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Negative parity $Λ$ and $Σ$ resonances coupled to pseudoscalar and vector mesons

K. P. Khemchandani^1,*, A. Martínez Torres^2,†, H. Nagahiro^1,3,‡, and A. Hosaka^1,§

¹Research Center for Nuclear Physics (RCNP), Mihogaoka 10-1, Ibaraki 567-0047, Japan
²Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
³Department of Physics, Nara Women’s University, Nara 630-8506, Japan

^*kanchan@rcnp.osaka-u.ac.jp
^†amartine@yukawa.kyoto-u.ac.jp
^‡nagahiro@rcnp.osaka-u.ac.jp
^§hosaka@rcnp.osaka-u.ac.jp

Phys. Rev. D 85, 114020 – Published 12 June, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.114020

Abstract

An exploration of the dynamically generated $Λ$ and $Σ$ 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 Weinberg-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 $Λ (1405)$ , $Λ (1670)$ found in previous works, we find resonances which coincide well with $Λ (2000)$ , $Σ (1750) S_{11}$ , $Σ (1940) D_{13}$ , $Σ (2000) S_{11}$ and predict three $Λ^{*}$ ’s with $J^{π} = 3 / 2^{-}$ and masses $1754 - i 2 MeV$ , $1862 - i 33 MeV$ , $2139 - i 14 MeV$ together with a broad $1 / 2^{-}$ $Σ^{*}$ 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 reliable information on the properties of such resonances.

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References (33)

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Please notice that in some cases we have a phase difference of $i$ (or $- i$ ) with respect to the corresponding couplings mentioned in Ref. [24] in order to be consistent with the definitions given by Eqs. (16) and (17).

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Negative parity $Λ$ and $Σ$ resonances coupled to pseudoscalar and vector mesons

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References (33)

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Negative parity Λ and Σ resonances coupled to pseudoscalar and vector mesons

Abstract

Article Text

References (33)

Negative parity $Λ$ and $Σ$ resonances coupled to pseudoscalar and vector mesons