Abstract
We study mesons through solving the coupled system of the gap equation for the quark propagator and the Bethe–Salpeter equation for the meson wavefunction. The gap equation and Bethe–Salpeter equation are in fact members of infinitely coupled Dyson–Schwinger equations of Green functions of QCD. To make it solvable, the system must be truncated. The simplest rainbow-ladder truncation is widely used but shows drawbacks in many aspects. To improve the simplest truncation, we analyze symmetries of the fundamental theory and solve the corresponding Ward–Green–Takahashi identities. Then, the elements of the coupled system, i.e., the quark-gluon vertex and the quark-antiquark scattering kernel, can be constructed accordingly.
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