Effective Field Theory analysis of ${}^3$He-$\alpha$ scattering data

TL;DR

This paper applies an Effective Field Theory to analyze low-energy ${}^3$He-$ alpha$ scattering data, achieving a detailed understanding of scattering parameters and their relation to nuclear reactions.

Contribution

It develops a hierarchical EFT framework up to NNLO for ${}^3$He-$ alpha$ scattering and uses Bayesian methods to constrain effective-range parameters with experimental data.

Findings

Effective-range parameters are well constrained up to $O(p^4)$.

Including analyzing power data is crucial for determining p-wave splitting.

Results are consistent with recent EFT analyses of ${}^3$He($ alpha$,$ abla$)${}^7$Be capture reactions.

Abstract

We treat low-energy $^3$He-$\alpha$ elastic scattering in an Effective Field Theory (EFT) that exploits the separation of scales in this reaction. We compute the amplitude up to Next-to-Next-to-Leading Order (NNLO), developing a hierarchy of the effective-range parameters that contribute at various orders. We use the resulting formalism to analyze data for recent measurements at center-of-mass energies of 0.38-3.12 MeV using the SONIK gas target at TRIUMF as well as older data in this energy regime. We employ a likelihood function that incorporates the theoretical uncertainty due to truncation of the EFT and use Markov Chain Monte Carlo sampling to obtain the resulting posterior probability distribution. We find that the inclusion of a small amount of data on the analysing power $A_y$ is crucial to determine the sign of the p-wave splitting in such an analysis. The combination of $A_y$ and SONIK data constrains all effective-range parameters up to $O(p^4)$ in both s- and p-waves quite well. The ANCs and s-wave scattering length are consistent with a recent EFT analysis of the capture reaction ${}^3$He($\alpha$,$\gamma$)${}^7$Be.