Abstract
Based on the recently proposed Roy-Steiner equations for pion-nucleon (πN) scattering [1], we derive a system of coupled integral equations for the \( \pi \pi \to \overline N N \) and \( \overline K K \to \overline N N \) S-waves. These equations take the form of a two-channel Muskhelishvili-Omnès problem, whose solution in the presence of a finite matching point is discussed. We use these results to update the dispersive analysis of the scalar form factor of the nucleon fully including \( \overline K K \) intermediate states. In particular, we determine the correction \( {\Delta_{\sigma }} = \sigma \left( {2M_{\pi }^2} \right) - {\sigma_{{\pi N}}} \), which is needed for the extraction of the pion-nucleon σ term from πN scattering, as a function of pion-nucleon subthreshold parameters and the πN coupling constant.
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Hoferichter, M., Ditsche, C., Kubis, B. et al. Dispersive analysis of the scalar form factor of the nucleon. J. High Energ. Phys. 2012, 63 (2012). https://doi.org/10.1007/JHEP06(2012)063
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DOI: https://doi.org/10.1007/JHEP06(2012)063