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

A. M. Gasparyan and E. Epelbaum

Phys. Rev. C 107, 044002 – Published 10 April 2023

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 nonperturbative effects. We consider the nucleon-nucleon interaction up to next-to-leading order in the chiral expansion. The leading-order interaction is treated nonperturbatively. 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.

Received 11 February 2023
Accepted 24 March 2023

DOI:https://doi.org/10.1103/PhysRevC.107.044002

Physics Subject Headings (PhySH)

Effective field theory Nonperturbative effects in field theory Nucleon-nucleon interactions Renormalization

Nuclear PhysicsParticles & Fields

Authors & Affiliations

A. M. Gasparyan ^* and E. Epelbaum ^†

Ruhr-Universität Bochum, Fakultät für Physik und Astronomie, Institut für Theoretische Physik II, D-44780 Bochum, Germany

^*ashot.gasparyan@rub.de
^†evgeny.epelbaum@rub.de

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Vol. 107, Iss. 4 — April 2023

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Images

Figure 1
The results of the leading-order (blue dashed lines) and next-to-leading-order (red solid lines) calculations for the ${}^{3}P_{0}$ partial wave without promoting the contact interaction. The bands indicate the variation of the one-pion-exchange cutoff within the range $Λ_{1 π} \in (300, 450)$ MeV for two left plots and within the range $Λ_{1 π} \in (450, 600)$ MeV for two right plots. The second and fourth plots correspond to the NLO potential with the regulator correction $δ_{Λ} V^{(0)}$ , while the results in the first and third plots are obtained without this term. The empirical phase shifts shown by black solid dots are from Ref. [41]. The plots were created using Matplotlib [43].
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Figure 2
The results of the leading-order (blue dashed lines) and next-to-leading-order (red solid lines) calculations for the ${}^{3}P_{0}$ partial wave with the contact term promoted to leading order. The bands indicate the variation of the one-pion-exchange cutoff within the range $Λ_{1 π} \in (300, 450)$ MeV for two left plots and within the range $Λ_{1 π} \in (450, 800)$ MeV for two right plots. The second and fourth plots correspond to the NLO potential with the regulator correction $δ_{Λ} V^{(0)}$ , while the results in the first and third plots are obtained without this term. The empirical phase shifts shown by black solid dots are from Ref. [41].
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Figure 3
The results of the leading-order (blue dashed lines) and next-to-leading-order (red solid lines) calculations for the ${}^{3}S_{1} − {}^{3}D_{1}$ channels with the contact term promoted to leading order. The bands indicate the variation of the cutoff of the LO potential within the range $Λ \in (300, 450)$ MeV for two left columns and within the range $Λ \in (450, 800)$ MeV for two right columns. The second and fourth columns correspond to the NLO potential with the regulator correction $δ_{Λ} V^{(0)}$ , while the results in the first and third columns are obtained without this term. The data are as in Figs. 1 and 2.
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Figure 4
The results of the leading-order (blue dashed lines) and next-to-leading-order (red solid lines) calculations for the ${}^{1}S_{0}$ partial wave without promoting the contact interaction quadratic in momentum. The bands indicate the variation of the cutoff of the LO potential within the range $Λ \in (300, 450)$ MeV for two left plots and within the range $Λ \in (450, 800)$ MeV for two right plots. The second and fourth plots correspond to the NLO potential with the regulator correction $δ_{Λ} V^{(0)}$ , while the results in the first and third plots are obtained without this term. The data are as in Figs. 1 and 2.
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Figure 5
The results of the leading-order (blue dashed lines) and next-to-leading-order (red solid lines) calculations for the ${}^{1}S_{0}$ partial wave with the contact interaction quadratic in momentum promoted to leading order. The bands indicate the variation of the cutoff of the LO potential within the range $Λ \in (300, 450)$ MeV for two left plots and within the range $Λ \in (450, 800)$ MeV for two right plots. The second and fourth plots correspond to the NLO potential with the regulator correction $δ_{Λ} V^{(0)}$ , while the results in the first and third plots are obtained without this term. The data are as in Figs. 1 and 2.
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