Revisiting proton–proton fusion in chiral effective field theory

Abstract

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.

Solar Models and Astrophysical S-factors Constrained by Helioseismic Results and Updated Neutrino Fluxes

“…The change in S 11 is much larger than the uncertainty of S 11 recommended by Adelberger et al (2011). However, the density in the central region with r  0.2 R e of this model is too low compared to the seismically inferred one, and the 7 Be and (1989) is larger than that of Adelberger et al (2011) and in good agreement with the new theoretical results of Acharya et al (2016Acharya et al ( , 2023 and De-Leon & Gazit (2023). And the value of S 33 of 5.15 MeV barns of Bahcall (1989) is lower than that of Adelberger et al (2011).…”

“…Using S 33 of Bahcall (1989) and S 17 of Bahcall & Pinsonneault (1992) to replace the corresponding S-factors of A11R (see Table 2), we constructed a rotating model BAR1. In order to reproduce the pp and pep neutrino fluxes determined by Bergström et al (2016), the value of S 11 needs to be increased to 4.13 × 10 −22 keV barns, which is consistent with the new results of De-Leon & Gazit (2023) and Acharya et al (2023) at the level of 1σ. The surface helium abundance and radius r cz of BAR1 agree with the seismically inferred ones at the level of 1σ (see Table 1).…”

“…The value of 4.07 × 10 −22 keV barns of S 11 is slightly lower than the central value of 4.10 × 10 −22 keV barns given by Acharya et al (2023) Figure 8. Rotation profiles of models as a function of radius.…”

“…There are usually several estimated values for a nuclear cross-section factor S(0) (astrophysical S-factor) in the literature. For example, there exist 0.0243 keV barns (Bahcall & Ulrich 1988), 0.0224 keV barns (Bahcall & Pinsonneault 1992), 0.0202 keV barns (Schramm & Shi 1994), 0.0274 keV barns (Liu et al 1996), or 0.0208 keV barns (Adelberger et al 2011, hereafter A11) for S 17 (0) of the 7 Be(p, γ) 8 B reaction and 3.940 × (1 ± 0.004) × 10 −22 keV barns (Park et al 2003), (4.01 ± 0.04) × 10 −22 keV barns (Adelberger et al 2011), (3.99 ± 0.14) × 10 −22 keV barns (Chen et al 2013), -+ 4.047 0.032 0.024 keV barns (Acharya et al 2016), (4.100 ± 0.037) × 10 −22 keV barns (Parker & Rolfs 1991;Acharya et al 2023), or (4.14 ± 0.07) × 10 −22 keV barns (De-Leon & Gazit 2023) for S 11 (0) of the pp reaction. The new theoretical predictions of S 11 (0) (Acharya et al 2016(Acharya et al , 2023De-Leon & Gazit 2023) are 1%-4% higher than the previously accepted value of Adelberger et al (2011) and differ in their uncertainty estimate (Chen et al 2013).…”

“…argued that extrapolating to the low energies to obtain S-factors relevant for solar fusion introduces a large uncertainty. The factor S 11 is not accurately predicted by the chiral effective field theory interactions at low chiral orders if the deuteron bound-state properties are not adequately reproduced (Acharya et al 2023). Bellinger & Christensen-Dalsgaard (2022) showed that when other aspects of the solar model are improved, it shall be possible using helioseismology and solar neutrinos to improve the precision of measurements of the nuclear cross-section factors in the pp chains and CNO cycles.…”