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.

12 pages, 5 figures

References in corpus (11)

• Chiral effective field theory and nuclear forces
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Renormalization of Singular Potentials and Power Counting
• Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves
• Efimov effect from functional renormalization
• Nucleon-nucleon scattering within a multiple subtractive renormalization approach
• Anomalous dimensions determine the power counting -- Wilsonian RG analysis of nuclear EFT --
• NN scattering in higher derivative formulation of baryon chiral perturbation theory
• ${}^1{S}_0$ 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 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
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• 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"
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• 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
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• 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