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arXiv · hep-ph/9611253

Aspects of chiral pion-nucleon physics

V. Bernard·N. Kaiser·Ulf-G. Meißner
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Abstract

The next-to-leading order chiral pion-nucleon Lagrangian contains seven finite low-energy constants. Two can be fixed from the nucleon anomalous magnetic moments and another one from the quark mass contribution to the neutron-proton mass splitting. We find a set of nine observables, which to one loop order do only depend on the remaining four dimension two couplings. These are then determined from a best fit. We also show that their values can be understood in terms of resonance exchange related to $Δ$ excitation as well as vector and scalar meson exchange. In particular, we discuss the role of the fictitious scalar-isoscalar meson. We also investigate the chiral expansion of the two P-wave scattering volumes $P_1^-$ and $P_2^+$ as well as the isovector S-wave effective range parameter $b^-$. The one-loop calculation is in good agreement with the data. The difference $P_1^- - P_2^+$ signals chiral loop effects in the $πN$ P-waves. The calculated D- and F-wave threshold parameters compare well with the empirical values.

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V. Bernard, N. Kaiser, Ulf-G. Meißner. 1997-01-28. Aspects of chiral pion-nucleon physics. https://doi.org/10.1016/s0375-9474(97)00021-3

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