Proton–proton fusion in effective field theory to fifth order

Abstract

The proton–proton fusion process pp [right arrow] de[superscript +] v[subscript e] is calculated at threshold to fifth order in pionless effective field theory. There are two unknown two-body currents contributing at the second and fourth orders. Combined with the previous results for ν[subscript e]d and ν[over bar][subscript e]d scattering, computed to third order in the same approach, we conclude that a ∼ 10% measurement of reactor ν[hyphen symbol above v][subscript e]d scattering measurement could constrain the pp [right arrow] de[superscript +]ν[subscript e] rate to ∼ 7% while a ∼ 3% measurement of ν[subscript e]d [right arrow] e[superscript −]pp could constrain the pp rate to ∼ 2%.