Anomalous dimensions determine the power counting: Wilsonian RG analysis of nuclear EFT

2006/05/31 by Koji Harada, Hirofumi Kubo
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #Nuclear physics research studies #Quantum Chromodynamics and Particle Interactions #hep-ph #hep-th #nucl-th

paper · pdf · doi:10.1016/j.nuclphysb.2006.10.001

published as Nucl.Phys.B758:304-329,2006 · explanation about the Legendre flow equation improved, an appendix added, figures replaced, typos corrected 35pages, 3 figures

arxiv created 2006/10/24 · openalex publication_date 2006/10/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Legendre flow equation, a version of exact Wilsonian renormalization group (WRG) equation, is employed to consider the power counting issues in Nuclear Effective Field Theory. A WRG approach is an ideal framework because it is nonperturbative and does not require any prescribed power counting rule. The power counting is determined systematically from the scaling dimensions of the operators at the nontrivial fixed point. The phase structure is emphasized and the inverse of the scattering length, which is identified as a relevant coupling, is shown to play a role of the order parameter. The relations to the work done by Birse, McGovern, and Richardson and to the Kaplan-Savage-Wise scheme are explained.

Citations

• The renormalization group and the ε expansion
• Chiral perturbation theory to one loop
• Exact evolution equation for the effective potential
• A momentum subtraction scheme for two-nucleon effective field theory
• The renormalization group: Critical phenomena and the Kondo problem
• Chiral perturbation theory: Expansions in the mass of the strange quark
• Phenomenological Lagrangians