Parameter-Free Calculation of the Solar Proton Fusion Rate in Effective Field Theory

Abstract

Spurred by the recent complete determination of the weak currents in two-nucleon systems up to ${\cal O}(Q^3)$ in heavy-baryon chiral perturbation theory, we carry out a parameter-free calculation of the solar proton fusion rate in an effective field theory that combines the merits of the standard nuclear physics method and systematic chiral expansion. Using the tritium beta-decay rate as an input to fix the only unknown parameter in the effective Lagrangian, we can evaluate with drastically improved precision the ratio of the two-body contribution to the well established one-body contribution; the ratio is determined to be (0.86\pm 0.05) %. This result is essentially independent of the cutoff parameter for a wide range of its variation (500 MeV \le \Lambda \le 800 MeV), a feature that substantiates the consistency of the calculation.