Regularization, renormalization and "peratization" in effective field theory for two nucleons

Abstract

We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, renormalization scheme dependence of the scattering amplitude can only be eliminated up to the order the calculations are performed. We further consider an effective theory for an exactly solvable quantum mechanical model which possesses a long- and short-range interaction to simulate pionful effective field theory. We discuss the meaning of low-energy theorems in this model and demonstrate their validity in calculations with a finite cutoff $\Lambda$ as long as it is chosen of the order of the hard scale in the problem. Removing the cutoff by taking the limit $\Lambda \to \infty$ yields a finite result for the scattering amplitude but violates the low-energy theorems and is, therefore, not compatible with the effective field theory framework.

22 pages, 2 figures, to appear in Eur. Phys. J. A

References in corpus (4)

• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• Renormalization of Singular Potentials and Power Counting
• Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory
• Renormalization of NN Interaction with Relativistic Chiral Two Pion Exchange

Cited by in corpus (98)

• Chiral effective field theory and nuclear forces
• Nuclear effective field theory: status and perspectives
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Three-body forces: From cold atoms to nuclei
• Consequences of Heavy Quark Symmetries for Hadronic Molecules
• Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Local chiral effective field theory interactions and quantum Monte Carlo applications
• The Heavy Quark Spin Symmetry Partners of the X(3872)
• Signatures of three-nucleon interactions in few-nucleon systems
• Symmetric nuclear matter with chiral three-nucleon forces in the self-consistent Green's functions approach
• Perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering
• Renormalizing Chiral Nuclear Forces: Triplet Channels
• Perturbative Renormalizability of Chiral Two Pion Exchange in Nucleon-Nucleon Scattering: P- and D-waves
• Short-range nuclear forces in singlet channels
• Heavy hadronic molecules with pion exchange and quark core couplings: a guide for practitioners
• Chiral dynamics of few- and many-nucleon systems
• Deriving the existence of $B{\bar{B}}^{\ast }$ bound states from the X(3872) and Heavy Quark Symmetry
• Power Counting of Contact-Range Currents in Effective Field Theory
• Weinberg's approach to nucleon-nucleon scattering revisited
• Non-perturbative methods for a chiral effective field theory of finite density nuclear systems
• Renormalizing Chiral Nuclear Forces: A Case Study of 3P0
• Nonperturbative renormalization of the chiral nucleon-nucleon interaction up to next-to-next-to-leading order
• How (not) to renormalize integral equations with singular potentials in effective field theory
• Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves
• The Time-Reversal- and Parity-Violating Nuclear Potential in Chiral Effective Theory
• Wilsonian renormalization group versus subtractive renormalization in effective field theories for nucleon--nucleon scattering
• New Ideas in Constraining Nuclear Forces
• First-principle calculations of Dark Matter scattering off light nuclei
• The Theory of Parity Violation in Few-Nucleon Systems
• Power Counting and Wilsonian Renormalization in Nuclear Effective Field Theory
• Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order
• Power Counting in Peripheral Partial Waves: The Singlet Channels
• Parity- and time-reversal-violating nuclear forces
• Power counting in chiral effective field theory and nuclear binding
• Perturbative $NN$ scattering in chiral effective field theory
• Infinite-cutoff renormalization of the chiral nucleon-nucleon interaction at N3LO
• Low-energy theorems for nucleon-nucleon scattering at unphysical pion masses
• Strangeness $S=-1$ hyperon-nucleon scattering in covariant chiral effective field theory
• Hidden charm molecules in finite volume
• Renormalization of the leading-order chiral nucleon-nucleon interaction and bulk properties of nuclear matter
• The multiple-scattering series in pion-deuteron scattering and the nucleon-nucleon potential: perspectives from effective field theory
• How to renormalize integral equations with singular potentials in effective field theory
• Towards a high precision calculation for the pion-nucleus scattering lengths
• Low-energy theorems for nucleon-nucleon scattering at $M_{\pi }=450$ MeV
• Towards baryon-baryon scattering in manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory
• Nucleon-nucleon interactions from dispersion relations: Elastic partial waves
• Deconstructing 1S0 nucleon-nucleon scattering
• Nucleon-nucleon scattering within a multiple subtractive renormalization approach
• The renormalisation group and nuclear forces
• Nucleon-nucleon interaction in chiral EFT with a finite cutoff: explicit perturbative renormalization at next-to-leading order
• Nature of $\mathbf{S}$-wave $\mathbf{NN}$ interaction and dibaryon production at nucleonic resonance thresholds
• Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
• Deuteron electromagnetic form factors in a renormalizable formulation of chiral effective field theory
• Do we know how to count powers in pionless and pionful effective field theory?
• Nucleon-Nucleon Interactions from Dispersion Relations: Coupled Partial Waves
• The N/D method with non-perturbative left-hand-cut discontinuity and the ${}^1{S}_0$ $NN$ partial wave
• A Consistency Test of EFT Power Countings from Residual Cutoff Dependence
• Description of light nuclei in pionless effective field theory using the stochastic variational method
• Effective range corrections from effective field theory with di-baryon fields and perturbative pions
• To the nature of nuclear force
• Nucleon-Nucleon scattering from the dispersive N/D method: next-to-leading order study
• Renormalization of chiral two pion exchange NN interactions with delta excitations: correlations in the partial wave expansion
• Power counting for nuclear forces in chiral effective field theory
• Power counting and renormalization group invariance in the subtracted kernel method for the two-nucleon system
• Bayesian Analysis of $\chi$EFT at Leading Order in a Modified Weinberg Power Counting Approach
• Renormalizability of leading order covariant chiral nucleon-nucleon interaction
• Effective field theory for shallow P-wave states
• Two-nucleon scattering in a modified Weinberg approach with a symmetry-preserving regularization
• Improved description of light nuclei through chiral effective field theory at leading order
• A new EFT approach to NN scattering problem
• Effective short-range interaction for spin-singlet P-wave nucleon-nucleon scattering
• Perturbative computations of neutron-proton scattering observables using renormalization-group invariant $\chi$EFT up to N${}^3$LO
• Self-consistent Green's functions with three-body forces
• Magnetic moments of $A=3$ nuclei with chiral effective field theory operators
• 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
• Towards modeling the short-range interactions of hidden/open charm pentaquark molecular states
• High-precision nuclear forces from chiral EFT: State-of-the-art, challenges and outlook
• Constraining the $DD{D}^{\ast }$ three-body bound state via the $Z_c(3900)$ pole
• Non-perturbative methods for NN singular interactions
• Properties of dibaryons in nuclear medium
• Renormalization of proton-proton fusion in chiral effective field theory
• Neutral pion photoproduction off 3H and 3He in chiral perturbation theory
• Low-energy theorems for neutron-proton scattering in $\chi$EFT using a perturbative power counting
• Calculations for nuclear matter and finite nuclei within and beyond energy--density--functional theories through interactions guided by effective field theory
• Recent Progress in the Theory of Nuclear Forces
• $NN$ scattering in ${}^3{S}_1{-}^3{D}_1$ channels of EFT ($/\pi$)
• Regulator constraints for the perturbative renormalizability of attractive triplets
• Reexamining the perturbative renormalizability of the coupled triplets
• Threshold neutral pion photoproduction off the tri-nucleon to O(q^4)
• Effective range expansion in various scenarios of EFT($\notpi$)
• Renormalization of NN Chiral EFT, my personal mixed feelings
• Renormalisation-group analysis of electromagnetic couplings in the pionless effective field theory
• Covariant propagator and chiral power counting
• Auxiliary counterterms and their role in effective field theory
• Renormalization of One-Pion Exchange in Higher Partial Waves in Chiral Effective Field Theory for Antinucleon-Nucleon System
• Anomalous mapping between pionfull and pionless EFT's