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

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 (0.9\pm 0.1) %. 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