Pions are neither perturbative nor nonperturbative: Wilsonian renormalization group analysis of nuclear effective field theory including pions

Abstract

Pionful nuclear effective field theory (NEFT) in the two-nucleon sector is examined from the Wilsonian renormalization group point of view. The pion exchange is cut off at the floating cutoff scale, $\Lambda$, with the short-distance part being represented as contact interactions in accordance with the general principle of renormalization. We derive the nonperturbative renormalization group equations in the leading order of the nonrelativistic approximation in the operator space including up to $\mathcal{O}(p^2)$ and find the nontrivial fixed points in the ${}^1{S}_0$ and ${}^3{S}_1$--${}^3{D}_1$ channels which are identified with those in the pionless NEFT. The scaling dimensions, which determine the power counting, of the contact interactions at the nontrivial fixed points are also identified with those in the pionless NEFT. We emphasize the importance of the separation of the pion exchange into the short-distance and the long-distance parts, since a part of the former is nonperturbative while the latter is perturbative.

minor changes, title changed

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Cited by in corpus (13)

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• Renormalizing Chiral Nuclear Forces: A Case Study of 3P0
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• The Two-Nucleon 1S0 Amplitude Zero in Chiral Effective Field Theory
• Implicit vs Explicit Renormalization and Effective Interactions
• Wilsonian renormalization group and the Lippmann-Schwinger equation with a multitude of cutoff parameters
• Effective field theory for shallow P-wave states
• Two-nucleon scattering in a modified Weinberg approach with a symmetry-preserving regularization
• Nucleon-nucleon scattering up to next-to-next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: peripheral phases
• Wilsonian renormalization group analysis of nonrelativistic three-body systems without introducing dimerons
• $NN$ scattering in ${}^3{S}_1{-}^3{D}_1$ channels of EFT ($/\pi$)
• Numerical study of renormalization group flows of nuclear effective field theory without pions on a lattice
• Renormalization of One-Pion Exchange in Higher Partial Waves in Chiral Effective Field Theory for Antinucleon-Nucleon System