One-loop renormalization of non-Abelian gauge theory and β function based on loop regularization method

All one-loop renormalization constants for non-Abelian gauge theory are computed in detail by using the symmetry-preserving loop regularization method proposed in Refs. 1 and 2. The resulting renormalization constants are manifestly shown to satisfy Ward Takahaski-Slavnov-Taylor identities, and lead to the well-known one loop beta function for non-Abelian gauge theory of QCD.(3-5) The loop regularization method is realized in the dimension of original field theories, it maintains not only symmetries but also divergent behaviors of original field theories with the introduction of two energy scales. Such two scales play the roles of characterizing and sliding energy scales as well as ultraviolet and infrared cutoff energy scales. An explicit check of those identities provides a clear demonstration how the symmetry-preserving loop regularization method can consistently be applied to non-Abelian gauge theories.