Meson–baryon scattering in resummed baryon chiral perturbation theory using time-ordered perturbation theory

Abstract

Integral equations for meson-baryon scattering amplitudes are obtained by utilizing time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of baryon chiral perturbation theory. Effective potentials are defined as sums of two-particle irreducible contributions of time-ordered diagrams and the scattering amplitudes are obtained as solutions of integral equations. Ultraviolet renormalizability is achieved by solving integral equations for the leading order amplitude and including higher order corrections perturbatively. As an application of the developed formalism, pion-nucleon scattering is considered.

The $${\varvec{\Lambda (1405)}}$$ in resummed chiral effective field theory

“…As shown in Ref. [60], our approach can be successfully applied to the pion-nucleon system. In the current work, we apply this framework to study meson-baryon systems with strangeness S = −1 at LO and investigate the nature of the S-wave (1405) resonance.…”

“…In this section we briefly outline the theoretical framework of our work, which is the three-flavor extension of the SU(2) formalism developed in Ref. [60].…”

“…The details of the formalism can be found in Ref. [60]. To keep the paper self-contained we provide below the basic ingredients of the three-flavor extension used here.…”

“…This scheme corresponds to including the contributions of an infinite number of meson-baryon counter-terms (details can be found in Refs. [60,61]). While it is, in principle, possible to generalize the applied subtractive scheme to arbitrary kinematical expansion points instead of considering an expansion about the threshold, see Ref.…”

“…Recently we have proposed a renormalizable approach to study meson-baryon scattering by utilizing time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of chiral perturbation theory [60]. Effective potentials are defined as the sums of all possible two-particle irreducible time-ordered diagrams, and the integral equations for the meson-baryon scattering amplitudes are derived in time-ordered perturbation theory.…”