Regularization, Renormalization and Range: The Nucleon-Nucleon Interaction from Effective Field Theory

Abstract

Regularization and renormalization is discussed in the context of low-energy effective field theory treatments of two or more heavy particles (such as nucleons). It is desirable to regulate the contact interactions from the outset by treating them as having a finite range. The low energy physical observables should be insensitive to this range provided that the range is of a similar or greater scale than that of the interaction. Alternative schemes, such as dimensional regularization, lead to paradoxical conclusions such as the impossibility of repulsive interactions for truly low energy effective theories where all of the exchange particles are integrated out. This difficulty arises because a nonrelativistic field theory with repulsive contact interactions is trivial in the sense that the $S$ matrix is unity and the renormalized coupling constant zero. Possible consequences of low energy attraction are also discussed. It is argued that in the case of large or small scattering lengths, the region of validity of effective field theory expansion is much larger if the contact interactions are given a finite range from the beginning.

7 pages

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Cited by in corpus (41)

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• Chiral 2pi exchange at order four and peripheral NN scattering
• Neutrino-Deuteron Scattering in Effective Field Theory at Next-to-Next-to Leading Order
• Coulomb Effects in Low Energy Proton-Proton Scattering
• Non-perturbative regularization and renormalization: simple examples from non-relativistic quantum mechanics
• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• Short-range interactions in an effective field theory approach for nucleon-nucleon scattering
• Low Energy Theorems For Nucleon-Nucleon Scattering
• Elastic and Inelastic Neutrino-Deuteron Scattering in Effective Field Theory
• The Polarizability of the Deuteron
• Parity Violation in Effective Field Theory and the Deuteron Anapole Moment
• An effective field theory for coupled-channel scattering
• Gamma-Deuteron Compton Scattering in Effective Field Theory
• Testing Low Energy Theorems in Nucleon-Nucleon Scattering
• Constraining the Leading Weak Axial Two-body Current by SNO and Super-K
• The Delta-Delta Intermediate State in 1S0 Nucleon-Nucleon Scattering From Effective Field Theory
• About the Equivalence of Cut-off and Renormalised Effective Field Theories
• Constraints on Two-Body Axial Currents from Reactor Antineutrino-Deuteron Breakup Reactions
• Chiral NN model and Ay puzzle
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• Scheming in Dimensional Regularization
• Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
• NNLO Calculation of Two-Nucleon Scattering in EFT for a Two Yukawa Toy Model
• Constraints on Axial Two-Body Currents from Solar Neutrino Data
• Tensor Polarized Gamma-Deuteron Compton Scattering in Effective Field Theory
• Deuteron Compton Scattering in Effective Field Theory: Spin-Dependent Cross Sections and Asymmetries
• Drell-Hearn-Gerasimov Sum-Rule for the Deuteron in Nuclear Effective Field Theory
• Deuteron Compton Scattering in Effective Field Theory And Spin-Independent Nucleon Polarizabilities
• Dynamical symmetry breaking of $\lambda {\varphi }^4$ in two loop effective potential
• What hath Weinberg wrought? Reflections on what Weinberg's papers on 'Nuclear Forces from Chiral Lagrangians' did and did not accomplish
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• Lattice methods and effective field theory