A chargeless complex vector matter field in supersymmetric scenario

In this paper we construct and study a formulation of a chargeless complex vector matter field in a supersymmetric framework. To this aim we combine two no-chiral scalar superfields in order to take the vector component field to build the chargeless complex vector superpartner where the respective field strength transforms as matter fields by a global $U(1)$ gauge symmetry. To the aim to deal with consistent terms without breaking the global $U(1)$ symmetry it imposes a choice to the complex combination revealing a kind of symmetry between the choices and eliminate the extra degrees of freedom consistently with the supersymmetry. As the usual case the mass supersymmetric sector contributes as a complement to dynamics of the model. We obtain the equations of motion of the Proca's type field, for the chiral spinor fields and for the scalar field on the mass-shell which show the same mass as expected. This work establishes the firsts steps to extend the analysis of charged massive vector field in a supersymmetric scenario.