We summarize the recent effective field theory (EFT) studies of low-energy electroweak reactions of astrophysical interest, relevant to big-bang nucleosynthesis. The zero energy astrophysical S(0) factor for the thermal proton radiative capture by deuteron is calculated with pionless EFT. The astrophysical S(0) factor is accurately determined to be S(0) = 0.243 eVb up to the leading order (LO). At zero energies, magnetic transition M1 gives the dominant contribution. The M1 amplitude is calculated up to the LO. A good, quantitative agreement between theoretical and experimental results is found for all observables. The demonstrations of cutoff independent calculation have also been presented.
