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

Abstract

We study the unitarized meson–baryon scattering amplitude at leading order in the strangeness $$S=-1$$ S = - 1 sector using time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of chiral effective field theory. By solving the coupled-channel integral equations with the full off-shell dependence of the effective potential and applying subtractive renormalization, we analyze the renormalized scattering amplitudes and obtain the two-pole structure of the $$\Lambda (1405)$$ Λ ( 1405 ) resonance. We also point out the necessity of including higher-order terms.

Meson-baryon scattering and Λ(1405) in chiral effective field theory

“…The πΣ invariant mass spectrum is presented in Ref. [7], which is in good agreement with experimental data. Furthermore, we calculated the coupling strengths of the initial/final transition channels, and found that the two poles of Λ(1405) have different coupling natures: the lower pole couples predominantly to the πΣ channel, and the higher pole couples strongly to the KN channel.…”

“…Next, in Ref. [7] we extended the TOPT framework to the S = −1 meson-baryon scattering, which has four coupled channels: KN, πΣ, ηΛ, and KΞ. Using the LO effective potential, we exactly solved the coupled-channel scattering equation (Eq.…”

“…Here we briefly present the major ingredients of our framework, the details can be found in Refs. [6,7]. First is to obtain the coupled-channel scattering equations in TOPT,…”

“…where the definition of symbols can be found in Ref. [7], one can calculate the time-ordered diagrams shown in Fig. 1 to obtain the effective potential.…”

“…To avoid these approximations or obstacles, in this work, we tentatively propose a renormalized framework for meson-baryon scattering using TOPT with the covariant chiral Lagrangians [6,7], which accompanies the research line of baryon-baryon scattering in Refs. [8][9][10].…”