Novel effects of the $W$-boson mass shift in the 3-3-1 model

The recent precision measurement of the $W$-boson mass reveals an exciting hint for the new physics as of the 3-3-1 model. We indicate that the 3-3-1 model contains distinct sources by itself that may cause the $W$-mass deviation, as measured, such as the tree-level $Z$-$Z^{\mathrm{\prime }}$ mixing, the tree-level $W$-$Y$ and $Z$-$Z^{\mathrm{\prime }}$-$X$ mixings, as well as the non-degenerate gauge vector $(X,Y)$ and new Higgs doublets. We point out that the gauge vector doublet negligibly contributes to this mass shift, whereas the rest of the effects with tree-level mixings governed by $Z$-$Z^{\mathrm{\prime }}$ and new Higgs doublets are significant. A discussion of scalar sextet contributions is also given.