Uncertainty estimates for proton-proton fusion

We calculate the proton-proton fusion cross section using chiral effective field theory ($\chi$EFT) and perform a rigorous analysis of the associated uncertainties. The statistical errors in the low-energy constants, which are fitted too scattering and bound-state observables in the pion-nucleon, nucleon-nucleon, and few-nucleon sectors, are propagated to the calculated cross section. We also investigate the sensitivity of the fusion cross section to the high-momentum cutoff of the $\chi$EFT. We extract a value for the zero-energy $S$-factor using a polynomial extrapolant and analyze the errors associated with this procedure. Our result is compared to that of another $\chi$EFT calculation in which the wave functions were represented in a truncated Hilbert space with discrete basis states.