Renormalization of nuclear chiral effective field theory with non-perturbative leading order interactions

Abstract

We extend the renormalizability study of the formulation of chiral effective field theory with a finite cutoff, applied to nucleon-nucleon scattering, by taking into account non-perturbative effects. We consider the nucleon-nucleon interaction up to next-to-leading order in the chiral expansion. The leading-order interaction is treated non-perturbatively. In contrast to the previously considered case when the leading-order interaction was assumed to be perturbative, new features related to the renormalization of the effective field theory are revealed. In particular, more severe constraints on the leading-order potential are formulated, which can enforce the renormalizability and the correct power counting for the next-to-leading order amplitude. To illustrate our theoretical findings, several partial waves in the nucleon-nucleon scattering, ${}^3{P}_0$, ${}^3{S}_1-{}^3{D}_1$ and ${}^1{S}_0$ are analyzed numerically. The cutoff dependence and the convergence of the chiral expansion for those channels are discussed.

arXiv comment44 pages, 5 figures

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