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There is no reason why the gauge symmetry extension is family universal as inthe standard model and the most well-motivated models, e.g. left-right symmetryand grand unification. Hence, we propose a simplest extension of the standardmodel -- a flavor-dependent $U(1)$ gauge symmetry -- and find the new physicsinsight. For this aim, the $U(1)$ charge, called $X$, is expressed as $X=x B+yL$ in which $x$ and $y$ are free parameters as functions of flavor index, e.g.for a flavor $i$ they take $x_i$ and $y_i$ respectively, where $B$ and $L$denote normal baryon and lepton numbers. Imposing a relation involved by thecolor number $3$, i.e.$-x_{1,2,\cdots,n}=x_{n+1,n+2,\cdots,n+m}=3y_{1,2,\cdots,n+m}\equiv 3z$, forarbitrarily nonzero $z$, we achieve a novel $U(1)$ theory with implied$X$-charge. This theory not only explains the origin of the number of observedfermion families but also offers a possible solution for both neutrino mass anddark matter, which differs from $B-L$ extension. Two typical models based onthis idea are examined, yielding interesting results for flavor-changingneutral currents and particle colliders, besides those of neutrino mass anddark matter.

Flavor-dependent $U(1)$ extension inspired by lepton, baryon and color numbers