The Most General and Renormalizable Maximal Abelian Gauge

We have constructed the most general gauge fixing term for the SU(2) Yang-Mills theory, which leaves the global U(1) gauge symmetry intact (i.e., the most general Maximal Abelian gauge). From the viewpoint of renormalizability, we point out the importance of an additional gauge fixing parameter that is not included in the ordinary gauge fixing term with the global SU(2) gauge symmetry. By requiring a number of symmetries without spoiling the renormalizability, we restrict the most general gauge to a minimum gauge which is considered to be the essential part of the maximal Abelian gauge. Then we demonstrate that a new parameter κ introduced in this gauge is very efficient in order to examine the renormalizability. In fact, we confirm the renormalizability of this gauge together with a new parameter κ by calculating explicitly the anomalous dimensions of all the parameters at one loop order.