Tritium \(\beta\)-decay and Proton-Proton Fusion in Pionless Effective Field Theory

Abstract

The Gamow-Teller and Fermi matrix elements, \({\left<\mathbf{GT}\right>}\) and \({\left<\mathbf{F}\right>}\), respectively, for tritium \(\beta\)-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 \({\left<\mathbf{GT}\right>}_{0}=0.9807\) and \({\left<\mathbf{F}\right>}_{0}=1\). Using an experimentally determined value for the tritium-\(\beta\) decay GT matrix element, the two-body axial current low energy constant is fixed at NLO yielding \(L_{1,A}=6.01\pm2.08\) 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.