On Deusons or Deuteronlike Meson-meson Bound States

The systematics of deuteronlike two-meson bound states, deusons, is discussed. Previous arguments that many of the present non-qq̄ states are such states are elaborated including, in particular, the tensor potential. For pseudoscalar states the important observation is made that the centrifugal barrier from the P-wave can be overcome by the 1/r and 1/r terms of the tensor potential. In the heavy meson sector one-pion exchange alone is strong enough to form at least deuteron-like BB̄ and BB̄ composites bound by approximately 50 MeV, while DD̄ and DD̄ states are expected near the threshold. Recently I suggested [1] that many of the best established light non-qq̄ candidates [2] are in fact deuteronlike meson-meson bound states or deusons. The idea, that deuteronlike bound states of two mesons might exist is certainly not new, but has been discussed generally only in passing whithin general phenomenological models for meson-meson bound states (See [3]–[13]), where pion exchange is not given special attention. After my first letter, Ericson and Karl [14] has also studied the strength of pion exchange with similar conclusions, and Manohar and Weise [15] have studied flavour exotic two B-meson bound states. The heavy meson systems are an interesting testing ground for these ideas, since the predictions are less ambiguous than for light states. One can write the one-pion exchange potential in an universal way by collecting all the constants into an overall number γ, the ”relative coupling number” which is a measure of the overall potential strength. Thus for NN one has γ SI = − 9 (τ1 · τ2)(σ1 · σ2), for (D∗D̄)±, γ I± = ∓τ1 · τ2 and for DD̄ γ V SI = −(τ1 · τ2)(Σ1 · Σ2). This number γ measures the relative strength of the potential compared to the contribution from one pair of quarks in a spin triplet and isospin triplet state for which γ SI = −1. For example for the deuteron γ 10 = 25/3 and for DD̄ in I=0, S=0, γ V 00 = 6. The larger γ is, the stronger is the attraction, and if it is negative there is repulsion. The universal one-pion exchange potential in r-space can then be written compactly: Vπ(r) = −γV0 [D · C(r) + S12(r̂) · T (r)] , (1) where D is a diagonal matrix, r̂ is the unit vector, and the r dependence is given by the functions C(r) = μ m2π e mπr , (2) T (r) = C(r)[1 + 3 μr + 3 (μr) ] , (3) and S12(r) is the tensor operator in r space, which, in general, connects different partial waves. In Eq. (1) we introduced the constant V0 = m 3 πg /(12πf ) ≈ 1.3 MeV, the numerical value of which is fixed by the πN coupling constant. Because of the singular behaviour of the tensor potential it must be regularized at small distances. The perhaps most natural method is to introduce a form factor at each πN vertex, such as (Λ − μ)/(Λ + t), which in r-space can be looked upon as a spherical pion source with rms radius R = √ 10/Λ. Invited talk at the Hadron93 International Conf. on Hadron Spectroscopy, Como, Italy 22.-25.6. 1993. HU-SEFT R 1993-13a The deuteron. Our prime reference state is of course the deuteron, the existence of which nobody doubts. It has been studied in great detail over the years (See Ref. [16] and the recent reviews [17], [18]). There one knows that the dominant binding energy comes from pion exchange between two colourless qqq clusters a proton and a neutron. One defines conventional basis vectors |S1 > and |D1 > such that the wave function is in general u(r)|S1 > +w(r)|D1 >. The deuteron potential Vd(r) can then be written in matrix form as: Vd(r) = − 25 3 V0 [(