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Is the "RG-invariant EFT'' for few-nucleon systems cutoff independent?
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Is the "RG-invariant EFT'' for few-nucleon systems cutoff independent?
abstract
We consider nucleon-nucleon scattering using the formulation of chiral effective field theory which is claimed to be renormalization group invariant. The cornerstone of this framework is the existence of a well-defined infinite-cutoff limit for the scattering amplitude at each order of the expansion, which should not depend on a particular regulator form. Focusing on the $^3P_0$ partial wave as a representative example, we show that this requirement can in general not be fulfilled beyond the leading order, in spite of the perturbative treatment of subleading contributions to the amplitude. Several previous studies along these lines, including the next-to-leading order calculation by Long and Yang [Phys. Rev. C84, 057001 (2011)] and a toy model example with singular long-range potentials by Long and van Kolck [Annals Phys. 323, 1304-1323 (2008)], are critically reviewed and scrutinized in detail.
Forward citations
Cited by 4 Pith papers
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EFT study of ^4He trimers and tetramers around unitarity limit yields binding energies and radii that converge to phenomenological potential results after including finite-range and four-body corrections.
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Bootstrapping Two-Nucleon Effective Field Theories
Bootstrap consistency checks show that the NLO chiral EFT potential for the 1S0 two-nucleon wave remains valid over a significantly wider energy range than the LO version when compared to Granada phase shifts.
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Perturbative calculations of light nuclei up to N$^3$LO in chiral effective field theory
Perturbative N3LO calculations in chiral EFT with RG-guided power counting yield robust predictions for light nuclei energies when calibrated on the tritium binding energy.
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Auxiliary counterterms and their role in effective field theory
Auxiliary counterterms provide exact cutoff independence in EFTs but encode no new physics and aid renormalization consistency and convergence.
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