  We present a power counting to include Coulomb effects in the three-nucleon
system in a low-energy pionless effective field theory (EFT). With this power
counting, the quartet S-wave proton-deuteron elastic scattering amplitude is
calculated. The calculation includes next-to-leading order (NLO) Coulomb
effects and next-to-next-to-leading order (NNLO) strong interaction effects,
with an estimated theoretical error of about 7 %. The EFT results agree with
potential model calculations and phase shift analysis of experimental data
within the estimated errors.

Nuclear Theory;Nuclear Experiment