ToMCCA-3: A realistic 3-body coalescence model

Abstract

The formation of light nuclei in high-energy collisions provides valuable insights into the underlying dynamics of the strong interaction and the structure of the particle-emitting source. Understanding this process is crucial not only for nuclear physics but also for astrophysical studies, where the production of rare antinuclei could serve as a probe for new physics. This work presents a three-body coalescence model based on the Wigner function formalism, offering a refined description of light-nucleus production. By incorporating realistic two- and three-body nuclear interaction potentials constrained by modern scattering and femtoscopic correlation data, our approach improves on traditional coalescence models. The framework is validated using event generators applied to proton-proton collisions at $\sqrt{s}=13$ TeV to predict the momentum spectra of light (anti) nuclear nuclei with mass number $A=3$, which are then compared with the experimental data from ALICE. Our results demonstrate the sensitivity of light nucleus yields to the choice of nuclear wave functions, emphasizing the importance of an accurate description of the coalescence process. This model lays the foundation for the extension of coalescence studies of $A=3$ light nuclei to a wider range of collision systems and energies.

Figures (9)

• Figure 1: (left) The ${}^3$He $p_\mathrm{T}$ spectra measured by ALICE ALICENuclei13TeV in pp collisions at $\sqrt{s}=13$ TeV in four intervals of multiplicity. The corresponding predictions for ToMCCA are shown as the colored bands. The width of the central line indicates the statistical uncertainty, while the shaded band shows the systematic uncertainties of $\pm17\%$ (see Sec. \ref{['sec:Uncertainties']}). (right) The ${}^3$He/p (${}^3$H/p) ratio as a function of $\langle\mathrm{d}\xspace N_\mathrm{ch}/\mathrm{d}\xspace\eta\rangle_{|\eta|<0.5}$ and comparison to the ALICE measurements ALICENuclei13TeVALICE:2021ovi. Different assumptions for the wave function are tested, only 2-body forces based on the $\text{Argonne }v_{18}$ potential, 2-body+3-body $\text{Argonne }v_{18}$+UIX wave function for ${}^3$He and ${}^3$H, as well as wave function based on the 2-body Minnesota potential. The predictions and the ALICE measurement for 13 TeV minimum bias collisions are shown as the squares and circles, magnified in the inlet. For the sake of visibility the points are shifted on the x-axis.
• Figure 2: (left) ${}^3$H/${}^3$He ratio as a function of $p_\mathrm{T}$ predicted by ToMCCA for high multiplicity (HM, $\langle\mathrm{d}\xspace N_\mathrm{ch}/\mathrm{d}\xspace\eta\rangle_{|\eta|<0.5}$=31.5) and minimum bias (MB, $\langle\mathrm{d}\xspace N_\mathrm{ch}/\mathrm{d}\xspace\eta\rangle_{|\eta|<0.5}$=6.9) collisions, using two different assumptions on the wave function (AV18+UIX and Minnesota). They are compared to the measurement by ALICE in HM pp collisions at $\sqrt{s}=13$ TeV. All predictions by ToMCCA are compatible with unity within 5% and with the measurement within two standard deviations. (right) Ratio of the ToMCCA predictions using several wave function assumptions to the ${}^3\text{He}\xspace$ one using AV18+UIX.
• Figure 3: (left) The ${}^3_\Lambda$H $p_\mathrm{T}$ spectra using the Congleton wave function predicted by ToMCCA for various multiplicities from $\langle\mathrm{d}\xspace N_\mathrm{ch}/\mathrm{d}\xspace\eta\rangle_{|\eta|<0.5}$=5.6 to $\langle\mathrm{d}\xspace N_\mathrm{ch}/\mathrm{d}\xspace\eta\rangle_{|\eta|<0.5}$=45.9 as well as minimum bias collisions. No experimental data is available for comparison at this time. The light shaded bands indicate the model uncertainties (see Sec. \ref{['sec:Uncertainties']}), the dark shaded bands represent statistical uncertainties. (right) Ratio of ${}^3_\Lambda$H/${}^3$He as a function of $p_\mathrm{T}$ for various multiplicity classes as well as minimum bias collisions. as predicted by ToMCCA using the Congleton wave function for ${}^3_\Lambda$H and $\text{Argonne }v_{18}$+UIX for ${}^3$He. The shaded bands indicate the combined statistical uncertainties. No model uncertainties are estimated for these ratios.
• Figure 4: (left) ${}^3_\Lambda$H/$\Lambda$ ratio predicted by ToMCCA using the Congleton wave function are shown as the purple band. The dashed and dot-dashed lines are predictions from Sun2019 using different assumptions for a Gaussian wave function. (right) The purple band shows the predictions of the $S_3$ parameter by ToMCCA using the Congleton wave function. The dashed and dot-dashed lines are the same model as on the left Sun2019.
• Figure 5: (left) Comparison of ToMCCA with ALICE deuteron ($(d+\overline{d})/2$)-spectra using the new parameterization of the source and the EPOS phase space. (right) Comparison of $B_2$ predictions by ToMCCA with the measurements of ALICE for pp collisions at $\sqrt{s}=5$ TeV. The colored bands indicate the previously determined 4.6% uncertainty on the predicted deuteron spectra, stemming from the experimental uncertainty of the proton spectra.