Unfolding the effects of final-state interactions and quantum statistics in two-particle angular correlations

Angular correlations of identified particles measured in ultrarelativistic proton-proton (pp) and heavy-ion collisions exhibit a number of features which depend on the collision system and particle type under consideration. Those features are produced by mechanisms, such as (mini)jets, elliptic flow, resonance decays, and conservation laws. In addition, of particular importance are those related to the quantum statistics (QS) and final-state interactions (FSIs). In this paper we show how to unfold the QS and FSI contributions in angular correlation functions by employing a Monte Carlo approach and using momentum correlations (femtoscopy), focusing on pp reactions. We validate the proposed method with pythia 8 Monte Carlo simulations of pp collisions at $\sqrt{s}=13\mathrm{TeV}$ coupled to calculations of QS and FSI effects with the Lednický and Lyuboshitz formalism and provide predictions for the unfolded effects. In particular, we show how those effects modify the shape of the angular correlation function with emphasis on pions and protons. Most importantly, specific structures observed in the near-side region for both baryon-baryon and baryon-antibaryon pairs, originating from the strong interaction, are unveiled with the proposed method.

Figure 1

Schematic of the angular correlation function $C(\mathrm{\Delta }\eta ,\mathrm{\Delta }\phi )$ showing contributions from various correlation sources.

Figure 2

Correlation functions in (left) femtoscopic and (right) angular representations of ${\pi }^{+}{\pi }^{+}$ pairs (first row), ${\pi }^{+}{\pi }^{-}$ pairs (second row), pp pairs (third row), and $\mathrm{p}\overline{\mathrm{p}}$ pairs (fourth row) from pythia 8 simulations, coupled to the Lednický and Lyuboshitz [15] formalism of pp collisions at $\sqrt{s}=13\mathrm{TeV}$, showing $C_{\mathrm{full}}$ (in green), $C_{\mathrm{QS}+\mathrm{FSI}}$ (in red), and $C_{\mathrm{base}}$ (in blue). For better visualization of the differences, the $\mathrm{\Delta }\phi$ projections are shifted by a constant value so that the baseline is at $C\left(\mathrm{\Delta }\phi \right)=0$.

Figure 3

Schematic showing which $k^{*}$ ranges in the femtoscopic correlation function corresponds to which $\mathrm{\Delta }\eta \mathrm{\Delta }\phi$ regions in the angular correlation.

Figure 4

Correlation functions $C_{\mathrm{QS}+\mathrm{FSI}}^{\mathrm{unfolded}}(\mathrm{\Delta }\eta ,\mathrm{\Delta }\phi )$ (left column) and $C_{\mathrm{QS}+\mathrm{FSI}}(\mathrm{\Delta }\eta ,\mathrm{\Delta }\phi )$ (middle column) in the angular representation of ${\pi }^{+}{\pi }^{+}, {\pi }^{+}{\pi }^{-}$, pp, and $\mathrm{p}\overline{\mathrm{p}}$ pairs from pythia simulated pp collisions, coupled to the Lednický and Lyuboshitz [15] formalism at $\sqrt{s}=13\mathrm{TeV}$. The right column shows the ratio of the ratio $C_{\mathrm{QS}+\mathrm{FSI}}(\mathrm{\Delta }\eta ,\mathrm{\Delta }\phi )/C_{\mathrm{QS}+\mathrm{FSI}}^{\mathrm{unfolded}}(\mathrm{\Delta }\eta ,\mathrm{\Delta }\phi )$.

Figure 5

Upper panels: projections of $C_{\mathrm{QS}+\mathrm{FSI}}(\mathrm{\Delta }\eta ,\mathrm{\Delta }\phi )$ (closed symbols) and $C_{\mathrm{QS}+\mathrm{FSI}}^{\mathrm{unfolded}}(\mathrm{\Delta }\eta ,\mathrm{\Delta }\phi )$ (open symbols) in $\mathrm{\Delta }\phi$ for $\left|\mathrm{\Delta }\eta \right|<1.3$ (left column) and in $\mathrm{\Delta }\eta$ for $-\frac{\pi }{2}<\mathrm{\Delta }\phi <\frac{\pi }{2}$ (right column) for ${\pi }^{+}{\pi }^{+}, {\pi }^{+}{\pi }^{-}$, pp, and $\mathrm{p}\overline{\mathrm{p}}$ pairs from pythia simulated pp collisions, coupled to the Lednický and Lyuboshitz [15] formalism, at $\sqrt{s}=13\mathrm{TeV}$. Lower panels: ratios of $C_{\mathrm{QS}+\mathrm{FSI}}^{\mathrm{unfolded}}$ to $C_{\mathrm{QS}+\mathrm{FSI}}$.

Figure 6

Upper panels: projections of $C_{\mathrm{base}}(\mathrm{\Delta }\eta ,\mathrm{\Delta }\phi )$ (closed symbols) and $C_{\mathrm{base}}^{\mathrm{unfolded}}(\mathrm{\Delta }\eta ,\mathrm{\Delta }\phi )$ (open symbols) in $\mathrm{\Delta }\phi$ for $\left|\mathrm{\Delta }\eta \right|<1.3$ (left column) and in $\mathrm{\Delta }\eta$ for $-\frac{\pi }{2}<\mathrm{\Delta }\phi <\frac{\pi }{2}$ (right column) for ${\pi }^{+}{\pi }^{+}$ pairs from pythia simulated pp collisions, coupled to the Lednický and Lyuboshitz [15] formalism at $\sqrt{s}=13\mathrm{TeV}$. For better visualization of the differences, the $\mathrm{\Delta }\eta$ projections are shifted by a constant value so that the baseline is at $C\left(\mathrm{\Delta }\eta \right)=0$. Lower panels: ratio of $C_{\mathrm{base}}^{\mathrm{unfolded}}$ to $C_{\mathrm{base}}$.

Figure 7

Upper panels: projections of $C_{\mathrm{full}}(\mathrm{\Delta }\eta ,\mathrm{\Delta }\phi )$ (closed symbols) and $C_{\mathrm{full}}^{\mathrm{unfolded}}(\mathrm{\Delta }\eta ,\mathrm{\Delta }\phi )$ (open symbols) in $\mathrm{\Delta }\phi$ for $\left|\mathrm{\Delta }\eta \right|<1.3$ (left column) and in $\mathrm{\Delta }\eta$ for $-\frac{\pi }{2}<\mathrm{\Delta }\phi <\frac{\pi }{2}$ (right column) for ${\pi }^{+}{\pi }^{+}$ pairs from pythia simulated pp collisions at $\sqrt{s}=13\mathrm{TeV}$. For better visualization of the differences, the $\mathrm{\Delta }\eta$ projections are shifted by a constant value so that the baseline is at $C\left(\mathrm{\Delta }\eta \right)=0$. Lower panels: ratio of $C_{\mathrm{full}}^{\mathrm{unfolded}}$ to $C_{\mathrm{full}}$.