E?ective Field Theory analysis of 3He-? scattering data

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