Tetraquark spectroscopy

Abstract

A complete classification of $qq \bar q \bar q$ tetraquark states in terms of the spin-flavour, colour and spatial degrees of freedom has been constructed. The permutational symmetry properties of both the spin-flavour and orbital parts of the $qq$ and $\bar{q}\bar{q}$ subsystems are discussed. This complete classification is general and model independent and it is useful both for model builders and experimentalists. The total wave functions are also explicitly constructed in the hypothesis of ideal mixing; this basis for tetraquark states will enable the eigenvalue problem to be solved for a definite dynamical model. An evaluation of the tetraquark spectrum is obtained from the Iachello mass formula for normal mesons, here generalized to tetraquark systems. This mass formula is a generalization of the Gell-Mann Okubo mass formula, whose coefficients have been upgraded by a study of the latest PDG data. The ground state tetraquark nonet is identified with $f_{0}(600),\kappa(800), f_{0}(980), a_{0}(980)$. The mass splittings predicted by the Iachello mass formula are in agreement with the KLOE, Fermilab E791 and BES experimental data.