Convergent perturbative nuclear effective field theory

TL;DR

This paper develops a nuclear effective field theory including pions, using a hybrid regularization scheme to treat long-distance pion exchange perturbatively, and demonstrates convergence with experimental phase shift data.

Contribution

It introduces a hybrid regularization method combining PDS and GDF for perturbative pion exchange in nuclear EFT, with analytic phase shift expressions and convergence validation.

Findings

Analytic phase shift formulas for key channels.

Convergence of perturbative expansion with data.

Effective theory matches experimental results.

Abstract

We consider the nuclear effective field theory including pions in the two-nucleon sector in the S waves up to including the next-to-next-to-leading order (NNLO) terms according to the power counting suggested by the Wilsonian renormalization group analysis done in a previous paper. We treat only the leading contact interaction nonperturbatively, and the rest, including the long-distance part of pion exchange, are treated as perturbations. To define the long-distance part, it is important to introduce a separation scale, or a cutoff. We employ a hybrid regularization, in which the loops with only contact interactions are regularized with Power Divergence Subtraction (PDS), while the loops with (long-distance part of) pion exchange are regularized with a Gaussian damping factor (GDF), to simplify the (nonperturbative) leading-order amplitudes. The scale introduced by PDS is identified with the cutoff of GDF up to a numerical factor. We emphasize that the introduction of the GDF requires a careful definition of the coupling constant for the pion exchange. We obtain the analytic expressions for the phase shifts for the $^1S_0$ and $^3S_1$-$^3D_1$ channels. By fitting them to the Nijmegen partial wave analysis data, it is shown that the effective theory expansion with perturbative long-distance part of pion exchange is converging.