Derivation of the effective chiral Lagrangian for pseudoscalar mesons fromQCD - art. no. 054011

We formally derive the chiral Lagrangian for low lying pseudoscalar mesons from the first principles of QCD considering the contributions from the nor mal part of the theory without taking an approximation. The derivation is b ased on the standard generating functional of QCD in the path integral form alism. The gluon-field integration is formally carried out by expressing th e result in terms of the physical Green's functions of the gluon. To integr ate over the quark held, we introduce a bilocal auxiliary field Phi(x,y) re presenting the mesons. We then develop a consistent way of extracting the l ocal pseudoscalar degree of freedom U(x) in Phi(x,y) and integrating out th e rest degrees of freedom such that the complete pseudoscalar degree of fre edom resides in U(x). With certain techniques, we work out the explicit U(x ) dependence of the effective action up to the p(4) terms in the momentum e xpansion, which leads to the desired chiral Lagrangian in which all the coe fficients contributed from the normal part of the theory are expressed in t erms of certain quark Green's functions in QCD. Together with the exsisting QCD formulas for the anomaly contributions, the present results lead to th e complete effective chiral Lagrangian for pseudoscalar mesons. The final r esult can be regarded as the fundamental QCD definition of the coefficients in the chiral Lagrangian. The relation between the present QCD definition of the p(2)-order coefficient F-0(2) and the well-known appoximate result g iven by Pagels and Stoker is discussed.