Fermion family number and the Z-Z$^{\prime}$ mixing in the 3-3-1 model with right-handed neutrinos

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Theoretical consistency of the 3-3-1 model with right-handed neutrinos demands that the number of family of fermions be exactly equal to three. In this brief report we show that such theoretical requirement results in a clean and severe bound on the Z-Z$^{\prime}$ mixing angle: $-3,979\times 10^{-3}<ϕ<1,309\times 10^{-4} {with 90% CL}$.
Minor modification in the conclusions, some refs added, to appear at MPLA

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