This paper presents the application of chiral perturbation theory to one-loop calculations in Quantum Chromodynamics (QCD). The authors expand the Green's functions of QCD in powers of the external momenta and quark masses, using the Ward identities of chiral symmetry to determine the expansion up to order $ p^4 $. These identities allow the identification of a few low-energy constants, which can be extracted from experimental data. The paper calculates the low-energy representation of various Green's functions, form factors, and the $ \pi\pi $ scattering amplitude, showing that the corrections of order $ M_{\pi}^2 $ to the scattering lengths and effective ranges are significant. The improved low-energy theorems agree well with measured phase shifts, and the differences between data and uncorrected soft pion theorems can be used to measure the scalar radius of the pion. The paper discusses the symmetries of the Green's functions, anomalies in the chiral symmetry, and the general form of the effective Lagrangian to order $ p^4 $. It also addresses the renormalization of the one-loop determinant and the use of dimensional regularization to handle ultraviolet divergences. The authors show that the low-energy constants can be determined from the parameters of the underlying theory, and that the effective Lagrangian must include additional constants to describe the next-to-leading order behavior. The paper concludes that the low-energy expansion of QCD is consistent with the observed data and that the scalar radius of the pion can be measured from the deviations between the data and the uncorrected soft pion theorems.This paper presents the application of chiral perturbation theory to one-loop calculations in Quantum Chromodynamics (QCD). The authors expand the Green's functions of QCD in powers of the external momenta and quark masses, using the Ward identities of chiral symmetry to determine the expansion up to order $ p^4 $. These identities allow the identification of a few low-energy constants, which can be extracted from experimental data. The paper calculates the low-energy representation of various Green's functions, form factors, and the $ \pi\pi $ scattering amplitude, showing that the corrections of order $ M_{\pi}^2 $ to the scattering lengths and effective ranges are significant. The improved low-energy theorems agree well with measured phase shifts, and the differences between data and uncorrected soft pion theorems can be used to measure the scalar radius of the pion. The paper discusses the symmetries of the Green's functions, anomalies in the chiral symmetry, and the general form of the effective Lagrangian to order $ p^4 $. It also addresses the renormalization of the one-loop determinant and the use of dimensional regularization to handle ultraviolet divergences. The authors show that the low-energy constants can be determined from the parameters of the underlying theory, and that the effective Lagrangian must include additional constants to describe the next-to-leading order behavior. The paper concludes that the low-energy expansion of QCD is consistent with the observed data and that the scalar radius of the pion can be measured from the deviations between the data and the uncorrected soft pion theorems.