How (not) to renormalize integral equations with singular potentials in effective field theory

Abstract

We discuss the connection between the perturbative and non-perturbative renormalization and related conceptual issues in the few-nucleon sector of the low-energy effective field theory of the strong interactions. General arguments are supported by examples from effective theories with and without pions as dynamical degrees of freedom. A quantum mechanical potential with explicitly specified short- and long-range parts is considered as an "underlying fundamental theory" and the corresponding effective field theory potential is constructed. Further, the problem of the effective field theoretical renormalization of the Skornyakov-Ter-Martyrosian equation is revisited.

arXiv comment12 pages, 5 figures

References in corpus (64)

• Modern Theory of Nuclear Forces
• Chiral effective field theory and nuclear forces
• Effective Field Theory for Few-Nucleon Systems
• A New Expansion for Nucleon-Nucleon Interactions
• Two-Nucleon Systems from Effective Field Theory
• Three-Nucleon Forces from Chiral Effective Field Theory
• Renormalization of the Three-Body System with Short-Range Interactions
• Few-Nucleon Forces and Systems in Chiral Effective Field Theory
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Nuclear forces from chiral Lagrangians using the method of unitary transformation II: The two-nucleon system
• Peripheral Nucleon-Nucleon Phase Shifts and Chiral Symmetry
• The Three-Boson System with Short-Range Interactions
• Renormalization of One-Pion Exchange and Power Counting
• Nucleon-Nucleon Scattering from Effective Field Theory
• Nuclear forces from chiral Lagrangians using the method of unitary transformation I: Formalism
• Towards a Perturbative Theory of Nuclear Forces
• Effective Theory of the Triton
• NNLO Corrections to Nucleon-Nucleon Scattering and Perturbative Pions
• Nuclear forces in the chiral limit
• Power counting with one-pion exchange
• A renormalisation-group treatment of two-body scattering
• Low Energy Expansion in the Three Body System to All Orders and the Triton Channel
• Singular Potentials and Limit Cycles
• Regularization, renormalization and "peratization" in effective field theory for two nucleons
• Perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering
• Renormalizing Chiral Nuclear Forces: Triplet Channels
• Renormalization of NN Interaction with Chiral Two Pion Exchange Potential. Non-Central Phases
• Renormalization of the Deuteron with One Pion Exchange
• Perturbative Renormalizability of Chiral Two Pion Exchange in Nucleon-Nucleon Scattering: P- and D-waves
• Chiral $3\pi$-exchange NN-potentials: results for representation invariant classes of diagrams
• Renormalization of the one-pion-exchange interaction
• The potential of effective field theory in NN scattering
• Chiral $2\pi$-exchange NN-potentials: Two-loop contributions
• Naive Dimensional Analysis for Three-Body Forces Without Pions
• Renormalization of Singular Potentials and Power Counting
• The three- and four-nucleon systems from chiral effective field theory
• Chiral dynamics of few- and many-nucleon systems
• Leading order relativistic chiral nucleon-nucleon interaction
• On the renormalization of the one-pion exchange potential and the consistency of Weinberg's power counting
• Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves
• Renormalization of Singlet NN-Scattering with One Pion Exchange and Boundary Conditions
• Wilsonian renormalization group versus subtractive renormalization in effective field theories for nucleon--nucleon scattering
• The Power Of Effective Field Theories In Nuclei: The Deuteron, NN Scattering and Electroweak Processes
• Effective chiral theory of nucleon-nucleon scattering
• Power Counting and Wilsonian Renormalization in Nuclear Effective Field Theory
• Removing Pions from Two-Nucleon Effective Field Theory
• Efimov effect from functional renormalization
• Recursive renormalization of the singlet one-pion-exchange plus point-like interactions
• Testing Low Energy Theorems in Nucleon-Nucleon Scattering
• Power Counting in Peripheral Partial Waves: The Singlet Channels
• About the Equivalence of Cut-off and Renormalised Effective Field Theories
• Two-pion exchange nucleon-nucleon potential:O(q^4) relativistic chiral expansion
• On the effectiveness of effective field theory in peripheral nucleon-nucleon scattering
• Relativistic $O(q^4)$ two-pion exchange nucleon-nucleon potential: configuration space
• Consistency of the effective-field-theory approach to the nucleon-nucleon interaction problem revisited
• Renormalization of ${}^1{S}_0$ NN scattering amplitude in effective field theory
• Nucleon-nucleon scattering within a multiple subtractive renormalization approach
• Anomalous dimensions determine the power counting -- Wilsonian RG analysis of nuclear EFT --
• The renormalisation group and nuclear forces
• NN scattering in higher derivative formulation of baryon chiral perturbation theory
• Renormalization of the three-boson system with short-range interactions revisited
• ${}^1{S}_0$ nucleon-nucleon scattering in the modified Weinberg approach
• Bakamjian-Thomas mass operator for the few-nucleon system from chiral dynamics
• Wilsonian renormalization group analysis of nonrelativistic three-body systems without introducing dimerons

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• Nuclear effective field theory: status and perspectives
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Hyperon-nucleon interaction within chiral effective field theory revisited
• What is ab initio in nuclear theory?
• Accurate relativistic chiral nucleon-nucleon interaction up to NNLO
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Parity- and time-reversal-violating nuclear forces
• Power counting in chiral effective field theory and nuclear binding
• Spin partners $W_{bJ}$ from the line shapes of the $Z_b(10610)$ and $Z_b(10650)$
• How to renormalize integral equations with singular potentials in effective field theory
• Can chiral EFT give us satisfaction?
• Towards baryon-baryon scattering in manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory
• Nucleon-nucleon interaction in chiral EFT with a finite cutoff: explicit perturbative renormalization at next-to-leading order
• Lambda-nucleon scattering in baryon chiral perturbation theory
• Do we know how to count powers in pionless and pionful effective field theory?
• Strong CP violation in nuclear physics
• Bayesian Analysis of $\chi$EFT at Leading Order in a Modified Weinberg Power Counting Approach
• Comment on "How (not) to renormalize integral equations with singular potentials in effective field theory"
• Renormalizability of leading order covariant chiral nucleon-nucleon interaction
• Reply to "Comment on "How (not) to renormalize integral equations with singular potentials in effective field theory"
• Effective field theory for shallow P-wave states
• Improved description of light nuclei through chiral effective field theory at leading order
• Perturbative computations of neutron-proton scattering observables using renormalization-group invariant $\chi$EFT up to N${}^3$LO
• Removing the Wigner bound in non-perturbative effective field theory
• A further study on the renormalization group aspect of perturbative corrections
• 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
• Renormalization of proton-proton fusion in chiral effective field theory
• Resonance parameters of the vector charmoniumlike state $G(3900)$
• Reexamination of antinucleon-nucleon interactions in covariant chiral effective field theory
• Low-energy theorems for neutron-proton scattering in $\chi$EFT using a perturbative power counting
• Regulator constraints for the perturbative renormalizability of attractive triplets
• Reexamining the perturbative renormalizability of the coupled triplets
• Renormalization of NN Chiral EFT, my personal mixed feelings
• Worldline Monte Carlo method for few body nuclear physics
• Residual cut-off dependence and power counting: the deuteron as a case study
• Cutoff effects in Hartree-Fock calculations at leading order of chiral effective field theory
• Auxiliary counterterms and their role in effective field theory
• Symmetries of the nucleon-nucleon $S$-matrix and effective field theory expansions
• Renormalization of One-Pion Exchange in Higher Partial Waves in Chiral Effective Field Theory for Antinucleon-Nucleon System