Abstract
Recent calculations of the pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit delta resonances are presented. Two-loop results of the widths of the Δ and Roper resonances are discussed in the framework of an effective field theory with nucleons, pions and the Roper and delta resonances as dynamical degrees of freedom.
Highlights
Usage of chiral effective field theory (EFT) is based on a very well motivated assumption that quantum chromodynamics (QCD) is a correct theory of the strong interaction
Based on the symmetries of QCD, chiral EFT aims at reproducing the S -matrix of QCD in low-energy region
Chiral EFT provides with a systematic expansion of physical quantities in powers of (small scale(s))/(large scale(s))
Summary
Usage of chiral effective field theory (EFT) is based on a very well motivated assumption that quantum chromodynamics (QCD) is a correct theory of the strong interaction. We present recent results of two-loop calculations of the widths of the ∆ and Roper resonances and a one-loop calculation of the pion-nucleon scattering in covariant baryon chiral perturbation theory (BChPT) with explicit delta resonances. For diagrams involving only pion and nucleon lines, we use the standard power counting of Refs. For diagrams with delta lines we apply the power counting of Ref. For s → m2∆ delta-propagator diverges, we need to sum up self-energy insertions, i.e. consider the dressed propagator Dμν(k) ∼ 1/(k/ − m∆ − Σ(k)) ∼ 1/(−Σ(k)) ∼ 1/p3, unless, as we did in our work, one uses the complex-mass scheme where the undressed propagator contains the width of the unstable particle and the re-summation is not necessary. To renormalize the loop diagrams we applied EOMS renormalization scheme of Refs. [8, 9] and its generalization for delta [10]
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