Testing Low Energy Theorems in Nucleon-Nucleon Scattering

Abstract

Low energy theorems have been derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading nontrivial order in an expansion based $Q$ counting, a scheme in which both $m_{\pi }$ and $1/a$ (where $a$ is the scattering length) are treated as small mass scales. Previous tests of these theorems based on coefficients extracted from scattering data indicate a pattern of gross violations which suggested serious problems for the perturbative treatment of pions implicit in $Q$ counting. We discuss the possibility that uncertainties associated with extracting the coefficients from the scattering data make such tests invalid. Here we show that errors in the s-wave phase shift extractions are sufficiently small to test direct test predictions from $Q$ counting at next to leading order. In particular we show that there exist low energy theorems for the sum of all terms in the effective range expansion beyond the first two which allow for precise tests. These low energy theorems fail badly which suggests that pionic aspects of $Q$ counting are not under control.

11 pages

Cited by in corpus (36)

• Modern Theory of Nuclear Forces
• Few-Nucleon Forces and Systems in Chiral Effective Field Theory
• Nuclear effective field theory: status and perspectives
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Regularization, renormalization and "peratization" in effective field theory for two nucleons
• Variation of Fundamental Couplings and Nuclear Forces
• A renormalisation group approach to two-body scattering in the presence of long-range forces
• Range Corrections to Doublet S-Wave Neutron-Deuteron Scattering
• Chiral dynamics of few- and many-nucleon systems
• How (not) to renormalize integral equations with singular potentials in effective field theory
• Renormalization of Singlet NN-Scattering with One Pion Exchange and Boundary Conditions
• Renormalization of NN-Scattering with One Pion Exchange and Boundary Conditions
• The NN scattering 3S1-3D1 mixing angle at NNLO
• Quartet S-wave p-d scattering in EFT
• Low-energy theorems for nucleon-nucleon scattering at unphysical pion masses
• The Long and Short of Nuclear Effective Field Theory Expansions
• How to renormalize integral equations with singular potentials in effective field theory
• Low-energy theorems for nucleon-nucleon scattering at $M_{\pi }=450$ MeV
• The Anapole Form Factor of the Deuteron
• Partially-Quenched Nucleon-Nucleon Scattering
• Consistency of the effective-field-theory approach to the nucleon-nucleon interaction problem revisited
• Deconstructing 1S0 nucleon-nucleon scattering
• Nucleon-nucleon scattering within a multiple subtractive renormalization approach
• Nucleon-nucleon interaction in chiral EFT with a finite cutoff: explicit perturbative renormalization at next-to-leading order
• Renormalization of the 1S0 One-Pion-Exchange NN Interaction in Presence of Derivative Contact Interactions
• Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
• Phases of QCD with nonvanishing isopin density
• Renormalization of $NN$ scattering: contact potential
• Effective range corrections from effective field theory with di-baryon fields and perturbative pions
• NN scattering in higher derivative formulation of baryon chiral perturbation theory
• Power counting and renormalization group invariance in the subtracted kernel method for the two-nucleon system
• Determination of Low-Energy Parameters of Neutron--Proton Scattering on the Basis of Modern Experimental Data from Partial-Wave Analyses
• Description of the two-nucleon system on the basis of the Bargmann representation of the S matrix
• Low-energy theorems for neutron-proton scattering in $\chi$EFT using a perturbative power counting
• Effective range expansion in various scenarios of EFT($\notpi$)
• Effective theory with dibaryons and perturbative pions