An Effective Field Theory and Bayesian Analysis of ³He-alpha scattering

We consider ³He-alpha scattering in an Effective Field Theory (EFT) built on the separation between the inherent scales in the ⁷Be and helium systems.  We develop the EFT up to next-to-next-to-leading order and construct a statistical model for the uncertainty due to truncation of the theory at that order~\cite{Furnstahl:2015}. We use the resulting formalism to analyze data for recent low energy measurements (0.7-4.0 MeV lab energy) of elastic ³He-alpha scattering obtained using the SONIK gas target at TRIUMF~\cite{Paneruthesis}.

We employ Bayesian statistics and MCMC sampling to analyze both these and older data. Constraints on the ⁷Be Asymptotic Normalization Coefficients (ANCs) from analysis of ³He(alpha,γ) are included via Bayesian priors. We find that in order to obtain the correct sign of the spin-orbit splitting in p-waves it is crucial to include data on the polarization observable A_y in the analysis. We obtain results for  scattering parameters for terms  up to O(k⁴) in the effective-range expansion of s- and p-waves  in this system. Results for the these parameters---including the s-wave ³He-alpha scattering length---will be presented.