• astrophysical S-factor
• chiral effective field theory
• proton-proton weak capture

The astrophysical S-factor for the proton-proton weak capture is calculated within chiral effective field theory over a range for the center-of-mass relative energy of 3-30 keV. In order to describe the A=2 bound and scattering states, two families of nuclear potentials are considered: a set of non-local potentials expressed in momentum-space available from LO to N4LO, with three different values for the high-momentum cutoff 450,500,550 MeV, and a set of local potentials expressed in coordinate-space with two different combination of the energy range for the fitting nuclear dataset, and two different values for the short- and long-range cutoffs. In order to reach an accuracy at the percent level, the electromagnetic potential includes contributions beyond the leading Coulomb interaction, such as two-photon exchange and vacuum polarization contributions. The initial proton-proton state is expanded in partial waves and only the 1S_0 contribution is included, as it is known that the other partial-waves effects are negligible. The weak axial current operator is also derived within chiral effective field theory, consistently with each adopted potential. The so-called low-energy constant entering the weak axial current operator is calibrated to reproduce the Gamow-Teller matrix element in tritium beta-decay. The S-factor as function of the relative energy S(E) is fitted with a polynomial around E=0. The value S(0) is found to be S(0)=4.069(28)e-23 MeV fm^2, where the theoretical uncertainty arises from the chiral order truncation of the weak current and from model-dependence. The central value for S(0) is obtained averaging between the results corresponding to the highest order (N3LO) available for both potentials and currents.