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

TL;DR

This paper applies Wilsonian renormalization group analysis to pionful nuclear effective field theory, revealing fixed points and scaling behaviors that connect to pionless EFT, and emphasizing the separation of pion exchange into short- and long-distance parts.

Contribution

It derives nonperturbative RG equations for pionful NEFT and identifies fixed points and scaling dimensions consistent with pionless NEFT, clarifying the role of pion exchange separation.

Findings

Identified nontrivial fixed points in key channels.

Determined scaling dimensions matching pionless NEFT.

Highlighted the importance of separating pion exchange parts.

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 $^1S_0$ and $^3S_1$--$^3D_1$ 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.