Anomalous dimensions determine the power counting -- Wilsonian RG analysis of nuclear EFT --
arXiv:nucl-th/0605004 · doi:10.1016/j.nuclphysb.2006.10.001
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.
explanation about the Legendre flow equation improved, an appendix added, figures replaced, typos corrected 35pages, 3 figures
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Cited by in corpus (16)
- Modern Theory of Nuclear Forces
- Nuclear effective field theory: status and perspectives
- Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
- Scattering Models for Ultracold Atoms
- Power Counting of Contact-Range Currents in Effective Field Theory
- How (not) to renormalize integral equations with singular potentials in effective field theory
- How to renormalize integral equations with singular potentials in effective field theory
- Functional renormalisation group for two-body scattering
- Pions are neither perturbative nor nonperturbative: Wilsonian renormalization group analysis of nuclear effective field theory including pions
- More about the Wilsonian analysis on the pionless NEFT
- Effective field theory for shallow P-wave states
- On the Wilsonian renormalization group equation for nuclear current operators
- New fixed points of the renormalisation group for two-body scattering
- Wilsonian renormalization group analysis of nonrelativistic three-body systems without introducing dimerons
- Numerical study of renormalization group flows of nuclear effective field theory without pions on a lattice
- Consistency between renormalization group running of chiral operator and counting rule -- Case of chiral pion production operator --