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

We present a systematic study of the normalized symmetric cumulants, NSC(n,m), at the eccentricity level in proton-proton interactions at $\sqrt s\!=\! 13$ 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 mid-to-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 $\varepsilon_2$ and $\varepsilon_3$ in ultra-central collisions, i.e. NSC(2,3)$<0$, is possible within the correlated scenario while it never occurs without correlations. 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 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].