Toward universal coalescence models for antideuteron production

Abstract

Cosmic-ray (CR) antinuclei, especially antideuteron $\overline{\rm D}$ and antihelium-3 nuclei ${}^3\overline{\rm He}$, are among the most promising messengers for indirect dark matter (DM) searches. This is because secondary production in CR interactions with the interstellar medium is strongly suppressed at kinetic energies $K\simeq (0.1 - 1)$ GeV/$n$, typically one to two orders of magnitude below fluxes expected in standard DM scenarios. From the theoretical side, the formation of $\overline{\rm D}$ and ${}^3\overline{\rm He}$ is governed by coalescence, whose dynamics cannot yet be reliably derived from first principles. Phenomenological approaches therefore introduce effective coalescence parameters, possibly dependent on collision energy and production environment (hadronic versus electroweak). In this work we show, for the first time, that a common set of physically motivated coalescence models can simultaneously reproduce collider data in two qualitatively different regimes: ALICE measurements of (anti)deuteron production in $pp$ collisions at $\sqrt{s}=(0.9 - 13)$ TeV and the ALEPH $\overline{\rm D}$ multiplicity in hadronic $Z$ decays at $\sqrt{s}=m_Z$. We test both simple event-by-event prescriptions based on a relative-momentum cutoff, finding a preferred coalescence scale $p_{\rm coal}\simeq 0.2$ GeV, and quantum-mechanical models in the Wigner formalism. In the latter, a Gaussian bound-state wavefunction gives a best-fit momentum width, corresponding to $δ\simeq 1.7$ fm, while a parameter-free implementation using the Argonne $v_{18}$ wavefunction (constrained by proton-neutron scattering data) agrees with ALICE spectra at the $\sim 25\%$ level. Overall, our results support an approximately universal coalescence description across energies and production environments, strengthening the theoretical basis for interpreting upcoming CR antinuclei searches.

Figures (11)

• Figure 1: Antiproton multiplicity $n_{\bar{p}}=N_{\bar{p}}/N_{\rm ev}$. Antiproton multiplicity in $pp$ collisions as a function of the (equivalent fixed-target) proton beam energy $E_p^{\rm LAB}$, compiled from Refs. Antinucci:1972ibNA61SHINE:2017fneNA49:2009brxPHENIX:2011rvuALICE:2011gmoALICE:2015ial. Black dots show the experimental measurements. The blue dashed curve is the prediction obtained with our energy-dependent PYTHIA 8.315 tune (see text), while the green dashed curve corresponds to the default PYTHIA 8.315 configuration.
• Figure 2: Validation of our PYTHIA tune with antiproton spectra. Top:$d^2n/(dp_T\,dy)$ in fixed-target $pp$ collisions at $\sqrt{s}=7.74$ GeV (NA61) for several rapidity bins $y$; spectra are rescaled by the factors indicated in the panel for readability NA61SHINE:2017fne. Middle: invariant cross section $f=(1/\pi)\,d^3\sigma/(dp_T^2\,dx_F)$ in fixed-target $pp$ at $\sqrt{s}=17.3$ GeV (NA49) for several $x_F$ bins, again rescaled by the indicated powers of ten NA49:2009brx. Bottom: midrapidity ($|y|<0.5$) $p_T$ spectra in $pp$ collisions measured by ALICE at $\sqrt{s}=0.9$, $7$, and $13$ TeV; the $7$ and $13$ TeV datasets are multiplied by factors $2$ and $4$, respectively, as indicated in the legend ALICE:2011gmoALICE:2015ialALICE:2020jsh. In all panels, the points denote data and solid curves the predictions from our tuned PYTHIA configuration.
• Figure 3: Normalized distribution of the $\bar{p}$--$\bar{n}$ pair separation $\Delta r$, in the pair reference frame, for antinucleons generated with our tuned PYTHIA setup in $pp$ collisions at $\sqrt{s}=7$ TeV. Contributions are shown separately for pairs in which both antinucleons originate from resonance decays (magenta), both originate from hadronization (blue), one originates from hadronization and the other from a resonance decay (orange), and for the inclusive sample of all $\bar{p}$--$\bar{n}$ pairs (yellow).
• Figure 4: Deuteron wavefunctions $\varphi_{\rm D}(r)$ used in the Wigner-based coalescence models: Gaussian (blue) and Argonne $v_{18}$Wiringa:1994wb S-wave and D-wave components (solid and dashed orange, respectively). The step-like profile corresponding to the $\Delta p+\Delta r$ model is also shown (green) for illustrative purposes, although it is not a Wigner-based prescription.
• Figure 5: Reduced $\chi^{2}$ profiles profiles as a function of $\Delta p_{\rm coal}\equiv p_{\rm coal}-p_{\rm coal}^{\rm ALEPH}$, where $p_{\rm coal}^{\rm ALEPH}$ is the best-fit for the coalescence parameter found by fitting ALEPH data as reported in Ref. DiMauro:2024kml, while $p_{\rm coal}$ is the best-fit obtained by fitting ALICE deuteron and antideuteron spectra measured at $\sqrt{s} = 0.9, 2.76, 7$, and $13$ TeV. The squared markers indicate the $\chi^2$ obtained when simulating the $D$ and $\overline{D}$ data at specific values of $p_{\rm{coal}}$. The curves represent the interpolations of the single $\chi^2$ points. We show the results for the following models: $\Delta p$ (dotted purple), $\Delta p+\Delta r$ (dashed magenta), and Gaussian (dash-dotted orange). In the Gaussian model we rescaled the $\delta$ parameter by a factor $0.11\,\mathrm{GeV}/1.80\,\mathrm{fm}$. For each model, the vertical solid line and the correspondingly colored shaded band denote the extracted best-fit value and its $1\sigma$ interval, respectively. Additionally, the blue shaded band represents the $1\sigma$ interval obtained from the ALEPH fit for the $\Delta p$ case, plotted for visual comparison.