10

Average values of the triangularity, ${\varepsilon }_3$, for $r_c=0$ (open blue circle), $r_c=0.4$ fm (open red square), $r_c=0,nc$ (solid grey triangle), and $\langle s_1\rangle$ fixed (solid purple circle) as a function of the centrality range.

Figure 11

Average values of ${\varepsilon }_2$ (solid markers) and ${\varepsilon }_3$ (open markers) for $\sqrt{s}=52.6$ GeV (solid and open blue circles), 7 TeV (solid and open red squares), and 13 TeV (solid and open grey triangles) as a function of their standard deviation. These energies correspond to ISR and runs I and II of the LHC, respectively.