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 pairwise 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 four-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 are included. The inclusion of 2q2q̄- and qq̄-channel coupling in our approach enables a wide variety of applications of our equations to other processes within the 2q2q̄ system, and to other two-particle plus two-antiparticle systems.