Effective Description of a Gauge Field and a Tower of Massive Vector Resonances

In this work we review an effective description of the interaction of a gauge field with a tower of massive vector fields by introducing a non-diagonal mass matrix in a gauge invariant way. Particular cases of the method with only one vector resonance have been used by the author elsewhere, nevertheless in this paper the method is developed in a general way and and we proof its main features for an arbitrary number of vector resonances. Additionally, we show how to couple the vector resonances with fermions. We find that the method can be useful in order to describe the low energy phenomenology of scenarios like Kaluza-Klein resonances of usual gauge bosons or Technicolor vector resonances and detailed examples are provided.