手征规范理论重整化中保持规范对称性
Maintaining Gauge Symmetry in Renormalizing Chiral Gauge Theories
摘要：
Breitenlohner和Maison（BM）的$γ_{5}$维数正则化方案需要有限的反项重整化来恢复规范对称性，在实际计算中实现这种有限重整化即使在单圈阶下也是一项艰巨的任务。在本文中，我们表明，有一个简单而直接的方法来获得这些有限计数器项，通过使用最右边的$γ_{5}$计划，我们移动所有的$γ_{5}$矩阵的最右边的位置，然后分析继续的尺寸。对于任何单圈费曼图，在最右边的$γ_{5}$格式中正则化的振幅和在BM格式中正则化的振幅之间的差可以容易地计算。手征阿贝尔-希格斯规范理论和手征非阿贝尔规范理论中所有1-圈图的差异被证明与恢复规范对称性所需的有限反项的振幅相同。
英文摘要：
It is known that the $γ_{5}$ 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 $γ_{5}$ scheme in which we move all the $γ_{5}$ 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 $γ_{5}$ 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.
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