Aspects of the ETH model of the pion-nucleon interaction

Abstract

The ETH model of the pion-nucleon ($\pi N$) interaction contains $t$-channel $\sigma$- and $\rho$-exchange graphs, as well as the $s$- and $u$-channel contributions with the well-established $s$ and $p$ baryon states with masses below $2$ GeV as virtual particles; the model amplitudes obey crossing symmetry and isospin invariance. In the present work, we give the analytical expressions for the model contributions to the $K$-matrix elements up to (and including) the $f$ waves. We also extract a new phase-shift solution after performing a partial-wave analysis of meson-factory ${\pi }^{\pm }p$ elastic-scattering data below $100$ MeV; included in our results now are also the effects of the variation of the $\sigma$-meson mass in the interval which is currently recommended by the Particle-Data Group. Finally, we revisit the subject of the $\pi N$ $\Sigma$ term and, using the model amplitudes, obtain $\Sigma =72.4\pm 3.1$ MeV. Our prediction agrees well with the result extracted with Olsson's method, after a few flaws in his paper [Phys. Lett. B 482 (2000) 50] were corrected.

66 pages, 8 figures

References in corpus (8)

• Extended Partial-Wave Analysis of piN Scattering Data
• Precision calculation of the pi^- deuteron scattering length and its impact on threshold pi-N scattering
• Improved description of the $\pi N$-scattering phenomenology in covariant baryon chiral perturbation theory
• Nucleon mass and sigma term from lattice QCD with two light fermion flavors
• On the size of the sigma meson and its nature
• Phase-shift analysis of low-energy ${\pi }^{\pm }p$ elastic-scattering data
• Determination of the s-wave pion-nucleon threshold scattering parameters from the results of experiments on pionic hydrogen
• Scalar and axial-vector mesons

Cited by in corpus (5)

• Roy-Steiner-equation analysis of pion-nucleon scattering
• The pion-nucleon sigma term from lattice QCD
• A brief history of the pion-nucleon coupling constant
• Systematic effects in the low-energy behavior of the current SAID solution for the pion-nucleon system
• Comparison of results for the electromagnetic form factors of the proton at low $Q^2$