Elastic pion-nucleon scattering in chiral perturbation theory: A fresh look

Abstract

Elastic pion-nucleon scattering is analyzed in the framework of chiral perturbation theory up to fourth order within the heavy-baryon expansion and a covariant approach based on an extended on-mass-shell renormalization scheme. We discuss in detail the renormalization of the various low-energy constants and provide explicit expressions for the relevant β-functions and the finite subtractions of the power-counting breaking terms within the covariant formulation. To estimate the theoretical uncertainty from the truncation of the chiral expansion, we employ an approach which has been successfully applied in the most recent analysis of the nuclear forces. This allows us to reliably extract the relevant low-energy constants from the available scattering data at low energy. The obtained results provide a clear evidence that the breakdown scale of the chiral expansion for this reaction is related to the ∆-resonance. The explicit inclusion of the leading contributions of the ∆-isobar is demonstrated to substantially increase the range of applicability of the effective field theory. The resulting predictions for the phase shifts are in an excellent agreement with the ones from the recent Roy-Steiner-equation analysis of pion-nucleon scattering. * dmitrij.siemens@rub.de †

Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

“…For more discussions on the choice of Λ b see ref. [77]. Now let us proceed with the details of the three different fits.…”

New insights on low energy $$\pi N$$ π N scattering amplitudes

“…Here we use the shadow pole location of N * (1440), which is the first resonance related to complicated couple-channel dynamics. 11 Since the chiral expansion is at the point s = u = M 2 + m 2 , t = 0, we set the distance between M 2 + m 2 and N * (1440) shadow pole location as the convergence radius r , and hence the cut-off on the left-hand cut is at…”

“…For instance, the low energy behavior of the π N elastic scattering amplitude, the pion nucleon σ -term and the relevant intermediate resonances, e.g., (1232), N * (1535) and N * (1440), have attracted sustained attentions, see, e.g., Refs. [3][4][5][6][7][8][9][10][11][12][13]. The N * (1535) and N * (1440) are of particular interest.…”

Meson-baryon scattering to one-loop order in heavy baryon chiral perturbation theory

“…[51]. In addition, the inclusion of the ∆ resonance substantially improves the convergence for πN scattering [52,53]. The calculations including these counterterm contributions in other channels and the ∆ resonance in πN channel will be done in forthcoming works.…”