³He(α,γ)⁷Be in effective field theory at next-to-next-to-leading order.

Recently in May 2024, the third decadal evaluation of solar reactions Solar Fusion 3 was completed. A new recommendation for α-³He radiative capture S-factor was made based on a reanalysis of older and more current measurements. The S-factor recommendation at the Gamow peak was made based on a next-to-leading order(NLO) halo effective field theory (EFT) calculation. In this work we sharpen the prediction based on a new next-to-next-leading order(NNLO) calculation. The calculation involved higher order two-body currents. The new operators were constructed using the auxiliary dimerfield formulation. This simplified the renormalization of the non-perturbative short-ranged and Coulomb interactions. A Bayesian analysis shows that adding the higher order contributions does not necessarily improve the evidence for the fits. This is consistent with the observation that the NLO fit describes the featuresof the low-energy data accurately, and adding extra fit parameters are not necessary. The central value of the S-factor remains unchanged but now withsmaller theory errors as suggested in Solar Fusion 3.