Maintaining Gauge Symmetry in Renormalizing Chiral Gauge Theories
Abstract
It is known that the γ5 scheme of Breitenlohner and Maison (BM) in dimensional regularization requires finite counter-term renormalization to restore gauge symmetry and implementing this finite renormalization in practical calculation is a daunting task even at 1-loop order. In this paper, we show that there is a simple and straightforward method to obtain these finite counter terms by using the rightmost γ5 scheme in which we move all the γ5 matrices to the rightmost position before analytically continuing the dimension. For any 1-loop Feynman diagram, the difference between the amplitude regularized in the rightmost γ5 scheme and the amplitude regularized in the BM scheme can be easily calculated. The differences for all 1-loop diagrams in the chiral Abelian-Higgs gauge theory and in the chiral non-Abelian gauge theory are shown to be the same as the amplitudes due to the finite counter terms that are required to restore gauge symmetry.