Explaining the D[sub sJ][sup ∗](2317)[sup +]

Abstract

The recently observed D * sJ (2317) + meson is explained as a scalar cs system which appears as a bound state pole, below threshold, in the DK scattering amplitude. The standard cs charmed scalar D s0 is found at about 2.9 GeV, with a width of some 150 MeV.For the scattering length of DK in S wave we predict 5 ± 1 GeV −1 . IntroductionThe D * sJ (2317) + state has, since its discovery [1] by the BABAR collaboration (see also Refs. [2,3]), raised several interesting questions on its nature [4][5][6][7][8][9][10][11][12][13][14][15]. However, the light-scalar-meson hypothesis from unitarization [16] has made important progress with the discovery of the D * sJ (2317) + 1 state (most likely J = 0). Not often it happens that in experiment a state is discovered which seems difficult to handle within other theories [17][18][19][20][21], but can be explained by the unitarization hypothesis without extra ingredients.Of course, this happened before with the light scalar mesons, which can easily be handled within a unitarized model for all non-exotic mesons [22], without making any distinction between the heavier scalar mesons and the light ones. But seventeen years after the publication of these results [16], their implications are still not fully understood, nor applied in data analysis.In UnitarizationIn the unitarization scheme, we describe meson-meson scattering by the wave equationThe operators H f and H c respectively describe the dynamics of two free mesons and of a confined quark-antiquark system. The latter is supposed to generate an infinity of confinement states.Transitions from confined quarks to free mesons, mediated by quark-antiquark-pair creation, is described by V t .By comparison of Eq. (1) with the usual expressions for scattering wave equations, we conclude that the generalized potential V for meson-meson scattering is given byWith the definitions given in Appendix A, in particular formulae (7), (17) and Table 1, we obtain for the partial-wave scattering phase shift generated by wave equation (1) the resultThe expression (3), which is an exact solution of Eq. (1) Another, in practice very useful approximation is inspired by the radial dependence of the transition potential V t , which is depicted in Ref.[25] for meson-meson scattering in the cases− , and J P = 0 + , We find there that V t is peaked at short distances. If we, moreover, take into account that eigenfunctions of the confinement Hamiltonian H c must also be of short range, then we may just define a transition radius a and approximate the spatial integrals of formula (17) by choosing a spherical delta shell U(r) = δ(r − a). In this case we end up with the expressionThis way we have pulled the p dependence outside the infinite summation over the radial confinement spectrum, which makes it much easier to handle truncations, as now the rest term does not depend on p and may thus be chosen constant. Our recent detailed analyses of scalar mesons have actually been performed in the approximation of formula (4). Our understanding of the sc...