EFT for electroweak processes of light nuclei

Recently we succeeded to make a reliable EFT prediction in a totally parameter-free manner for the $S$ factors for the solar $pp$ and $hep$ processes, $p+p\to d+e^{+}+{\nu }_e$ and $\text{He}3+p\to \text{He}4+e^{+}+{\nu }_e$. The strategy used in there is to embed a highly sophisticated standard nuclear physics approach (SNPA) exploiting realistic potentials into an EFT framework, that we refer to as EFT*. Up to next-next-to-leading order in chiral expansion, it turnes out that there is effectively only one counter-term relevant to this process, the coefficient of which – (${\widehat{d}}^R$) – has been renormalized to reproduce the experimental value of the tritium-beta decay. Our study has also led to {\em very} accurate EFT calculations on two-body weak processes that also receive contributions from the ${\widehat{d}}^R$ term, $\mu -d$ capture rate, and $\nu -d$ scattering cross section.