Deuterium-Proton Fusion in an Effective Field Theory Constructed from On-Shell Amplitudes

Abstract

Big Bang nucleosynthesis (BBN) predicts the primordial deuterium abundance to a precision now limited by the nuclear reactions that burn deuterium. For the simplest of them, proton-deuteron radiative capture, d + p -> γ+ 3He [d(p,γ)3He], the precise LUNA data sit below the ab initio benchmark, and BBN reaction networks split on which to adopt. We develop an effective field theory (EFT) expanding in the finite size of the nuclei, building the amplitude with modern on-shell methods that enumerate every tree-level structure consistent with symmetries without the need for an explicit Lagrangian. A global Bayesian fit to the capture data and nuclear-theory priors returns S(0) = 0.209 +/- 0.008 eV b and traces the offset from the ab initio benchmark to a single natural-sized next-to-leading contact term (t_E1 ~ -0.15, the fractional shift of the electric-dipole amplitude) -- equivalently a ~15% lower effective 3He asymptotic normalization. We estimate the leading EFT truncation errors and identify an elastic d-p observable that would separate them. Our results suggest that amplitude methods enable systematic and complete tree-level construction and matching of EFTs for low-energy nuclear reactions.