How to renormalize integral equations with singular potentials in effective field theory

Abstract

We briefly review general concepts of renormalization in quantum field theory and discuss their application to solutions of integral equations with singular potentials in the few-nucleon sector of the low-energy effective field theory of QCD. We also describe a particular subtractive renormalization scheme and consider a specific application to a toy-model with a singular potential serving as its effective field theoretical leading-order approximation.

arXiv comment9 pages, 2 figures, extends the discussion, matches published version in EPJA

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Cited by in corpus (23)

• Nuclear effective field theory: status and perspectives
• Parity- and time-reversal-violating nuclear forces
• Power counting in chiral effective field theory and nuclear binding
• Nucleon-nucleon interaction in chiral EFT with a finite cutoff: explicit perturbative renormalization at next-to-leading order
• Constructing chiral effective field theory around unnatural leading-order interactions
• Strong CP violation in nuclear physics
• Renormalizability of leading order covariant chiral nucleon-nucleon interaction
• Effective field theory for shallow P-wave states
• Improved description of light nuclei through chiral effective field theory at leading order
• A further study on the renormalization group aspect of perturbative corrections
• Removing the Wigner bound in non-perturbative effective field theory
• The $\Lambda (1405)$ in resummed chiral effective field theory
• Nucleon-nucleon scattering up to next-to-next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: peripheral phases
• Non-perturbative methods for NN singular interactions
• Resonance parameters of the vector charmoniumlike state $G(3900)$
• Reexamining the perturbative renormalizability of the coupled triplets
• Ab initio models of atomic nuclei: challenges and new ideas
• Worldline Monte Carlo method for few body nuclear physics
• Renormalization of a Contact Interaction on a Lattice
• Renormalization of NN Chiral EFT, my personal mixed feelings
• Symmetries of the nucleon-nucleon $S$-matrix and effective field theory expansions
• Efficient emulator for solving three-nucleon continuum Faddeev equations with chiral three-nucleon force comprising any number of contact terms
• Renormalization of One-Pion Exchange in Higher Partial Waves in Chiral Effective Field Theory for Antinucleon-Nucleon System