The Coulomb corrections to tritium β-decay in pionless effective field theory

In pionless effective field theory, several weak-interaction processes depend on a single unknown low-energy constant L_1,A at next-to-leading order (NLO). For instance, the determination of L_1,A is crucial for calculating the cross-sections of muon-deuterium capture in the MuSun experiment and proton-proton fusion. Building upon our previous work extracting L_1,A from the tritium β-decay half-life by computing the Fermi and Gamow-Teller matrix elements up to NLO in the absence of Coulomb, we now consider the impact of Coulomb corrections on those results. We will discuss the addition of Coulomb effects using a strictly perturbative approach, which has been proven to work for the ³He system despite the non-perturbative nature of Coulomb interactions at low momenta.