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The astrophysical S-factor for proton-proton weak capture is calculated inchiral effective field theory over the center-of-mass relative-energy range0--100 keV. The chiral two-nucleon potential derived up tonext-to-next-to-next-to leading order is augmented by the full electromagneticinteraction including, beyond Coulomb, two-photon and vacuum-polarizationcorrections. The low-energy constants (LEC's) entering the weak currentoperators are fixed so as to reproduce the A=3 binding energies and magneticmoments, and the Gamow-Teller matrix element in tritium beta decay.Contributions from S and P partial waves in the incoming two-proton channel areretained. The S-factor at zero energy is found to be S(0)=(4.030 +/- 0.006) x10^{-23} MeV fm^2, with a P-wave contribution of 0.020 x 10^{-23} MeV fm^2. Thetheoretical uncertainty is due to the fitting procedure of the LEC's and to thecutoff dependence.

The proton-proton weak capture in chiral effective field theory