Using one-boson-exchange Bethe-Salpeter equations, the authors find possible S-wave bound states in isoscalar D*Dbar*/B*Bbar* and in the 0(1+) and 1(2+) doubly heavy systems, with the isovector hidden-heavy channels unbound within the parameter scan.
$X(3872)$ as a four-quark state in a Dyson-Schwinger/Bethe-Salpeter approach
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abstract
We generalise the framework of Dyson-Schwinger and Bethe-Salpeter equations for four-quark states to accommodate the case of unequal quark masses. As a first application, we consider the quantum numbers $I(J^{PC})=0(1^{++})$ of the $X(3872)$ and study the four-quark states with quark contents $cq\bar{q}\bar{c}$ and $cs\bar{s}\bar{c}$. Their Bethe-Salpeter amplitudes are represented by a basis of heavy-light meson-meson, hadro-charmonium and diquark-antidiquark operators, which allows for a dynamical distinction between different internal configurations. In both cases we find the heavy-light meson-meson component to be dominant. For the putative $X(3872)$ we obtain a mass of $3916(74)$ MeV; the corresponding $cs\bar{s}\bar{c}$ state is predicted at $4068(61)$ MeV.
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Possible Bound States in the $D^\ast\bar D^\ast$/$B^\ast\bar B^\ast$ and $D^\ast D^\ast$/$\bar B^\ast\bar B^\ast$ Systems within the Bethe-Salpeter Formalism
Using one-boson-exchange Bethe-Salpeter equations, the authors find possible S-wave bound states in isoscalar D*Dbar*/B*Bbar* and in the 0(1+) and 1(2+) doubly heavy systems, with the isovector hidden-heavy channels unbound within the parameter scan.