We review the results of the most recent calculation for the astrophysical S-factor of the weak proton-proton capture reaction, over a range for the center-of-mass relative energy of 0-100 keV. The so-called chiral effective field theory approach is used, where the chiral twonucleon potential is derived up to next-to-next-to-next-to leading order and is augmented by the full electromagnetic interaction. The low-energy constants (LEC's) entering the weak current operators are fixed so as to reproduce the A = 3 binding energies and magnetic moments, and the Gamow-Teller matrix element in tritium β-decay. Contributions from S and P partial waves in the incoming two-proton channel are retained. The S-factor at zero energy is found to be ~ 1% larger than the value reported in the literature, mostly due to the P-waves contributions.
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