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computing the signal significances, we will select a window as large as either one width of the Z ′ B − L boson or twice the di-lepton mass resolution $^{3}$, whichever the largest. The half windows in the invariant mass distributions respectively read, for the “early scenario”: 

and for the “improved scenario”: 

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Our choice reflects the fact that what we will observe is in fact the convolution between the Gaussian detector resolution and the Breit-Wigner shape of the peak, and such convolution will be dominated by the largest of the two. Our approach is to take the convolution width exactly equal to the resolution width or to the peak width, whichever is largest $^{4}$, and to count all the events within this window. Finally, only 68% of signal events are considered: intrinsically, when the the peak width is dominating, effectively (by rescaling the signal), otherwise. 

In figure 1 we compare the LHC resolutions for electrons for the two aforementioned scenarios (eqs. (11) and (13)) with Γ$_{Z}$ ′ / 2. It is clear that, whichever the Z ′ B − L mass, for a value of the coupling g ′ 1 smaller than roughly 0 . 4, the peak will be dominated by the early experimental resolution, i.e., the half window will contain an amount of signal as big as the one produced with | M$_{ℓℓ}$ − M$_{Z}$ ′ | = Γ$_{Z}$ ′ / 2. The region of interest in the parameter space we are going to study almost always fulfils the condition g ′ 1 < 0 . 4, as we will see from the plots in the following section. The muon resolution is much worse and in such a plot it would be an order of magnitude higher than the other curves. Hence, for this final state, the peak is always dominated by the experimental resolution, for the values of the gauge coupling 

