Revisiting proton-proton fusion in chiral effective field theory

We calculate the $S$-factor for proton-proton fusion using chiral effective field theory interactions and currents. By performing order-by-order calculations with a variety of chiral interactions that are regularized and calibrated in different ways, we assess the uncertainty in the $S$-factor from the truncation of the effective field theory expansion and from the sensitivity of the $S$-factor to the short-distance axial current determined from three- and four-nucleon observables. We find that $S(0)=(4.100\pm0.019\mathrm{(syst)}\pm0.013\mathrm{(stat)}\pm0.008(g_A))\times10^{-23}~\mathrm{MeV\,fm}^2\,,$ where the three uncertainties arise, respectively, from the truncation of the effective field theory expansion, use of the two-nucleon axial current fit to few-nucleon observables and variation of the axial coupling constant within the recommended range. The increased value of $S(0)$ compared to previous calculations is mainly driven by an increase in the recommended value for the axial coupling constant and is in agreement with a recent analysis based on pionless effective field theory.