Precision calculation of ${}^3$He$(\alpha ,\gamma {)}^7$Be for solar physics

We calculate the cross section for radiative capture ${}^3$He$(\alpha ,\gamma {)}^7$Be at next-to-next-to-leading order (NNLO). At this order of perturbation, momentum dependent two-body currents make their first appearance. We provide a model-independent construction of these currents from gauge and Galilean invariance, where the general framework for constructing higher-order two-body currents in low-energy effective field theories becomes evident. The ${}^3$He$(\alpha ,\gamma {)}^7$Be astrophysical S-factor $S_{34}(0)=0.564_{-0.015}^{+0.17}$ keV b is obtained from a Bayesian analysis at NNLO, with an additional nominal theoretical uncertainty $\pm 0.017$ keV b of 3%.