Wilsonian RG and Redundant Operators in Nonrelativistic Effective Field Theory

Abstract

In a Wilsonian renormalization group (RG) analysis, redundant operators, which may be eliminated by using field redefinitions, emerge naturally. It is therefore important to include them. We consider a nonrelativisitic effective theory (the so-called ``pionless'' Nuclear Effective Field Theory) as a concrete example and show that the off-shell amplitudes cannot be renormalized if the redundant operators are not included. The relation between the theories with and without such redundant operators is established in the low-energy expansion. We perform a Wilsonian RG analysis for the \textit{off-shell} scattering amplitude in the theory with the redundant operator.

5 pages in two columns, no figures; corrected typos, a version to be published in PLB

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Cited by in corpus (16)

• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• Scattering Models for Ultracold Atoms
• Renormalization Group Analysis of Boundary Conditions in Potential Scattering
• Anomalous dimensions determine the power counting -- Wilsonian RG analysis of nuclear EFT --
• Implicit vs Explicit Renormalization and Effective Interactions
• Pions are neither perturbative nor nonperturbative: Wilsonian renormalization group analysis of nuclear effective field theory including pions
• The N/D method with non-perturbative left-hand-cut discontinuity and the ${}^1{S}_0$ $NN$ partial wave
• More about the Wilsonian analysis on the pionless NEFT
• Two-nucleon scattering in a modified Weinberg approach with a symmetry-preserving regularization
• Renormalization group analysis of nuclear current operators
• On the Wilsonian renormalization group equation for nuclear current operators
• Van der Waals forces and Photon-less Effective Field Theories
• Wilsonian renormalization group analysis of nonrelativistic three-body systems without introducing dimerons
• Implicit and explicit renormalization: two complementary views of effective interactions
• 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 --