Uncertainty quantification for proton–proton fusion in chiral effective field theory

We compute the S-factor of the proton–proton (pp) fusion reaction using chiral effective field theory (χEFT) up to next-to-next-to-leading order (NNLO) and perform a rigorous uncertainty analysis of the results. We quantify the uncertainties due to (i) the computational method used to compute the pp cross section in momentum space, (ii) the statistical uncertainties in the low-energy coupling constants of χEFT, (iii) the systematic uncertainty due to the χEFT cutoff, and (iv) systematic variations in the database used to calibrate the nucleon–nucleon interaction. We also examine the robustness of the polynomial extrapolation procedure, which is commonly used to extract the threshold S-factor and its energy-derivatives. By performing a statistical analysis of the polynomial fit of the energy-dependent S-factor at several different energy intervals, we eliminate a systematic uncertainty that can arise from the choice of the fit interval in our calculations. In addition, we explore the statistical correlations between the S-factor and few-nucleon observables such as the binding energies and point-proton radii of ^2,3H and ³He as well as the D-state probability and quadrupole moment of ²H, and the β-decay of ³H. We find that, with the state-of-the-art optimization of the nuclear Hamiltonian, the statistical uncertainty in the threshold S-factor cannot be reduced beyond 0.7%.