[Paper Review] Renormalization and Universality of NN interactions in Chiral Quark and Soliton Models

E. Ruiz Arriola, A. Calle Cordón|ArXiv.org|Oct 7, 2009

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper proposes that renormalization in chiral quark and soliton models suppresses short-distance sensitivity in nucleon-nucleon (NN) interactions, enabling universal low-energy behavior despite differing high-energy components. By imposing consistent renormalization conditions, the models achieve natural SU(3) symmetry values and reduce fine-tuning, with departures from universality revealing nucleon structure details.

ABSTRACT

We use renormalization as a tool to extract universal features of the NN interaction in quark and soliton nucleon models, having the same long distance behaviour but different short distance components. While fine tuning conditions in the models make difficult to fit NN data, the introduction of suitable renormalization conditions supresses the short distance sensitivity. Departures from universality are equivalent to extracting information on the model nucleon structure.

Motivation & Objective

• To identify universal features of NN interactions across chiral quark and soliton models with identical long-distance behavior but different short-distance components.
• To address the persistent fine-tuning problem in One-Boson-Exchange (OBE) models, particularly in the $^{1}S_{0}$ channel, where large coupling constants are required.
• To demonstrate that renormalization conditions can suppress short-distance sensitivity, thereby reducing reliance on arbitrary form factors and vertex functions.
• To explore how deviations from universality encode information about nucleon structure, especially in the context of SU(4) Wigner symmetry and $N$-$\Delta$ splitting.
• To establish a framework where low-energy constants are determined by renormalization rather than ad hoc parameter fitting, improving theoretical consistency.

Proposed method

• Apply renormalization techniques to quark and soliton models of the nucleon, focusing on short-distance regularization to eliminate model dependence.
• Use the $V_{\rm lowk}$ renormalization group approach to coarse-grain the NN potential, extracting universal low-energy behavior.
• Implement renormalization conditions that are mutually compatible with the removal of cut-offs, ensuring short-distance insensitivity.
• Analyze the role of contact interactions, particularly One-Gluon-Exchange (OGE), in breaking SU(4) symmetry and generating $N$-$\Delta$ mass splitting.
• Compare the behavior of the $^{1}S_{0}$ and ${}^{3}S_{1}$ channels under Wigner symmetry assumptions, using identical functions ${\cal A}(p)$, ${\cal B}(p)$, ${\cal C}(p)$, ${\cal D}(p)$ in the scattering equations.
• Use the $\alpha_{{}^{1}S_{0}} = -23.74\,{\rm fm}$ and $\alpha_{{}^{3}S_{1}} = 5.42\,{\rm fm}$ scattering lengths as input to test the validity of Wigner symmetry breaking via counterterms.

Experimental results

Research questions

• RQ1 To what extent can renormalization conditions suppress short-distance sensitivity in NN interactions across different quark and soliton models?
• RQ2 How do fine-tuning issues in OBE models—especially in the $^{1}S_{0}$ channel—arise from short-distance singularities, and can they be resolved via renormalization?
• RQ3 What is the role of the $N$-$\Delta$ mass splitting in breaking Wigner SU(4) symmetry, and how is this related to short-distance gluonic interactions?
• RQ4 Can universal low-energy behavior in NN scattering be extracted independently of model-specific short-distance components through renormalization?
• RQ5 How do contact interactions like OGE contribute to breaking SU(4) symmetry and explain the observed $N$-$\Delta$ mass splitting?

Key findings

• Renormalization conditions successfully suppress short-distance sensitivity in NN interactions, allowing models with different short-distance components to reproduce universal low-energy behavior.
• The introduction of renormalization conditions reduces the need for extreme fine-tuning of coupling constants, enabling the use of natural SU(3) values for $g_{\omega NN}$.
• Departures from universality in the models are directly linked to information about nucleon structure, particularly through short-distance gluonic interactions.
• The $^{1}S_{0}$ and ${}^{3}S_{1}$ phase shifts are well reproduced using identical functions ${\cal A}(p)$, ${\cal B}(p)$, ${\cal C}(p)$, ${\cal D}(p)$, with differences arising solely from the experimentally distinct scattering lengths.
• Wigner SU(4) symmetry is found to be a long-distance symmetry broken only by short-distance counterterms, with the $N$-$\Delta$ mass splitting arising from OGE interactions.
• The $1/\alpha_{{}^{3}S_{1}} - 1/\alpha_{{}^{1}S_{0}}$ difference is shown to be ${\cal O}(M_{\Delta} - M_{N})$, with a computable coefficient, confirming the role of short-distance physics in breaking SU(4) symmetry.