A modern effective field theory is exploited to pin down accurately the flux S factors for the pp and hep processes in the Sun. The technique used is to combine the high accuracy established in few-nucleon systems of the "standard nuclear physics approach" (SNPA) and the systematic power counting of chiral perturbation theory (ChPT) into a consistent effective field theory framework. Using highly accurate wave functions obtained in the SNPA and working to N 3 LO in the chiral counting for the current, we make totally parameter-free and error-controlled predictions for the pp and hep processes in the Sun. We also discuss the convergence with respect to chiral expansion.