AdS-QCD quark–antiquark potential, meson spectrum and tetraquarks

The AdS/QCD correspondence predicts the structure of the quark–antiquark potential in the static limit. We use this piece of information together with the Salpeter equation (Schrödinger equation with relativistic kinematics) and a short range hyperfine splitting potential to determine quark masses and the quark potential parameters from the meson spectrum. The agreement between theory and experimental data is satisfactory, provided one considers only mesons comprising at least one heavy quark. We use the same potential (in the one-gluon-exchange approximation) and these data to estimate the constituent diquark masses. Using these results as input we compute tetraquark masses using a diquark–antidiquark model. The masses of the states X(3872) or Y(3940) are predicted rather accurately. We also compute tetraquark masses with open charm and strangeness. Our result is that tetraquark candidates such as Ds (2317), Ds (2457) or X(2632) can hardly be interpreted as diquark–antidiquark states within the present approach.