Tritium -decay and Proton-Proton Fusion in Pionless Effective Field Theory

The Gamow-Teller and Fermi matrix elements, and, respectively, for tritium -decay are calculated to next-to-leading order (NLO) in pionless effective field theory in the absence of Coulomb and isospin violation giving the leading order predictions ₀=0. 9807 and ₀=1. Using an experimentally determined value for the tritium- decay GT matrix element, the two-body axial current low energy constant is fixed at NLO yielding L₁, ₀=6. 012. 08 fm^3 at the renormalization scale of the physical pion mass, which agrees with predictions based on naive dimensional analysis. Finally, the consequences of Wigner-SU (4) spin-isospin symmetry are considered for the Gamow-Teller matrix element.