Probing the $Z^{\prime }$ sector of the minimal $B-L$ model at future Linear Colliders in the $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ process

Abstract

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 $Z^{\prime }$ boson within the minimal $B-L$ model. In such a model, wherein the Standard Model gauge group is augmented by a broken $U(1{)}_{B-L}$ symmetry -- with $B(L)$ being the baryon(lepton) number -- the emerging $Z^{\prime }$ mass is expected to be in the above energy range. We carry out a detailed comparison between the discovery regions mapped over a two-dimensional configuration space ($Z^{\prime }$ 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 $Z^{\prime }$ models, we confirm that leptonic machines, as compared to the CERN hadronic accelerator, display an additional potential in discovering a $B-L$ $Z^{\prime }$ 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.

15 pages, 15 figures. LaTeX. To appeared in JHEP. Added a Section explaining the model, added references, changed Fig. 9, explained LC/LHC resolution and corrected typos

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