Roy-Steiner equations for pion-nucleon scattering

  • C. DitscheEmail author
  • M. Hoferichter
  • B. Kubis
  • U.-G. Meißner


Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and unitarity relations required for the lowest partial waves. In order to suppress the dependence on the high energy regime we also consider once- and twice-subtracted versions of the equations, where we identify the subtraction constants with subthreshold parameters. Assuming Mandelstam analyticity we determine the maximal range of validity of these equations. As a first step towards the solution of the full system we cast the equations for the \(\pi \pi \to \overline N N\) partial waves into the form of a Muskhelishvili-Omnès problem with finite matching point, which we solve numerically in the single-channel approximation. We investigate in detail the role of individual contributions to our solutions and discuss some consequences for the spectral functions of the nucleon electromagnetic form factors.


Chiral Lagrangians QCD 


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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • C. Ditsche
    • 1
    Email author
  • M. Hoferichter
    • 1
  • B. Kubis
    • 1
  • U.-G. Meißner
    • 1
    • 2
  1. 1.Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical PhysicsUniversität BonnBonnGermany
  2. 2.Institut für Kernphysik, Institute for Advanced Simulation, and Jülich Center for Hadron PhysicsForschungszentrum JülichJülichGermany

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