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 $\He3+p \to \He4 + e^+ + \nu_e$. 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 -- ($\hat d^R$) -- 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 $\hat d^R$ term, $\mu-d$ capture rate, and $\nu-d$ scattering cross section.