Negative parity $\Lambda$ and $\Sigma$ resonances coupled to pseudoscalar and vector mesons

Abstract

An exploration of the dynamically generated $\Lambda$ and $\Sigma$ resonances has been made in the vector meson-baryon (VB) systems coupled to pseudoscalar meson-baryon (PB) channels. The VB interactions are obtained from the Lagrangians written within the hidden local symmetry which, in addition to Yukawa-type vector-baryon-baryon (VBB) vertices, naturally gives rise to a contact interaction. Using the VBB vertices, we calculate the $t$-, $s$- and $u$-channel diagrams considering the octet baryon exchange in the latter two cases. For the PB channels we rely on the the Weingberg-Tomozawa interactions and calculate the PB $\leftrightarrow$ VB transition amplitudes extending the Kroll-Ruderman theorem by replacing the photon by the vector mesons. In addition to the low-lying $\Lambda (1405)$, $\Lambda (1670)$ found in previous works, we find resonances which coincide well with: $\Lambda (2000)$, $\Sigma (1750)S_{11}$, $\Sigma (1940)D_{13}$, $\Sigma (2000)S_{11}$ and predict three ${\Lambda }^{\ast }$'s with $J^{\pi }=3/2^{-}$ and masses: $1754-i2$ MeV, $1862-i33$ MeV, $2139-i14$ MeV together with a broad $1/2^{-}$ ${\Sigma }^{\ast }$ with mass $\sim$ 1430 MeV. We find that most of these next-to-low-lying states couple weakly with the pseudoscalar mesons, which implies that it is important to study the reactions with VB final states in order to obtain a reliable information on the properties of such resonances.