From the deuteron to deusons, an analysis of deuteronlike meson-meson bound states

Abstract

A systematic study of possible deuteronlike twomeson 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 pseudoscalar³ P ₀ pseudoscalar-vector$(P\bar V)$ and vector-vector$(V\bar V)$ channels the important observation is made that the centrifugal barrier from theP-wave can be overcome by the 1/r ² and 1/r ³ terms of the tensor potential. In the heavy meson sector one-pion exchange alone is strong enough to form at least deuteronlike$B\bar B*$ and$B*\bar B*$ composites bound by approximately 50 MeV. Composites of$D\bar D*$ and$D*\bar D*$ 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 areI=0, andJ ^PC=0⁻⁺, 1⁺⁺ for the$P\bar V$ states andI=0,J ^PC=0⁺⁺, O⁻⁺, 1⁺⁻ and 2⁺⁺ for the$V\bar V$ composites. In$B\bar B*$ the states:η ^b(≈10545),χ _b1(≈10562) are predicted and in$B*\bar B*$, one finds the states:η ^b(≈10590),χ _bQ (≈10582),h _b(≈10608),χ _b2(≈10602). Near the$D\bar D*$ threshold the states:η ^c(≈3870),χ _c0(3870) are predicted, and near the$D*\bar D*$ threshold one finds the states:χ _b0(≈4015),η ^c(≈4015),h _c(≈4015),χ _c2(≈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. Thus, although one cannot conclude with certainty it to be the case, this fact does favour the picture that the η (1440) and thef ₁ (1420) are mainly$K\bar K*$ composites and thef ₀(1710) mainly a$K*\bar K*$ bound state, while thef ₀(1515) andf ₂(1520) could be predominantly$(\rho \rho \pm \omega \omega )/\sqrt 2$ composites. If the predicted$D\bar D*$ and$D*\bar D*$ states are found, these would support this interpretation of the light states. In channels with exotic flavour orCP quantum numbers pion exchange is generally repulsive or quite weak. Therefore one does not expect that such deuteronlike bound states exist, althoughB*B* may be an exception.