  We develop a framework for deriving Dyson-Schwinger Equations (DSEs) and
Bethe-Salpeter Equation (BSE) in QCD at large $N_c$ limit. The starting point
is a modified form (with auxiliary fields) of QCD generating functional. This
framework provides a natural order-by-order truncation scheme for DSEs and BSE,
and the kernels of the equations up to any order are explicitly given. Chiral
symmetry (at chiral limit) is preserved in any order truncation, so it
exemplifies the symmetry preserving truncation scheme. It provides a method to
study DSEs and BSE beyond the Rainbow-Ladder truncation, and is especially
useful to study contributions from non-Abelian dynamics (those arise from gluon
self-interactions). We also derive the equation for the quark-ghost scattering
kernel, and discuss the Slavnov-Taylor identity connecting the quark-gluon
vertex, the quark propagator and the quark-ghost scattering kernel.
