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

The Gamow-Teller and Fermi matrix elements, <GT> and <F>, respectively, for tritium β-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 <GT>₀=0.9807 and <F>₀=1. Using an experimentally determined value for the tritium-β decay GT matrix element, the two-body axial current low energy constant is fixed at NLO yielding L1,A=6.01±2.08 fm³ 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.