The Long and Short of Nuclear Effective Field Theory Expansions

Abstract

Nonperturbative effective field theory calculations for NN scattering seem to break down at rather low momenta. By examining several toy models, we clarify how effective field theory expansions can in general be used to properly separate long- and short-range effects. We find that one-pion exchange has a large effect on the scattering phase shift near poles in the amplitude, but otherwise can be treated perturbatively. Analysis of a toy model that reproduces 1S0 NN scattering data rather well suggests that failures of effective field theories for momenta above the pion mass can be due to short-range physics rather than the treatment of pion exchange. We discuss the implications this has for extending the applicability of effective field theories.

22 pages, 9 figures, references corrected, minor modifications

Cited by in corpus (22)

• Effective Field Theory for Few-Nucleon Systems
• Few-Nucleon Forces and Systems in Chiral Effective Field Theory
• Nuclear effective field theory: status and perspectives
• Renormalization of One-Pion Exchange and Power Counting
• Towards a Perturbative Theory of Nuclear Forces
• Rearranging Pionless Effective Field Theory
• Neutrino-Deuteron Scattering in Effective Field Theory at Next-to-Next-to Leading Order
• Range Corrections to Doublet S-Wave Neutron-Deuteron Scattering
• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• Towards complete leading-order predictions for neutrinoless double $\beta$ decay
• Determining the leading-order contact term in neutrinoless double $\mathbf{\beta }$ decay
• String Theory on AdS Orbifolds
• Proton-proton fusion in pionless effective theory
• The Two-Nucleon 1S0 Amplitude Zero in Chiral Effective Field Theory
• Improved convergence of chiral effective field theory for 1S0 of NN scattering
• Consistency of the effective-field-theory approach to the nucleon-nucleon interaction problem revisited
• Pions in the Pionless Effective Field Theory
• A Consistency Test of EFT Power Countings from Residual Cutoff Dependence
• Chiral potentials, perturbation theory, and the 1S0 channel of NN scattering
• A short review on the compositeness of the $X(3872)$
• Nucleon-nucleon scattering with perturbative pions: The uncoupled $P$-wave channels
• Symmetries of the nucleon-nucleon $S$-matrix and effective field theory expansions