Mean field solutions to singlet hopping and superconducting pairing within a two-band Hubbard model

The mean field Green function solution of the two-band singlet-hole Hubbard model for high-$T\text{sb}c$ superconductivity in cuprates (Plakida, N.M. et al., Phys. Rev. B51, 16599 (1995), JETP 97, 331 (2003)) involves expressions of higher order correlation functions describing respectively the singlet hopping and the superconducting pairing. Rigorous derivation of their values is reported based on the finding that specific invariant classes of polynomial Green functions in terms of the Wannier overlap coefficients $\nu \text{sb}ij$ exist.