Effective Meson Field Theory from QCD

We give a simple and straightforward procedure of how to construct an effective meson Lagrangian from QCD Lagrangian. We integrate the methods of Gasser, Leutwyler, Alkofer and Reinhardt and use the derivative expansion scheme to derive the low energy effective Lagrangian for meson fields to $O(p^4)$. In this paper, why the meson particle can be treated as the goldstone mode is very clear. In our calculation the result in $O(p^2)$ is the same as in the chiral perturbation theory, but the result in $O(p^4)$ is different from that in literature. We will discuss the discrepancies and give some remarks on our result.