Brane fluctuation and the electroweak chiral Lagrangian

We use the external field method to study the electroweak chiral Lagrangian of the extra dimension model with brane fluctuation. Under the assumption that the contact terms between the matters of the standard model and KK excitations are heavily suppressed, we use the standard procedure to integrate out the quantum fields of KK excitations and the equation of motion to eliminate the classic fields of KK excitations. At one-loop level, we find that up to the order $O(p^4)$, due to the momentum conservation of the fifth dimension and the gauge symmetry of the zero modes, there is no constraint on the size of extra dimension. This result is consistent with the decoupling theorem. However, meaningful constraints can come from those operators in $O(p^6)$, which can contribute considerably to some anomalous vector couplings and can be accessible in the LC and LHC.