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

Abstract : We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the $S$- and $P$-partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the $D$ and $F$ waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation.
Document type :
Journal articles
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http://hal.in2p3.fr/in2p3-01335911
Contributor : Sophie Heurteau <>
Submitted on : Wednesday, June 22, 2016 - 2:46:47 PM
Last modification on : Wednesday, September 16, 2020 - 4:09:25 PM

### Citation

De-Liang Yao, D. Siemens, V. Bernard, E. Epelbaum, A. M. Gasparyan, et al.. Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances. Journal of High Energy Physics, Springer Verlag (Germany), 2016, 05, pp.038. ⟨10.1007/JHEP05(2016)038⟩. ⟨in2p3-01335911⟩

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