Parameter-free effective field theory calculation for the solar proton-fusion and hep processes

Abstract

Spurred by the recent complete determination of the weak currents in two-nucleon systems up to O(Q 3 ) in heavy-baryon chiral perturbation theory, we carry out a parameter-free calculation of the threshold S-factors for the solar pp (proton-fusion) and hep processes in an effective field theory that combines the merits of the standard nuclear physics method and systematic chiral expansion. The power of the EFT adopted here is that one can correlate in a unified formalism the weak-current matrix elements of two-, three-and four-nucleon systems. Using the tritium β-decay rate as an input to fix the only unknown parameter in the theory, we can evaluate the threshold S factors with drastically improved precision; the results are Spp(0) = 3.94×(1 ± 0.004)×10 −25 MeV-b and S hep (0) = (8.6 ± 1.3)×10 −20 keV-b. The dependence of the calculated S-factors on the momentum cutoff parameter Λ has been examined for a physically reasonable range of Λ. This dependence is found to be extremely small for the pp process, and to be within acceptable levels for the hep process, substantiating the consistency of our calculational scheme.

Effects of Three-Nucleon Forces and Two-Body Currents on Gamow-Teller Strengths

“…The 2BCs enter at NNLO and depend on the LECs c D , c 3 , c 4 of the chiral interaction [37,38]. The triton half-life yields an empirical value for E A 1 emp , which constrains c D and c E .…”

Publisher’s Note: Heavy-baryon chiral perturbation theory approach to thermal neutron capture onHe3[Phys. Rev. C83, 034006 (2011)]

“…In view of the fact that the previous theoretical estimations of the hep S-factor ranged over two orders of magnitude [7], this is a remarkable feat. A direct test of this theoretical result, however, is not possible because of the unfeasibility of the hep cross section measurement.…”

“…Given the close similarity between hen and hep, it is expected that comparison between theory and experiment for the hen case offers valuable information on the validity of the theoretical framework employed for the hep calculation in Ref. [7]. This gives an additional motivation for carrying out a detailed study of hen.…”

“…In this paper we report on a parameter-free MEEFT calculation for the hen cross sec-tion at threshold, adopting essentially the same method as used in [7]. #1 In MEEFT the transition operators are derived from the systematic expansion of the heavy-baryon chiral perturbation theory (HBChPT), and the nuclear MEs are obtained by sandwiching these operators between the wave functions generated from a high-precision phenomenological nuclear potential.…”

“…[1,2] for a recent review) and motivated a series of elaborated studies [3][4][5][6]. Park et al [7] developed an effective field theory (EFT) approach, which has come to be known as "more-effective EFT" (MEEFT for short) [8] and, with the use of MEEFT, they calculated the hep S-factor with an estimated accuracy of about 15 %.…”