Nonlocal long-range separable potentials in a two-nucleon toy model require nonlocal counterterms at NLO, and a two-pion-exchange-like nonlocal term cannot be renormalized without moving that structure into the leading-order potential.
The unrenormalized NLO amplitude is given by T2 = ¯RV2R.(33) For the separable potential defined in Eq
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Renormalizability and nonrenormalizability of nonlocal potentials
Nonlocal long-range separable potentials in a two-nucleon toy model require nonlocal counterterms at NLO, and a two-pion-exchange-like nonlocal term cannot be renormalized without moving that structure into the leading-order potential.