Spinor--spinor Bethe--Salpeter equations with vector and axial-vector gluons

Wick-rotated spinor--spinor Bethe--Salpeter equations are investigated for systems bound to zero total mass by the exchange of vector and axial-vector gluons. At small relative coordinates, the interaction is assumed to be dominated by vector propagators which are chosen in a form suggested by theories of spontaneously broken gauge symmetries. Short-distance expansions are studied for the solutions belonging to representations (1/2N, 1/2N) of O(4). Particular attention is paid to the boundary conditions in order to formulate a well defined eigenvalue problem. All solutions of the indicial equations are explicitly given for arbitrary values of N; the indices involve the coupling parameters characterizing the short-distance behavior of the interaction. (auth)