  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.
