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Perturbative $χ$EFT calculations of the deuteron and triton up to N$^2$LO

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 $Λ\approx 1200$ MeV. We analyze exceptional cutoffs in the $^3P_0$ and $^3S_1 \mathrm{-}^3D_1$ 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 $^3P_0$ 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 $^3S_1 \mathrm{-}^3D_1$ channel remedies the effect of this exceptional cutoff on the ground state energy of the deuteron, but not for the triton.