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Roy-Steiner equations for pion-nucleon scattering | | C. Ditsche
; M. Hoferichter
; B. Kubis
; U.-G. Meißner
; | | Date: |
21 Mar 2012 | | Abstract: | 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
$pipi oar NN$ partial waves into the form of a Muskhelishvili-Omn’es
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. | | Source: | arXiv, 1203.4758 | | Services: | Forum | Review | PDF | Favorites | |
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