An important feature of the Z ′ gauge boson in the B − L model is the chiral structure of its couplings to fermions: since the B − L charges do not distinguish between left-handed and right-handed fermions, the B − L neutral current is purely vector-like, with a vanishing axial part $^{2}$. As a consequence, we decided not to study the asymmetries of the decay products stemming from Z ′ B − L boson, given their trivial distribution at the peak, the region we study here. However, asymmetries become important in the interference region, especially just before the Z ′ boson peak, where the Z − Z ′ interference will effectively provide an asymmetric distribution somewhat milder than the case in which there is no Z ′ boson. This is a powerful method of discovery and identification of a Z ′ boson and it will be reported on separately. The study we present in this paper has been performed using the CalcHEP package [24]. The model under discussion had been implemented in this package using the LanHEP tool [25], as already discussed in Ref. [10]. The process we are interested in is di-lepton production. We define our signal as pp → γ, Z, Z ′ B − L → ℓ $^{+}$ℓ − ( ℓ = e, µ ), i.e., all possible sources together with their mu- tual interferences, and the background as pp → γ, Z → ℓ $^{+}$ℓ − ( ℓ = e, µ ), i.e., SM Drell-Yan production (including interference). No other sources of background, such as W W , ZZ , W Z , or tt have been taken into account. These can be suppressed or/and are insignificant [4, 32]. For both the signal and the background, we have assumed standard acceptance cuts (for both electrons and muons) at the LHC: and we apply the following requirements on the di-lepton invariant mass, M$_{ℓℓ}$ , depending on whether we are considering electrons or muons. We distinguish two different scenarios: an “early” one (for √$_{s}$ = 7, 10 TeV) and an “improved” one (for √$_{s}$ = 14 TeV), and, in the chosen scalar masses and mixing angle: m h$_{1}$ = 125 GeV, m h$_{2}$ = 450 GeV and α = 0 . 01. Such values are allowed by the study of the unitarity bound [22], as well as of the triviality bound [23], of the scalar sector. 2 That is, g V Z ′ = g L Z ′ + g R Z ′ 2 , g A Z ′ = g R Z ′ − g L Z ′ 2 = 0, hence g R Z ′ = g L Z ′ . On the contrary, Majorana neutrinos have pure axial couplings [18]. 5 p ℓ T > 10 GeV , | η $^{ℓ}$| < 2 . 5 ( ℓ = e, µ ) , (10) III. COMPUTATIONAL DETAILS