Why Ξ(1690) and Ξ(2120) are so narrow

Abstract

The Ξ baryons are expected to be naturally narrower as compared to their nonstrange and strange counterparts since they have only one light quark and, thus, their decay involves producing either a light meson and doubly strange baryon or both meson and baryon with strangeness which involves, relatively, more energy. In fact, some Ξ's have full widths of the order of even 10-20 MeV when, in principle, they have a large phase space to decay to some open channels. Such is the case of Ξ(1690), for which the width has been found to be of the order of 10 MeV in the latest BABAR and BELLE data. In this manuscript we study why some Ξ's are so narrow. Based on a coupled channel calculation of the pseudoscalar meson-baryon and vector meson-baryon systems with chiral and hidden local symmetry Lagrangians, we find that the answer lies in the intricate hadron dynamics. We find that the known mass, width, spin-parity and branching ratios of Ξ(1690) can be naturally explained in terms of coupled channel meson-baryon dynamics. We find another narrow resonance which can be related to Ξ(2120). We also look for exotic states Ξ + and Ξ −− but find none. In addition we provide the cross sections forKΛ,KΣ → πΞ which can be useful for understanding the enhanced yield of Ξ reported in recent studies of heavy ion collisions.

Ξ(1690)− production in the K−p→

“…For the φ production, s-channel Λ, u-channel proton, and t-channel K − exchange diagrams are included in the calculation, as shown in Fig. 1 Here, we assume that the Ξ(1690) − has a spin-parity of J p = 1/2 − , as suggested by theoretical works [5,8] and reported by the BaBar Collaboration [13]. To compute the invariant amplitudes for the K − p → K + K − Λ reaction, we use the effective Lagrangian densities for the interaction vertices as follows:…”

“…Three-star states include Ξ(1690) − , Ξ(1820)(J p = 3/2 − ), Ξ(1950), and Ξ(2030). The third state of Ξ has not yet been confirmed between Ξ(1620) and Ξ(1690) − , and theoretical model predictions are still controversial [2][3][4][5][6][7][8]. The existence of Ξ(1620) near ΛK is dubious and requires further experimental confirmation with higher statistics.…”

Ξ(1690)− Resonance Production via K−p → K+K−Λ

“…S = −2 three-star baryon states include Ξ(1690) − , Ξ(1820)(J p = 3/2 − ), Ξ(1950), and Ξ(2030). The third state of Ξ has not yet been confirmed between Ξ(1620) and Ξ(1690) − [2][3][4][5][6][7][8]. Ξ(1690) − is near the ΣK threshold, and its existence has been firmly established by several experiments [9][10][11][12].…”

“…Here, we assume that the Ξ(1690) − has a spin-parity of J p = 1/2 − , as suggested by theoretical works [5,8] and reported by the BaBar Collaboration [13]. To compute the invariant amplitudes for the K − p → K + K − Λ reaction, we use the effective Lagrangian densities for the interaction vertices as follows:…”

“…The coupling constants for the s-wave resonances, Λ(1405) and Λ(1670), are obtained from the chiral unitary model [16], where the resonances are generated dynamically by the coupled-channel method with the Weinberg-Tomozawa (WT) chiral interaction. The couplings for Ξ(1690) and Ξ(1820) are estimated by ChUM [8] and the SU(6) relativistic quark model [5], respectively. Regarding the coupling constants with two hyperon resonances, such as g KΛ * Ξ * and g KΣ * Ξ * , there is no experimental nor theoretical information available.…”