The production of light (anti-)nuclei in high-energy collisions has long posed an apparent paradox: how can loosely-bound systems such as the anti-deuteron with a binding energy of only 2.23 MeV be formed and survive in the extreme hot and dense hadronic environment emerging from proton-proton (pp) and heavy-ion collisions, where characteristic thermal energies exceed 100 MeV? A new femtoscopy analysis published on Nature [1] by the ALICE Collaboration at the Large Hadron Collider (LHC) delivers the clearest answer to date. By measuring pion-deuteron momentum correlations in high-multiplicity pp collisions at TeV, the experiment demonstrated that most (anti-)deuterons are not produced directly at hadronization, but instead originating from meson-catalyzed reactions [2] following the decay of short-lived baryonic resonances, most notably the Δ(1232). This result provides long-sought microscopic insight into how fragile (anti-)nuclei emerge in ultra-relativistic hadronic environments, from collider events to cosmic rays.

Light nuclei and antinuclei, such as deuterons (d), tritons (³H), helium-3 (³He), helium-4 (⁴He), and their antiparticles, have been measured with increasing precision across collision systems and energies, from heavy-ion collisions to pp collisions [3-11]. This phenomenon, known as ‘little bang nucleosynthesis’ [2, 12] or ‘snowballs in hell’ [13, 14], connects directly to fundamental questions about matter-antimatter symmetry [15], phase transitions in quantum chromodynamics (QCD) [16, 17], and dark-matter searches [18, 19].

While their integrated yields are often described surprisingly well by the statistical hadronization model of quark-gluon plasma [20], their microscopic formation remains far from settled [21-24]. The deuteron’s binding energy is two orders of magnitude smaller than the temperature of hadronic matter produced in pp or Pb+Pb collisions. In such an environment, “direct” emission from the hadronization of quark-gluon plasma or the chemical freeze-out hypersurface appears implausible, and any loosely-bound system produced early would almost certainly be destroyed by subsequent hadronic rescatterings. Final-state coalescence models offer a different scenario in which nucleons close in phase space can merge into bound states at the very late kinetic freeze-out [25-28]. In the microscopic transport approach, it has been shown that pion-catalyzed reactions (e.g. , ) do not significantly change the deuteron production in central Pb+Pb and Au+Au collisions [29], but reduce the triton and Helium-3 yield by approximately a factor of 1.8 [2]. For the forward pion-catalyzed reaction , it can be viewed as a two-step process of πN → Δ and ΔN → πd, and a deuteron is produced via nucleon fusion following a N decay. The decay pion is kinematically correlated with the nucleon that subsequently participates in forming the deuteron. This correlation manifests as a distinct Δ resonant structure in the pion-deuteron correlation function in momentum space, as the reaction rate reaches maximum at relative momenta reflecting the Δ mass and decay kinematics [2].

The ALICE measurement exploits this signature through pion-deuteron (π-d) femtoscopy [1]. Femtoscopy analyzes momentum correlations at relative distances down to order of 1 fm (10^-15 m) [30-33] and has become a precision tool for studying strong interactions [34-37] and exotic hadrons [38]. The new ALICE data reveal a pronounced resonance peak associated with Δ decay, providing direct evidence that (anti-)deuterons form predominantly through resonance-fed secondary processes.

The key experimental observable is the momentum correlation function,(1)where k^* is the momentum of either particle in the pair rest frame. denotes the distribution of relative momenta for particle pairs from the same event, while provides an uncorrelated reference constructed by combining particles from different events. The factor normalizes the correlation function so that C(k^*) approaches unity at large k^*.

Intriguing correlations can arise from final-state strong and Coulomb interactions [39, 40], quantum statistics [39], or resonance decays [40]. In general, attractive interactions enhance C(k^*) at low k^*, whereas repulsive interactions suppress it.

ALICE measures π⁺-d and correlations in high-multiplicity pp collisions at TeV with excellent particle identification, achieving purities of 99–100%. The correlation functions are shown in Fig. 1 exhibit a prominent peak associated with Δ resonance decay. The data are then modeled using(2)where ϵ(k^*) accounts for momentum resolution, B(k^*) for residual backgrounds, and λ_gen for the fraction of genuine pairs. The genuine correlation function includes Coulomb and strong interactions plus the Δ contribution, and is computed via CATS [41] assuming an effective source radius fm.

Fig. 1Full-screen View

(Color online) Measured π^--d (upper panel) and π⁺-d (lower panel) correlation functions compared with model fits. The brown cross-hatched bands show the contributions from the Δ resonance, the blue bands the Coulomb interaction, and the teal diagonally hatched bands the residual background. The magenta bands represent the total fit. Figure taken from Ref. [1]

Final-state Coulomb and strong interactions generate a monotonic enhancement (suppression) for π^- -d (π⁺-d) pairs at low relative momentum (k^* < 50 MeV/c), while the Δ resonance produces strong peaks around MeV/c in both correlation functions.

By integrating the Δ peak, ALICE finds that of detected deuterons contain a nucleon produced in a Δ decay. Accounting for all short-lived resonances yields a total resonance-fed fraction of . Thus, meson-catalyzed fusion with resonance-decay nucleons overwhelmingly dominates (anti-)deuteron formation at the LHC.

This conclusion is reinforced by a recent theoretical study [42] that reproduces the observed resonant structure in both pion-proton (π-p) and pion-deuteron (π-d) correlation functions by solving relativistic kinetic equations for on an event-by-event basis. The model–data comparison further indicates a downward in-medium shift of the Δ(1232) mass by approximately 70 MeV/c² [1]. Such a reduction, from GeV/c² to 1.162 GeV/c² may reflect strong in-medium modifications, possibly linked to partial chiral-symmetry restoration [43]. Traditional coalescence models reproduce only about half of the observed peak, and statistical hadronization fails to generate any resonance structure, highlighting the unique discriminatory power of pion-nucleus femtoscopy for unraveling (anti-)nuclei production mechanisms.

In summary, ALICE has uncovered the dominant mechanism of (anti-)deuteron formation at the LHC using the novel technique of pion-nucleus correlation femtoscopy. The measurement provides the first compelling evidence that most (anti-)deuterons originate from resonance decays followed by pion-catalyzed fusion rather than direct emission. This finding resolves a long-standing puzzle in light-nucleus production and establishes a clear microscopic pathway for (anti-)nucleosynthesis in high-energy collisions.

A complete understanding of these results calls for further studies on the in-medium properties of light nuclei and advances in relativistic kinetic theory that incorporate multi-body correlations and off-shell quantum effects at high temperatures [44, 45]. Extending femtoscopy measurements to heavier (hyper-)nuclei will open new opportunities to probe their formation mechanisms and may even help constrain the production of exotic hadronic states [38, 46-48] in hot and dense matter.