Proton-proton fusion in effective field theory

The rate for the fusion process p+→pd+e⁺+νₑ is calculated using nonrelativistic effective field theory. Including the four-nucleon derivative interaction, results are obtained in next-to-leading order in the momentum expansion. This reproduces the effects of the effective range parameter. Coulomb interactions between the incoming protons are included nonperturbatively in a systematic way. The resulting fusion rate is independent of specific models and wave functions for the interacting nucleons. At this order in the effective Lagrangian there is an unknown counterterm which limits the numerical accuracy. Assuming the counterterm to have a natural magnitude, the result is consistent with previous nuclear physics calculations.