Low-lying ud anti-s anti-s configurations in a non-relativistic constituent quark model

TL;DR

This study calculates energies of low-lying ud anti-s anti-s configurations using a non-relativistic quark model, exploring potential contributions and parameter effects, and identifies a possible tetraquark candidate near the K*K* threshold.

Contribution

It introduces a detailed analysis of ud anti-s anti-s states in a non-relativistic quark model, considering various potential contributions and parameter choices, and suggests a candidate for a tetraquark state.

Findings

The masses of all configurations are above meson-meson thresholds when using baryon-sized parameters.

Adjusting the meson size parameter can lower the J^P=1^+ state below the K*K* threshold.

The J^P=1^+ state with I=0 has a small KK^* component and weak coupling to the KK^* channel.

Abstract

The energies of the low-lying isoscalar and isovector ud anti-s anti-s configurations with spin-parity J^P=0^+, 1^+, and 2^+ are calculated in a non-relativistic constituent quark model by use of the variational method. The contributions of various parts of the quark-quark interacting potentials including the s-channel interaction are investigated, and the effect of different forms of confinement potential is examined. The model parameters are determined by the same method as in our previous work, and they still can satisfactorily describe the nucleon-nucleon scattering phase shifts and the hyperon-nucleon cross sections. The parameters of the s-channel interaction are fixed by the masses of K and K^* mesons, for which the size parameter is taken to be two possible values. When it is chosen as the same as baryons', the numerical results show that the masses of all the ud anti-s anti-s configurations are higher than the corresponding meson-meson thresholds. But when the size parameter for the K and K^* mesons is adjusted to be smaller than that for the baryons, the ud anti-s anti-s configuration with I=0 and J^P=1^+ is found to lie lower than the K^*K^* threshold, furthermore, this state has a very small KK^* component and the interaction matrix elements between this state and KK^* is comparatively small, thus its coupling to the KK^* channel will consequently be weak and it might be regarded as a possible tetraquark candidate.