  We calculate the coefficients in the effective chiral Lagrangian from QCD,
which includes pseudo-scalar mesons and vector mesons (with hidden symmetry),
up to O(p4). This encompasses both the normal and anomalous parts. Our work
builds on a previous study that derived the chiral Lagrangian from first
principles of QCD, where the low-energy coefficients are defined in terms of
specific Green's functions in QCD. This research extends our earlier efforts
that focused on calculating the low-energy coefficients of the chiral
Lagrangian for pure pseudo-scalar mesons. This marks the first calculation of
chiral Lagrangian coefficients for vector mesons from QCD, particularly for the
important parameters a and g, which are typically considered inputs in existing
literature. Notably, the regularization method used previously is inadequate
for this broader scope. We find that cut-off regularization yields reasonable
results for both pseudo-scalar mesons and vector mesons, though it has certain
limitations. Finally, we demonstrate that our method aligns with the Weinberg
sum rules.
