Masses of Heavy and Light Scalar Tetraquarks in a Non-relativistic Quark Model

Abstract

Scalar tetraquark states are studied within the diquark-antidiquark picture in a non-relativistic approach. We consider two types of confining potentials, a quadratic and a linear one, to which we also add spin-spin, isospin-isospin, and spin-isospin interactions. We calculate the masses of the scalar diquarks and of the ground-state open and hidden charmed and bottom scalar tetraquarks. Our results indicate that the scalar resonances $D_{0}^{\ast}(2400)$ and $D_{s}(2632)$ have a sizable tetraquark amount in their wave function, while, on the other hand, it turns out that the scalar states $D_{s0}^{\ast}(2317)$ and $X(3915)$ should not be considered as being predominantly diquark-antidiquark bound states. We also investigate the masses of light scalar diquarks and tetraquarks, which are comparable to the measured masses of the light scalar mesons.