Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order

TL;DR

This paper employs effective field theory to analyze three-boson systems at N$^2$LO, providing precise predictions for atom-dimer scattering and examining convergence patterns in Helium-4 atom models.

Contribution

It extends SREFT calculations to N$^2$LO for three-boson systems, offering improved accuracy and insights into convergence and scheme dependence.

Findings

N$^2$LO phase-shift predictions have <0.2% higher-order corrections.

Predictions for Helium-4 atom-dimer scattering are accurate below 0.2%.

Deep trimer binding energy shows poor convergence.

Abstract

We use an effective field theory for short-range forces (SREFT) to analyze systems of three identical bosons interacting via a two-body potential that generates a scattering length, $a$, which is large compared to the range of the interaction, $\ell$. The amplitude for the scattering of one boson off a bound state of the other two is computed to next-to-next-to-leading order (N$^2$LO) in the $\ell/a$ expansion. At this order, two pieces of three-body data are required as input in order to renormalize the amplitude (for fixed $a$). We apply our results to a model system of three Helium-4 atoms, which are assumed to interact via the TTY potential. We generate N$^2$LO predictions for atom-dimer scattering below the dimer breakup threshold using the bound-state energy of the shallow Helium-4 trimer and the atom-dimer scattering length as our two pieces of three-body input. Based on the convergence pattern of the SREFT expansion, as well as differences in the predictions of two renormalization schemes, we conclude that our N$^2$LO phase- shift predictions will receive higher-order corrections of $< 0.2$%. In contrast, the prediction of SREFT for the binding energy of the "deep" trimer of Helium-4 atoms displays poor convergence.