Spin, Parity, and Nature of theΞ(1620)Resonance

Abstract

Using a unitary extension of chiral perturbation theory with a lowest-order s-wave SU(3) chiral Lagrangian we study low-energy meson-baryon scattering in the strangeness S=-2 sector. A scattering-matrix pole is found around 1605 MeV which corresponds to an s-wave Xi resonance with J(P)=1/2(-). We identify this resonance with the Xi(1620) state, quoted by the Particle Data Group with I=1/2 but with unknown spin and parity. The addition of the S=-2 state to the recently computed Lambda(1670), Sigma(1620), and N(1535) states completes the octet of J(P)=1/2(-) resonances dynamically generated in this chiral unitary approach.

Dynamical generation of hyperon resonances

“…(1) around the Λ(1405) and the Λ(1670) for isospin I = 0 and around the Σ(1620) in I = 1. The same approach in S = −2 leads to the resonance Ξ(1620) [ 11] and in S = 0 to the N * (1535) [ 12,13], this latter one also generated dynamically in Ref. [ 12].…”

Quark-mass dependence of baryon resonances

“…Using the subtraction scales as free parameters, as advocated in [25,26,16], may be viewed as promoting the counter terms of chiral order Q 3 to be unnaturally large. If the subtraction scales are chosen far away from their natural values (7) the resulting loop functions are in conflict with chiral power counting rules [12].…”

“…A detailed test of the naturalness of the Q 3 counter terms was performed within the χ-BS(3) scheme [2] demonstrating good convergence in the channels studied without any need for promoting the counter terms of order Q 3 . Possible correction terms in the approach followed in [25,26,16] have so far not been studied systematically for meson-baryon scattering. Moreover, if the scheme advocated in [25,26,16] were applied in all eleven isospin strangeness sectors with J P = 1 2 − a total number of 26 subtraction parameters arise.…”

“…Selecting only the operators that are leading in the large-N c limit of QCD out of the ten Q 3 operators only four survive [2]. For consistency and before applying the approach of [25,26,16] to all isospin strangeness channels, it would be highly desirable to address the above mismatch of parameters. Our scheme has the advantage that once the parameters describing subleading effects are determined in a subset of sectors one has immediate predictions for all sectors (I, S).…”

Penta-Quark States with Strangeness, Hidden Charm and Beauty

“…On theoretical side, the unquenched quark model provides totally different predictions of 1/2 − strangeness baryons. For example, the classical quenched quark models [44] predict the 1/2 − Σ * and Ξ * to be around 1650 MeV and 1760 MeV, respectively, while the unquenched quark models expect them to be around 1400 MeV and 1550 MeV [3,4,13], or 1450 MeV and 1620 MeV [45][46][47], respectively. It is necessary to check the predictions of hyperon resonances in these unquenched quark models with new data.…”