Measurement of the p$-Σ^+$ correlation function in pp collisions at $\sqrt{\textit{s}}=13$ TeV

TL;DR

This work reports the first measurement of the femtoscopic $p$-$\Sigma^{+}$ correlation function in high-multiplicity $pp$ collisions at $\sqrt{s}=13$ TeV with the ALICE detector, employing a missing-mass reconstruction for $\Sigma^{+}$ and machine-learning–assisted PID to achieve high reconstruction efficiency and purity. The correlation function is analyzed within the Koonin--Pratt formalism using a data-driven Gaussian-core source with $R\approx 0.98$ fm and full two-particle wave functions that include Coulomb and both singlet and triplet $N\Sigma$ interactions, smeared to account for momentum resolution. By comparing the measured $C(k^*)$ to several $p$-$\Sigma^{+}$ potentials, the study disfavors strong triplet repulsion and extracts scattering lengths $a_s \approx -3.0$ fm and $a_t \approx +0.25$ fm, with modest model dependence. These results provide the most stringent constraints to date on the $N\Sigma$ interaction and demonstrate ALICE's capability to perform precision femtoscopy in the strange sector, informing neutron-star matter studies and guiding future Run 3–4 measurements.

Abstract

In this letter, the first measurement of the femtoscopic correlation of protons and $Σ^+$ hyperons is presented and used to study the p$-Σ^+$ interaction. The measurement is performed with the ALICE detector in high-multiplicity triggered pp collisions at $\sqrt{s} = 13$ TeV. The $Σ^+$ hyperons are reconstructed using a missing-mass approach in the decay channel to $\textrm{p} + π^0$ with $π^0\rightarrowγγ$, while both $Σ^+$ and protons are identified using a machine learning approach. These techniques result in a high reconstruction efficiency and purity, which allows the measurement of the p$-Σ^+$ correlation function for the first time. Thanks to the high significance achieved in the p$-Σ^+$ correlation signal, it is possible to discriminate between the predictions of different models of the N$-Σ$ interaction and to accomplish a first determination of the p$-Σ^+$ scattering parameters.

Figures (4)

• Figure 1: Left panel: Invariant-mass distribution of $\Sigma^{+}$ candidates in 0.0 $< p_{\rm T} <$ 4.0 $\rm GeV/\it{c}$ (black markers) with MC template fits: signal (blue markers), background (green markers), and total (red markers). The used missing-mass reconstruction method leads to a non-Gaussian shape of the distribution. The ratio of the data and the MC total distribution is shown in the lower panel. Right panel: Comparison of the $p_{\rm T}$ spectrum of $\Sigma^{+}$ using the reconstruction method introduced in this paper with the corresponding spectrum measured in Ref. ALICE:2025hqt. The ratio of the spectra is shown in the lower panel. The spectra are in good agreement, indicating that the reconstruction method and the purity determination work well over the full $p_{\rm T}$ range.
• Figure 2: p--$\Sigma^+$ correlation function in high-multiplicity triggered pp collisions at $\sqrt{s}=13$ TeV. The statistical uncertainties are drawn as bars and the systematic ones as boxes. The data points are shifted to the center of gravity of the mixed-event distribution. The data points show the measurement, containing both the genuine contribution as well as the contributions from feed-down and misidentification. The model calculations are weighted by the genuine $\lambda$ parameter and smeared by the momentum resolution to allow a comparison with data. Left: Correlation function with several model calculations using the full wave functions and the effective Gaussian parametrization of the source. The uncertainty bands arise from the uncertainty of the source size. Right: Decomposition of the theoretical correlation functions into the singlet (dashed lines) and triplet (dash-dotted lines) contributions. The contributions are multiplied by their statistical weights and added to the Coulomb-only function scaled by 1 – ji, which illustrates the influence of the given contribution on the total correlation function (solid lines).
• Figure 3: Exclusion plots obtained for the Reid-like A (left panel) and Gaussian (1.8 fm) (right panel) potentials as described in the text. The agreement with the data as a function of the singlet and triplet scattering lengths in multiples of the standard deviation is shown together with the model predictions given in Tab. \ref{['Modelparams']}.
• Figure A.1: p--$\Sigma^+$ correlation function in high-multiplicity triggered pp collisions at $\sqrt{s}=13$ TeV with several model calculations using the full wave functions and the effective Gaussian parametrization of the source. The blue and magenta regions correspond to all parameter sets within the 1$\sigma$ contours of Fig \ref{['excluplot']}. The Jülich '04 meson-exchange model, which resides within the 1$\sigma$ contours, is shown as a black line. For comparison, the SMS NLO (V2) is also shown as a green line.