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We consider a gauge symmetry extension of the standard model given by$SU(3)_C\otimes SU(2)_L\otimes U(1)_X\otimes U(1)_N\otimes Z_2$ with minimalparticle content, where $X$ and $N$ are family dependent but determining thehypercharge as $Y=X+N$, while $Z_2$ is an exact discrete symmetry. In ourscenario, $X$ (while $N$ is followed by $X-Y$) and $Z_2$ charge assignments areinspired by the number of fermion families and the stability of dark matter, asobserved, respectively. We examine the mass spectra of fermions, scalars, andgauge bosons, as well as their interactions, in presence of a kinetic mixingterm between $U(1)_{X,N}$ gauge fields. We discuss in detail the phenomenologyof the new gauge boson and the right-handed neutrino dark matter stabilized by$Z_2$ conservation. We obtain parameter spaces simultaneously satisfying therecent CDF $W$-boson mass, electroweak precision measurements, particlecolliders, as well as dark matter observables, if the kinetic mixing parameteris not necessarily small.

Phenomenology of a minimal extension of the standard model with a family-dependent gauge symmetry