Stueckelberg Mechanism and Chiral Lagrangian for Z' Boson

Traditional Stueckelberg Mechanism is shown equivalent to set up a gauged U(1) chiral Lagrangian and fix special gauge. With this mechanism, the original electro-weak chiral Lagrangian is inlarged by including an extra U(1) symmetry to represent physics for $Z'$ boson. We build up complete list of electro-weak chiral Lagrangian up to order of $p^4$ including $Z'$ and higgs bosons. The most general mixing among neutral gauge bosons is diagonalized completely and the connections among these operators to triple, quartic couplings involving $Z'$ boson and to that in traditional electro-weak chiral Lagrangian are made.