We formally derive the chiral Lagrangian for low lying pseudoscalar mesons from the first principles of QCD considering the contributions from the normal part of the theory without taking approximation.The derivation is based on the standard generating functional of QCD in the path integral formalism.The gluon-field integration is formally carried out by expressing the result in terms of physical Green's functions of the gluon. To integrate over the quark-field, we introduce a bilocal auxiliary field Φ(x, y) representing the mesons. We then develop a consistent way of extracting the local pseudoscalar degree of freedom U (x) in Φ(x, y) and integrating out the rest degrees of freedom such that the complete pseudoscalar degree of freedom resides in U (x). With certain techniques, we work out the explicit

At the energy [Formula: see text] of LEPII, we carry out the calculation in the process [Formula: see text] in the framework of the one-generation technicolor model. The results show that the process is immeasurably small in the one-generation TC model.

We consider the rare top quark decays in the framework of the top-color-assisted technicolor ͑TC2͒ model. We find that the contributions of top-pions and top-Higgs-bosons predicted by the TC2 model can enhance the SM branching ratios by as much as 6 -9 orders of magnitude; i.e., in the extreme case, the orders of magnitude of branching ratios are Br(t→cg)ϳ10 Ϫ5 , Br(t→cZ)ϳ10 Ϫ5 , Br(t→c␥)ϳ10 Ϫ7 . With reasonable values of the parameters in the TC2 model, such rare top quark decays may be testable in future experiments. Therefore, rare top quark decays provide a unique way to test the TC2 model.