NARROW RESONANCES IN THE DIQUONIUM SYSTEM

We study the diquonium qqq» q» system within the chromopotential confining model. Unexpectedly, we find narrow resonances for S-wave intercluster angular momenta. These resonances, with widths of the order of 10 MeV, are located just below the radially excited meson levels, indicating that these new states are bound states ("molecules") of (qq»)N=1 with (qq»)N=0, for example, for the first resonance. Although we start from a confining potential, we show that the scattering problem can be treated with the usual methods of scattering theory, essentially because the residual potential between the asymptotic meson-meson states (van der Waals force) decreases fast enough. We are dealing with a multichannel scattering problem for which we use a truncated four-quark Schrödinger equation. Our choice of trial functions in the variational calculation ensures us that the resonances that we find are not artifacts of the method: we only introduce meson-meson states in which the system can apparently decay without any problem by quark rearrangement. We particularize to the case of the harmonic-oscillator potential, where the separate conservation of intercluster orbital angular momenta simplifies the problem. Moreover, the computation of the T matrix reduces then to the inversion of a matrix of finite dimension. We discuss the limits of the model: in particular, decays of these states by quark pair creation will enlarge their widths. © 1990 The American Physical Society.