The proton-deuteron system in pionless EFT revisited

We provide a detailed discussion of the low-energy proton-deuteron system in pionless effective field theory, considering both the spin-quartet and doublet S-wave channels. Extending and amending our previous work on the subject, we calculate the He-3-H-3 binding energy difference both perturbatively (using properly normalized trinucleon wave functions) and non-perturbatively by resumming all. (a) Coulomb diagrams in the doublet channel. Our non-perturbative result agrees well with a calculation that involves the full off-shell Coulomb T-matrix. Carefully examining the cutoff-dependence in the doublet channel, we present numerical evidence for a new three-nucleon counterterm being necessary at next-to-leading order if Coulomb effects are included. Indeed, such a term has recently been identified analytically. We furthermore make a case for a simplified Coulomb power counting that is consistent throughout the bound-state and scattering regimes. Finally, using a 'partially screened' full off-shell Coulomb T-matrix, we investigate the importance of higher-order Coulomb corrections in low-energy quartet-channel scattering.