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Pion-nucleon scattering in chiral perturbation theory (I): Isospin-symmetric case

Authors
Journal
Nuclear Physics A
0375-9474
Publisher
Elsevier
Publication Date
Volume
640
Issue
2
Identifiers
DOI: 10.1016/s0375-9474(98)00452-7
Keywords
  • Hadronic Physics

Abstract

Abstract We construct the complete effective chiral pion-nucleon Lagrangian to third order in small momenta based on relativistic chiral perturbation theory. We then perform the so-called heavy baryon limit and construct all terms up to and including order 1 m 2 with fixed and free coefficients. As an application, we discuss in detail pion-nucleon scattering. In particular, we show that for this process andto third order, the 1 m expansion of the Born graphs calculated relativistically can be recovered exactly in the heavy baryon approach without any additional momentum-dependent wave function renormalization. We fit various empirical phase shifts for pion laboratory momenta between 50 and 100 MeV. This leads to a satisfactory description of the phase shifts up to momenta of about 200 MeV. We also predict the threshold parameters, which turn out to be in good agreement with the dispersive analysis. In particular, we can sharpen the prediction for the isovector S-wave scattering length, 0.083 M π −1 ⩽ a 0+ − ⩽ 0.093 M π −1. We also consider the subthreshold parameters and give a short comparison to other calculations of πN scattering in chiral perturbation theory or modifications thereof.

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