Short-distance production of three particles with large scattering length

TL;DR

This work analyzes short-distance production of three-particle states with a large scattering length using pionless EFT, solving Faddeev-type equations for point production in both three-boson and three-neutron systems. The three-boson sector exhibits near-threshold Efimov-like resonances in the production energy distribution, while the three-neutron sector shows no resonance and is governed by non-relativistic conformal (unitary) scaling, with $R(E) \propto E^{\Delta-5/2}$ and $\Delta$ values $4.66622$, $4.27272$, and $5.60498$ for $S$, $P$, and $D$ channels, respectively. Effective-range corrections are found to be small and largely perturbative, confirming conformal predictions in the accessible energy range. The results are in qualitative and quantitative agreement with JWKB analyses and available experimental data for the three-neutron continuum, and they motivate extending the formalism to four-neutron systems to interpret upcoming tetraneutron observations. Overall, the work clarifies how short-distance production encodes universal few-body dynamics near unitarity and the interplay between Efimov physics and conformal symmetry.

Abstract

The short-distance production of multi-particle states in high-energy nuclear reactions provides a unique way to study the low-energy properties of few-body systems. In particular, the production amplitude of multi-neutron systems is strongly constrained by an approximate conformal symmetry of the underlying theory. We calculate the full amplitude for the short-distance production of three particles with large scattering length in leading order pionless EFT, focusing on the cases of three neutrons and three spinless bosons. We investigate the signature of low-energy resonances and other correlations in the relative energy distributions. For the case of neutrons, we compare to the predictions from approximate conformal symmetry close to the unitary limit and calculate the range corrections up to next-to-next-to leading order.

Figures (11)

• Figure 1: Integral equation for the point-production amplitude of a particle-dimer system with total energy $E$ and total momentum $\mathbf{P}=0$. Single (double) lines denote particles (dimers), while $g_3$ is the strength of the point source that creates the particle-dimer pair.
• Figure 2: Fully symmetrized point-production amplitude $\bar{\Gamma}_l$ for three bosons. The bosons are produced with total energy $E$ in their center-of-mass, such that the total momentum is $\mathbf{P}=0$. The outgoing bosons are on-shell with the momenta given in the figure.
• Figure 3: Anti-symmetrized point-production amplitude $\bar{\Gamma}_l$ for three neutrons. The neutrons are produced with total energy $E$ in their center-of-mass, such that the total momentum is $\mathbf{P}=0$. The outgoing neutrons are on-shell with the momenta and spins indicated in the figure.
• Figure 4: The point-production distribution for the three-boson system with $\Lambda = 179.9$ fm$^{-1}$ and $a=-12.6$ fm, corresponding to $a_- / a = 1.5$, for different values of the artificial imaginary part of the energy $E$. The curves for the two smallest values are indistinguishable. In the limit $\Im E \rightarrow$ 0 the physical amplitude is obtained.
• Figure 5: The physical point-production distribution in the limit Im E $\to 0$ for different ratios of $a_-/a$. The parameter values are $\Lambda=179.9$ fm$^{-1}$ and $a=-15.12, -12.6, -10.8,$ and $-9.45$ fm.