Interactions of the deuteron with a hadronic medium

TL;DR

This work analyzes deuteron interactions with the hadronic medium formed in high-energy nuclear collisions by treating the deuteron as a weakly bound molecule and applying a quasi-free description of $d\\pi$ processes. It constructs $N\\pi$ amplitudes from a hybrid framework blending a chiral perturbation theory background with Breit–Wigner resonances, then computes vacuum and thermally averaged cross sections that feed a kinetic-rate equation for $N_d$ under Bjorken-like expansion, with SHM and COM initial conditions. The main finding is that the final deuteron yield $N_d(\\tau_F) \\approx 0.015$ is largely independent of the initial production mechanism, implying strong memory loss of the initial state due to in-medium hadronic interactions. This suggests the late-stage hadronic environment sets the observable deuteron abundance, making it a robust probe of hadronic-phase conditions in heavy-ion collisions.

Abstract

We investigate the interactions of the deuteron with light mesons during the hadronic phase in heavy-ion collisions. We treat the deuteron as a weakly bound state and employ the quasi-free approximation to describe the $dπ$ interaction. The underlying elementary $Nπ$ amplitudes are described by a hybrid effective model, combining the non-resonant background from chiral perturbation theory with resonant contributions via Breit-Wigner parameterizations. These amplitudes are used to calculate the vacuum and thermally-averaged cross-sections for deuteron dissociation and production, namely, $d + π\rightarrow N + N' + π$ and the corresponding inverse reaction. We then use these cross sections in a rate equation to estimate the time evolution of the deuteron multiplicity. For the initial conditions we consider two models: the statistical hadronization model and the coalescence model, where the deuteron is treated as a hadronic molecule. Our findings suggest that the final deuteron yield does not retain a memory of its initial production mechanism.

Figures (6)

• Figure 1: Tree-level diagrams contributing to the $d\pi$ reactions, according to the quasi-free approximation approach quase_livre, in which they are considered as the sum over the processes where the pion scatters from one of the constituent nucleons, with the complementary nucleon acting as a spectator in each case. Diagrams (a) and (b) stand for processes involving the $s$-channel $N^{(\prime)}\pi \to N^{(\prime)}\pi$ scattering, (c) and (d) for processes involving the $u$-channel $N^{(\prime)}\pi \to N^{(\prime)}\pi$ scattering, and (e) and (f) for processes involving the contact-type $N^{(\prime)}\pi \to N^{(\prime)}\pi$ scattering.
• Figure 2: Experimental cross sections for the $p\pi^+$ elastic, $p\pi^+$ total and $d\pi^+$ total scattering processes extracted from Ref ParticleDataGroup:2024cfk.
• Figure 3: Cross section of the process $p\pi^+ \to p\pi^+$ as a function of the CM energy $\sqrt{s}$.
• Figure 4: Vacuum cross section of the process $d\pi^+ \to NN^\prime\pi^+$, and the total $d\pi \to NN^\prime\pi$ as a function of $\sqrt{s}$ to be used in the thermally-averaged cross section.
• Figure 5: Thermally-averaged cross section for the process $d\pi \to NN^\prime\pi$.