From the Deuteron to Deusons, an Analysis of Deuteronlike Meson-Meson Bound States

Abstract

A systematic study of possible deuteronlike two-meson bound states, {\it 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. In the heavy meson sector one-pion exchange alone is strong enough to form at least deuteron-like $B{\bar{B}}^{\ast }$ and $B^{\ast }{\bar{B}}^{\ast }$ composites bound by approximately 50 MeV. Composites of $D{\bar{D}}^{\ast }$ and $D^{\ast }{\bar{D}}^{\ast }$ 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, In $B{\bar{B}}^{\ast }$ one predictss the states: ${\eta }_b(\approx 10545),{\chi }_{b1}(\approx 10562)$, and in $B^{\ast }{\bar{B}}^{\ast }$ one finds the states: ${\eta }_b(\approx 10590),{\chi }_{b0}(\approx 10582),h_b(\approx 10608),{\chi }_{b2}(\approx 10602)$. Near the $D{\bar{D}}^{\ast }$ threshold the states: ${\eta }_c(\approx 3870),{\chi }_{c0}(\approx 3870)$ are predicted, and near the $D^{\ast }{\bar{D}}^{\ast }$ threshold one finds the states: ${\chi }_{b0}(\approx 4015),{\eta }_c(\approx 4015),h_c(\approx 4015),{\chi }_{c2}(\approx 4015)$. Within the light meson sector pion exchange gives strong attraction for $P\bar{V}$ and $V\bar{V}$ systems with quantum numbers where the best non-$q\bar{q}$ candidates exist, although pion exchange alone is not strong enough to support such bound states.

Comments: 24pages in latex, 6 figures (not included), HU-SEFT R 1993-12