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

TL;DR

This paper calculates the proton-proton fusion S-factor using chiral effective field theory up to NNLO, rigorously analyzing various sources of uncertainty and their impact on the results, with implications for nuclear astrophysics.

Contribution

It provides a comprehensive uncertainty quantification for the proton-proton fusion S-factor within chiral EFT, including statistical, systematic, and methodological uncertainties, and explores correlations with other nuclear observables.

Findings

Uncertainty in the S-factor cannot be reduced below 0.7%.

Systematic uncertainties from the fit interval are eliminated.

Correlations between S-factor and nuclear observables are analyzed.

Abstract

We compute the $S$-factor of the proton-proton ($pp$) fusion reaction using chiral effective field theory ($\chi$EFT) 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 $\chi$EFT, (iii) the systematic uncertainty due to the $\chi$EFT 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 $^{2,3}$H and $^3$He as well as the $D$-state probability and quadrupole moment of $^2$H, and the $\beta$-decay of $^{3}$H. 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%.