FROM THE DEUTERON TO DEUSONS, AN ANALYSIS OF DEUTERONLIKE MESON-MESON BOUND-STATES

A systematic study of possible deuteronlike two-meson bound states, deusons, is presented. Previous arguments that many such bound states may exist are elaborated with detailed arguments and numerical calculations including, in particular, the tensor potential. This tensor potential which is crucial for the deuteron binding is shown to be very important also in the mesonic case. Especially, in the pseudoscalar P-3(0) pseudoscalar-vector (PVBAR) and vector-vector (VVBAR) channels the important observation is made that the centrifugal barrier from the P-wave can be overcome by the 1/r2 and 1/r3 terms of the tensor potential. In the heavy meson sector one-pion exchange alone is strong enough to form at least deuteron-like BB*BAR and B*B*BAR composites bound by approximately 50 MeV. Composites of DD*BAR and D*D*BAR states bound by pion exchange alone are expected near the thresholds, while in the light meson sector one generally needs some additional short range attraction to form bound states. The quantum numbers of these states are I=0, and J(PC)=0-+, 1++ for the PVBAR states and I=0, J(PC)=0++, 0-+, 1+- and 2++ for the VVbar composites. In BB*BAR the states: eta(b)(almost-equal-to 10 545), chi(b1)(almost-equal-to 10 562) are predicted and in B*B*BAR one finds the states: eta(b)(almost-equal-to 10 590), chi(b0)(almost-equal-to 10582), h(b)(almost-equal-to 10608), chi(b2)(almost-equal-to 10602). Near the DD* threshold the states: eta(c)(almost-equal-to 3870), chi(c0)(3870) are predicted, and near the D*D*BAR threshold one finds the states: chi(b0)(almost-equal-to 4015), eta(c)(almost-equal-to 4015), h(c)(almost-equal-to 4015), chi(c2)(almost-equal-to 4015). Within the light meson sector pion exchange gives strong attraction for PVBAR and VVBAR systems with quantum numbers where the best non-qqBAR candidates exist, although pion exchange alone is not strong enough to support such bound states. Thus, although one cannot conclude with certainty it to be the case, this fact does favour the picture that the eta(1440) and the f1(1420) are mainly KK*BAR composites and the f0(1710) mainly a K*K*BAR bound state, while the f0(1515) and f2(1520) could be predominantly (rhorho +/- omegaomega)/square-root 2 composites. If the predicted DD*BAR and D*D*BAR states are found, these would support this interpretation of the light states. In channels with exotic flavour or CP quantum numbers pion exchange is generally repulsive or quite weak. Therefore one does not expect that such deuteronlike bound states exist, although B*B*BAR may be an exception.