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The energies of the low-lying isoscalar and isovector ud anti-s anti-sconfigurations with spin-parity J^P=0^+, 1^+, and 2^+ are calculated in anon-relativistic constituent quark model by use of the variational method. Thecontributions of various parts of the quark-quark interacting potentialsincluding the s-channel interaction are investigated, and the effect ofdifferent forms of confinement potential is examined. The model parameters aredetermined by the same method as in our previous work, and they still cansatisfactorily describe the nucleon-nucleon scattering phase shifts and thehyperon-nucleon cross sections. The parameters of the s-channel interaction arefixed by the masses of K and K^* mesons, for which the size parameter is takento be two possible values. When it is chosen as the same as baryons', thenumerical results show that the masses of all the ud anti-s anti-sconfigurations are higher than the corresponding meson-meson thresholds. Butwhen the size parameter for the K and K^* mesons is adjusted to be smaller thanthat 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 avery small KK^* component and the interaction matrix elements between thisstate and KK^* is comparatively small, thus its coupling to the KK^* channelwill consequently be weak and it might be regarded as a possible tetraquarkcandidate.

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