Tritium β-decay and pp fusion in Pionless Effective Field Theory

At low energies, pp fusion, which is relevant for stellar and Big Bang nucleosynthesis, and tritium β-decay both depend on a two-nucleon axial current contribution described by the low-energy constant L_1,A at next-to-leading order (NLO). Using pionless effective field theory, we compute the Fermi and Gamow-Teller matrix elements of tritium β-decay up to NLO. We then extract the L_1,A parameter from the tritium half-life and use it to predict the transition matrix element for pp fusion. We will also discuss the consequences of Wigner-SU(4) symmetry in the calculation of the Fermi and Gamow-Teller matrix elements for tritium β-decay.