Maintaining gauge symmetry in renormalizing chiral gauge theories

It is known that the gamma(5) scheme of Breitenlohner and Maison in dimensional regularization requires finite counterterm 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 counterterms by using the rightmost gamma(5) scheme in which we move all the gamma(5) 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 gamma(5) scheme and the amplitude regularized in the Breitenlohner and Maison 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 counterterms that are required to restore gauge symmetry.