Note on the BRST Mass Generation of a Vector Field. The Case of Couplings to N=4 Real Scalars

The main aim of this paper is to apply a procedure, different from the Higgs mechanism, by which one may generate mass for a vector field in the context of its interactions to a set of N = 4 real scalar fields. This goal will be attained via implementing the general multi-step program from [1] adapted to the present context: (1) we start from a free theory in D = 4 whose Lagrangian action is expressed like the sum between the Maxwell action for a single vector field and that for a collection of N = 4 massless real scalar fields; (2) we construct a general class of gauge theories whose free limit is that from step (1) by means of the deformation of the solution to the master equation [2] and [3] with the help of local BRST cohomology [4-6]. On the one hand, the setup described so far does not account in any way for the Higgs mechanism. On the other hand, it will be proved to produce the next results: (A) the vector field acquires mass; (B) the scalar fields gain gauge transformations, by contrast to the free limit, but the associated gauge algebra remains Abelian; (C) the propagator of the massive vector field emerging from the gauge-fixed action behaves, in the limit of large Euclidean momenta, like that from the massless case.