Effective theory of ³H and ³He

We present a new perturbative expansion for pionless effective field theory with Coulomb interactions in which at leading order (LO) the spin-singlet nucleonnucleon channels are taken in the unitarity limit. Presenting results up to next-to-leading order for the Phillips line and the neutrondeuteron doubletchannel phase shift, we find that a perturbative expansion in the inverse ¹S₀ scattering lengths converges rapidly. Using a new systematic treatment of the protonproton sector that isolates the divergence due to one-photon exchange, we renormalize the corresponding contribution to the ³H ³He binding energy splitting and demonstrate that the Coulomb force in pionless EFT is a completely perturbative effect in the trinucleon bound-state regime. In our new expansion, the LO is exactly isospin-symmetric. At next-to-leading order, we include isospin breaking via the Coulomb force and two-body scattering lengths, and find for the energy splitting (E_B (³He) E_B (³H)) ^NLO (-0.86 ± 0.17) MeV.