Symmetric cumulants as a probe of the proton substructure at LHC energies

Abstract

We present a systematic study of the normalized symmetric cumulants, NSC(n,m), at the eccentricity level in proton-proton interactions at √ s = 13 TeV within a wounded hot spot approach. We focus our attention on the influence of spatial correlations between the proton constituents, in our case gluonic hot spots, on this observable. We notice that the presence of short-range repulsive correlations between the hot spots systematically decreases the values of NSC(2,3) and NSC(2,4) in midto ultra-central collisions while increases them in peripheral interactions. In the case of NSC(2,3) we find that, as suggested by data, an anti-correlation of ε2 and ε3 in ultra-central collisions, i.e. NSC(2,3) < 0, is possible within the correlated scenario while it never occurs without correlations when the number of gluonic hot spots is set to three. We attribute this fact to the decisive role of correlations on enlarging the probability of interaction topologies that reduce the value of NSC(2,3) and, eventually, make it negative. Further, we explore the dependence of our conclusions on the number of hot spots, the values of the hot spot radius and the repulsive core distance. Our results add evidence to the idea that considering spatial correlations between the subnucleonic degrees of freedom of the proton may have a strong impact on the initial state properties of proton-proton interactions [1].

Primordial non-Gaussianity in heavy-ion collisions

“…Adding the contributions of Eqs. (20), (21) and (22), one obtains: The expression of c n {4} coincides with that derived in [7] for n = 2, and then extended in [8] to n = 3. The result for SC(3, 2) is new.…”

“…(14). It is directly proportional to the 3-point function of the density field C 3 , as the contribution (21) to the kurtosises. For identical pointlike sources, Eq.…”

“…The full expressions of the cumulants to leading order in the perturbative expansion are obtained by summing the contributions of Eqs. (20), (21), (22):…”

“…This is a general valid approach for large systems such as nucleus-nucleus collisions. Small systems (proton-nucleus and proton-proton collisions [21][22][23][24]) are not considered here. For simplicity, the calculations in the main body of this article are carried out for central collisions (i.e., at zero impact parameter).…”

Dipole evolution: perspectives for collectivity and γ*A collisions

“…This would increase the total and elastic cross sections at low √ s, while the effect at higher √ s could be tuned away by a slightly smaller value of r max or α s . Other studies of proton substructure [71] has indicated that the number of hot-spots required for a satisfactory qualitative description -25 - of LHC data is larger than three, but at the same time, previous studies of the Mueller dipole formalism in the DIPSY event generator [61] indicated that a triangle configuration of initial dipoles is the most suitable choice for a good description of the cross sections. A study of this sort will therefore likely have to rely on attemps of simultaneous description of both sub-structure and cross sections, and will be referred to a future study.…”