Abstract
We discuss the formulation of a non-relativistic effective field theory for two-body P-wave scattering in the presence of shallow states and critically address various approaches to renormalization proposed in the literature. It is demonstrated that the consistent renormalization involving only a finite number of parameters in the well-established formalism with auxiliary dimer fields corresponds to the inclusion of an infinite number of counterterms in the formulation with contact interactions only. We also discuss the implications from the Wilsonian renormalization group analysis of P-wave scattering.
Highlights
In the early 1990s, Weinberg has argued that nuclear forces and low-energy nuclear dynamics can be systematically analyzed using an effective chiral Lagrangian [1,2]
It is important to keep in mind that the numerical values and, the relative importance of bare parameters depend on the cutoff and are controlled by the Wilsonian renormalization group (RG) equations [17], while the renormalized couplings depend on the renormalization scales as dictated by the Gell-Mann and Low RG equations [18,19,20]
Our paper is organized as follows: in Sect. 2, we briefly review the formulations of halo effective field theory (EFT) for Sand P-wave systems proposed in the literature and summarize the findings to be critically examined
Summary
In the early 1990s, Weinberg has argued that nuclear forces and low-energy nuclear dynamics can be systematically analyzed using an effective chiral Lagrangian [1,2]. One needs to specify whether the power counting for the effective Lagrangian is formulated in terms of bare or renormalized parameters. While this issue is irrelevant in the purely mesonic sector of chiral EFT if one uses dimensional regularization (DR), things start becoming more complicated already in the single-nucleon sector. Starting from the two-nucleon sector, it seems impossible to find a formulation that would allow one making no distinction between the power counting being applied to the bare or the renormalized parameters In this context, it is important to keep in mind that the numerical values and, the relative importance of bare parameters depend on the cutoff and are controlled by the Wilsonian renormalization group (RG) equations [17], while the renormalized couplings depend on the renormalization scales as dictated by the Gell-Mann and Low RG equations [18,19,20].
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