Incorporating dimer fields into the effective field theory resolves poles in the C-matrix from the angular momentum barrier, yielding cutoff-insensitive leading-order fits to nucleon-nucleon phase shifts up to the pion threshold.
NNLO Corrections to Nucleon-Nucleon Scattering and Perturbative Pions
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abstract
The 1S0, 3S1, and 3D1 nucleon-nucleon scattering phase shifts are calculated at next-to-next-to-leading order (NNLO) in an effective field theory. Predictions for the 1P1, 3P0, 3P1, 3P2, 1D2, 3D2, and 3D3 phase shifts at this order are also compared with data. The calculations treat pions perturbatively and include the NNLO contributions from order $Q_r^3$ and $Q_r^4$ radiation pion graphs. In the 3S1, 3D1, 3P0, and 3P2 channels we find large disagreement with the Nijmegen partial wave analysis at NNLO. These spin triplet channels have large corrections from graphs with two potential pion exchange which do not vanish in the chiral limit. We compare our results to calculations within the Weinberg approach, and find that in some spin triplet channels the summation of potential pion diagrams seems to be necessary to reproduce the observed phase shifts. In the spin singlet channels the nonperturbative treatment of potential pions does not afford a significant improvement over the perturbative approach.
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After removing renormalization-scheme-dependent short-distance parts, the scrutinized three-nucleon forces yield small contributions to neutron and symmetric nuclear matter equations of state, aligning with standard chiral EFT expectations.
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Dimer Effective Field Theory
Incorporating dimer fields into the effective field theory resolves poles in the C-matrix from the angular momentum barrier, yielding cutoff-insensitive leading-order fits to nucleon-nucleon phase shifts up to the pion threshold.
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Scrutiny of the new class of three-nucleon forces
After removing renormalization-scheme-dependent short-distance parts, the scrutinized three-nucleon forces yield small contributions to neutron and symmetric nuclear matter equations of state, aligning with standard chiral EFT expectations.