Universal behavior of $p$-wave proton-proton fusion near threshold

Abstract

We calculate the $p$-wave contribution to the proton-proton fusion $S$ factor and its energy derivative in pionless effective field theory (EFT) up to next-to-leading order. The leading contributions are given by a recoil piece from the Gamow-Teller and Fermi operators, and from relativistic $1/m$ suppressed weak interaction operators. We obtain the value of $(2.5\pm 0.3)\times 10^{-28}\mathrm{MeV}\mathrm{f}{\mathrm{m}}^2$ for the $S$ factor and $(2.2\pm 0.2)\times 10^{-26}\mathrm{f}{\mathrm{m}}^2$ for its energy derivative at threshold. These are smaller than the results of a prior study that employed chiral EFT by several orders of magnitude. We conclude that, contrary to what has been previously reported, the $p$-wave contribution does not need to be considered in a high-precision determination of the $S$ factor at astrophysical energies. Combined with the chiral EFT calculation of Acharya {\it et al.} [Phys. Lett. B \bf{760}, 584 (2016)] for the $s$-wave channel, this gives a total threshold $S$ factor of $S(0)=(4.047_{-0.032}^{+0.024})\times 10^{-23}{\mathrm{MeV}\mathrm{fm}}^2$.

arXiv comment5 pages, 2 figures

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