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Investigating the p-$π^{\pm}$ and p-p-$π^{\pm}$ dynamics with femtoscopy in pp collisions at $\sqrt{s} = 13$ TeV

ALICE Collaboration

TL;DR

This study uses femtoscopy to probe pion–nucleon dynamics in high-multiplicity pp collisions at $\sqrt{s}=13$ TeV. By analyzing two-particle $p$--$\pi^{\pm}$ correlations with a Resonance Source Model and the CATS framework, the authors extract a common, $m_T$-dependent particle-emitting source across hadron pairs and characterize resonance modifications, notably for $\Delta(1232)$. They also develop a three-body cumulant formalism to isolate genuine three-body effects in $p$--$p$--$\pi^{\pm}$ systems, finding nonzero cumulants that indicate beyond-pairwise interactions and coupling of the pion to multiple nucleons. The results have implications for transport models of small collision systems and for understanding multi-nucleon pion dynamics relevant to QCD at low energy and in dense baryonic matter.

Abstract

The interaction between pions and nucleons plays a crucial role in hadron physics. It represents a fundamental building block of the low-energy QCD dynamics and is subject to several resonance excitations. This work studies the p-$π^{\pm}$ dynamics using femtoscopic correlations in high-multiplicity pp collisions at $\sqrt{s} = 13$ TeV measured by ALICE at the LHC. As the final-state interaction between protons and pions is well constrained by scattering experiments and the study of pionic hydrogen, the results give access to information on the particle-emitting source in pp collisions using the femtoscopy methods. The scaling of the source size of primordial protons and pions against their pair transverse mass is extracted. The results are compared with the source sizes studied with p$-$p, $\text{p--K}^+$, and $π^{\pm}$-$π^{\pm}$ pairs by ALICE in the same collision system and are found to be in agreement for the different particle pairs. This reinforces recent findings by ALICE of a common emission source for all hadron-pairs in pp collisions at LHC energies. Furthermore, the p-p-$π^{\pm}$ systems are studied using three-particle femtoscopy in pp collisions at $\sqrt{s} = 13$ TeV. The presence of three-body effects is analyzed utilizing the cumulant expansion method. In this formalism, the known two-body interactions are subtracted in order to isolate the three-body effects. For both, p-p-$π^{+}$ and p-p-$π^{-}$, a non-zero cumulant is found, indicating effects beyond pairwise interactions. These results give information on the coupling of the pion to multiple nucleons.

Investigating the p-$π^{\pm}$ and p-p-$π^{\pm}$ dynamics with femtoscopy in pp collisions at $\sqrt{s} = 13$ TeV

TL;DR

This study uses femtoscopy to probe pion–nucleon dynamics in high-multiplicity pp collisions at TeV. By analyzing two-particle -- correlations with a Resonance Source Model and the CATS framework, the authors extract a common, -dependent particle-emitting source across hadron pairs and characterize resonance modifications, notably for . They also develop a three-body cumulant formalism to isolate genuine three-body effects in ---- systems, finding nonzero cumulants that indicate beyond-pairwise interactions and coupling of the pion to multiple nucleons. The results have implications for transport models of small collision systems and for understanding multi-nucleon pion dynamics relevant to QCD at low energy and in dense baryonic matter.

Abstract

The interaction between pions and nucleons plays a crucial role in hadron physics. It represents a fundamental building block of the low-energy QCD dynamics and is subject to several resonance excitations. This work studies the p- dynamics using femtoscopic correlations in high-multiplicity pp collisions at TeV measured by ALICE at the LHC. As the final-state interaction between protons and pions is well constrained by scattering experiments and the study of pionic hydrogen, the results give access to information on the particle-emitting source in pp collisions using the femtoscopy methods. The scaling of the source size of primordial protons and pions against their pair transverse mass is extracted. The results are compared with the source sizes studied with pp, , and - pairs by ALICE in the same collision system and are found to be in agreement for the different particle pairs. This reinforces recent findings by ALICE of a common emission source for all hadron-pairs in pp collisions at LHC energies. Furthermore, the p-p- systems are studied using three-particle femtoscopy in pp collisions at TeV. The presence of three-body effects is analyzed utilizing the cumulant expansion method. In this formalism, the known two-body interactions are subtracted in order to isolate the three-body effects. For both, p-p- and p-p-, a non-zero cumulant is found, indicating effects beyond pairwise interactions. These results give information on the coupling of the pion to multiple nucleons.

Paper Structure

This paper contains 14 sections, 18 equations, 15 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Event and track selection
  3. Study of the proton--pion system
  4. Two-particle correlation function
  5. Modeling of two-particle correlation function of proton--pion
  6. Results
  7. Analysis of proton--proton--pion three-particle system
  8. Three-particle correlation function
  9. Results
  10. Summary
  11. Two-Particle Correlation Functions
  12. Details on the modeling of the test correlation functions
  13. Two-Particle Momentum Smearing
  14. The ALICE Collaboration

Figures (15)

  • Figure 1: Upper panel: The experimental correlation function of $\text{p--}\uppi^+$ pairs (black) as a function of the pair relative momentum $k^*$ in several intervals of the pair $m_\text{T}$: (a) $[0.54, 0.75)\text{ GeV}/c^2$, (b) $[0.75, 0.95)\text{ GeV}/c^2$, (c) $[0.95, 1.2)\text{ GeV}/c^2$, (d) $[1.2, 1.5)\text{ GeV}/c^2$, (e) $[1.5, 2.0)\text{ GeV}/c^2$, and (f) $[2.0, 2.5)\text{ GeV}/c^2$. The lines (boxes) show the statistical (systematic) uncertainties of the experimental data. The red bands show the fit result according to Eq. \ref{['Eq. ProtonPion Exp Fit']}. The single contributions of correlated background (green), final-state interaction (blue), and $\Delta^{++}(1232)$ (yellow) are presented by the respective colored bands. The width of the bands represents the uncertainty from the fitting procedure. Lower panel: point-by-point $n_\sigma$ between the overall fit and the experimental data.
  • Figure 2: Results for the (a) $\Delta^{++}$ spectral temperature and (b) width as a function of the pair transverse mass $m_\text{T}$ for the $\Delta^{++}(1232)$ with the statistical (lines) and systematic (boxes) uncertainties.
  • Figure 3: Extracted source size $r_\text{core}$ of primordial $\text{p--}\uppi^+$ pairs as a function of the pair transverse mass. The results are compared with the $r_\text{core}$ extracted from p--p pairs ppSourceErratum as well as $\uppi^\pm$--$\uppi^\pm$ and $\text{p--}\text{K}^+$ pairs ALICE:2023sjd in HM pp collisions at $\sqrt{s}=13$ TeV by ALICE. The lines (boxes) show the statistical (systematic) uncertainties. The gray band represents the extrapolated scaling of p--p pairs ppSourceErratum.
  • Figure 4: Upper panel: The $\text{p--}\uppi^-$ experimental correlation function is shown in black as a function of the pair relative momentum $k^*$ for several intervals of the pair $m_\text{T}$: (a) $[0.54, 0.75)\text{ GeV}/c^2$, (b) $[0.75, 0.95)\text{ GeV}/c^2$, (c) $[0.95, 1.2)\text{ GeV}/c^2$, (d) $[1.2, 1.5)\text{ GeV}/c^2$, (e) $[1.5, 2.0)\text{ GeV}/c^2$, and (f) $[2.0, 2.5)\text{ GeV}/c^2$. The lines and boxes show the statistical and systematic uncertainties of the experimental data, respectively. The fit results according to Eq. \ref{['Eq. ProtonAntiPion Exp Fit']} are depicted by the red bands. Contributions of correlated background, final-state interaction, and $\Delta^{0}(1232)$ are shown as the green, blue, and yellow bands, respectively. The width of the bands represents the uncertainty from the fitting procedure. Lower panel: point-by-point $n_\sigma$ between the overall fit and the experimental data.
  • Figure 5: Extracted (a) $\Delta^0$ spectral temperature and (b) width as a function of the pair transverse mass $m_\text{T}$ for the $\Delta^{0}(1232)$. The lines show the statistical uncertainties, while the boxes represent the systematic uncertainties.
  • ...and 10 more figures