Proton–proton fusion in effective field theory to fifth order

The proton–proton fusion process pp→de+νe 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 νed and ν̄ed scattering, computed to third order in the same approach, we conclude that a ∼10% measurement of reactor ν̄ed scattering measurement could constrain the pp→de+νe rate to ∼7% while a ∼3% measurement of νed→e−pp could constrain the pp rate to ∼2%.