Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory

Abstract

We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the ∆(1232) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.

Chiral dynamics of/with unstable particles

“…Last but not least, the resulting phase shifts are found to be in a very good agreement with the ones determined within the project B.3 in the framework of Roy-Steiner (RS) equations, where detailed error estimates of all input quantities, the solution procedure and truncations was performed [27][28][29]. As a representative example, we show in in Fig.…”

“…5 our predictions for selected S-and P-waves along with the estimated truncation errors in comparison with the results from Ref. [27].…”

“…Phase shifts obtained from the Δ-full covariant ChPT at leading one-loop order. Dots with error bars stand for the RS phase shifts [27] while circles without error bars represent the phase shifts from the George Washington partial wave analysis [32]. The solid (red) line represents the result of Fit III of Ref.…”

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

“…Tree and one-loop diagrams up to order O(p 3 ) contributing to the πN N vertex function are shown in figure 5. The result up to leading one-loop order can be written as 16) where g (2),loop πN represents the very lengthy loop contribution which is not given explicitly in this paper (also the loop contributions to g πN ∆ coupling, discussed below). The coupling g πN is renormalized in the EOMS scheme and we have checked that the divergences and PCBTs from the loop contributions can indeed be canceled by counter terms generated by g and d 18 − 2d 16 .…”

“…[6][7][8][9][10][11][12][13]). Roy-Steiner equations for the pion-nucleon scattering have been also analysed recently [14][15][16][17]. In the low-energy region a systematic and powerful tool to study πN scattering is provided by chiral perturbation theory (ChPT) [18][19][20][21].…”