Perturbative $\chi$EFT calculations of the deuteron and triton up to N${}^2$LO

Abstract

We extend previous studies of the deuteron and triton ground-state energies to next-to-next-to-leading order (N${}^2$LO) in chiral effective field theory, employing a power counting in which subleading interactions are treated perturbatively. Triton calculations are performed using the no-core shell model, and we demonstrate converged perturbative results for regulator cutoffs up to $\Lambda \approx 1200$ MeV. We analyze exceptional cutoffs in the ${}^3{P}_0$ and ${}^3{S}_1{-}^3{D}_1$ nucleon-nucleon channels and find a resulting cutoff dependence in the triton ground-state energy at N${}^2$LO. The effect associated with the exceptional cutoff in the ${}^3{P}_0$ channel can be mitigated by redefining the leading-order wave function within the freedom allowed by the effective field theory. The same approach applied in the ${}^3{S}_1{-}^3{D}_1$ channel remedies the effect of this exceptional cutoff on the ground state energy of the deuteron, but not for the triton.