Covariant equations for the tetraquark and more

We derive covariant equations for a system of two quarks and two antiquarks where the effect of quark-antiquark annihilation is taken into account. In our approach, only pair-wise interactions are retained, while all possibilities of overcounting are excluded by (i) keeping terms in the kernel that are consistent with a meson-meson and diquark-antidiquark substructure, and (ii) introducing 4-body equations with a novel structure that specifically avoids the generation of overcounted terms. The resulting tetraquark bound state equations are given for the case of general two-body interactions, and for the specific case of separable interactions that lead to a description of the tetraquark in terms of meson-meson and diquark-antidiquark degrees of freedom where the effects of quark-antiquark annihilation is included. The inclusion of $2q2\bar{q}$- and $q\bar{q}$-channel coupling in our approach enables a wide variety of applications of our equations to other processes within the $2q2\bar{q}$ system, and to other 2-particle plus 2-antiparticle systems.

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