The Z' boson of the minimal B-L model at future Linear Colliders in e+e- --> mu+mu-

We study the capabilities of future electron-positron Linear Colliders, with centre-of-mass energy at the TeV scale, in accessing the parameter space of a $Z^{\mathrm{\prime }}$ boson within the minimal $B-L$ model. We carry out a detailed comparison between the discovery regions mapped over a two-dimensional configuration space ($Z^{\mathrm{\prime }}$ mass and coupling) at the Large Hadron Collider and possible future Linear Colliders for the case of di-muon production. As known in the literature for other $Z^{\mathrm{\prime }}$ models, we confirm that leptonic machines, as compared to the CERN hadronic accelerator, display an additional potential in discovering a $Z^{\mathrm{\prime }}$ boson as well as in allowing one to study its properties at a level of precision well beyond that of any of the existing colliders.