Diquark and light four-quark states

Abstract

Four-quark states with different internal clusters are discussed within the constituent quark model. It is pointed out that the diquark concept is not meaningful in the construction of a tetraquark interpolating current in the QCD sum rule approach, and hence existing sum-rule studies of four-quark states are incomplete. An updated QCD sum-rule determination of the properties of diquark clusters is then used as input for the constituent quark model to obtain the masses of light $0^{++}$ tetraquark states ({\it i.e.\} a bound state of two diquark clusters). The results support the identification of $\sigma (600)$, $f_0(980)$ and $a_0(980)$ as the $0^{++}$ light tetraquark states, and seem to be inconsistent with the tetraquark state interpretation of the new BES observations of the near-threshold $p\bar{p}$ enhancements, X(1835) and X(1812), with the possible exception that X(1576) may be an "exotic" first orbital excitation of $f_0(980)$ or $a_0(980)$.

Comments: 7 pages, 4 eps figures, RevTex, two figures and some references added, published version in PRD