I. INTRODUCTION The evidence for non vanishing (although very small) neutrino masses is so far possibly the only hint for new physics beyond the Standard Model (SM) [1]. It is noteworthy that the accidental U (1)$_{B}$$_{−}$$_{L}$ global symmetry is not anomalous in the SM with massless neutrinos, but its origin is not well understood. It thus becomes appealing to extend the SM to explain simultaneously the existence of both (i.e., neutrino masses and the B − L global symmetry) by gauging the U (1)$_{B}$$_{−}$$_{L}$ group thereby generating a Z ′ state. This requires that the fermion and scalar spectra are enlarged to account for gauge anomaly cancellations. The results of direct searches constrain how this may be done [2–6]. Minimally, this requires the addition of a scalar singlet and three right-handed neutrinos, one per generation [7, 8], which could dynamically trigger the see-saw mechanism explaining the smallness of the SM neutrino masses [9]. Within this model, the masses of the heavy neutrinos are such that their discovery falls within the LHC reach in a large portion of parameter space [10, 11]. Recently, a plethora of papers have been published studying the phenomenology of the B − L model at colliders. They have dealt with the detectability of the Z ′ at the LHC [10, 12–15] and at a future Linear Collider (LC) [16, 17], some analyses concentrating on the Z ′ decaying via heavy neutrinos, in particular into three [10] and four [11] leptons in the final state, with distinctive displaced vertices due to long lived neutrinos, a clear signature of physics beyond the SM. Also, the testability at the LHC of the see-saw mechanism in this model has been evaluated in detail [18]. In general, studies of this model focus on a specific non-disfavoured point in the param- eter space and do not perform a systematic analysis of the entire space. The Z ′ B − L boson is also not always considered as a traditional benchmark for generic collider reach studies [2, 12, 19, 32] or data analysis [4–6]. We have therefore performed a (parton level) discovery potential study for the LHC in the Z ′ sector of the B − L model. In the light of the LHC plan of action for the next years [21], we considered the CM energies of 7 TeV and 14 TeV, together with 10 TeV as an eventual intermediate CM energy as originally planned. The integrated luminosities that we considered are up to 1 fb − 1 for both 7 TeV and 10 TeV, and 100 fb − 1 for 14 TeV. We also included a comparison with the Tevatron reach for its expected 10 fb − 1 of integrated luminosity. We chose to study the di-lepton channel (both electrons and muons), the cleanest and most sensitive Z ′ boson decay channel in our model at colliders. 2