The Three-body Force and the Tetraquark Interpretation of Light Scalar Mesons

Abstract

We study the possible tetraquark interpretation of light scalar meson states $a_0(980)$, $f_0(980)$, $\kappa$, $\sigma$ within the framework of the non-relativistic potential model. The wave functions of tetraquark states are obtained in a space spanned by multiple Gaussian functions. We find that the mass spectra of the light scalar mesons can be well accommodated in the tetraquark picture if we introduce a three-body quark interaction in the quark model. Using the obtained multiple Gaussian wave functions, the decay constants of tetraquarks are also calculated within the ``fall apart'' mechanism.