We investigate $W$ interpretations for the ATLAS 2 TeV diboson anomalies. The roles of the unitarity sum rules, which ensure the perturbativity of the longitudinal vector boson scattering amplitudes, are emphasized. We find the unitarity sum rules an
d the custodial symmetry are powerful enough to predict various nontrivial relations among $WWZ$, $WZW$, $WWh$, $WWh$ and $ZZh$ coupling strengths in a model independent manner. We also perform surveys in the general parameter space of $W$ models and find the ATLAS 2 TeV diboson anomalies may be interpreted as a $W$ particle of the three site moose model, i.e., a Kaluza-Klein like particle in a deconstructed extra dimension model. It is also shown that the non standard-model-like Higgs boson is favored by the present data to interpret the ATLAS diboson anomalies as the consequences of the $W$ and $Z$ bosons.
Introducing arbitrary number of neutral Higgs bosons in the electroweak symmetry breaking sector, we derive a set of conditions among Higgs couplings which need to be satisfied to maintain the unitarity of the high energy scattering amplitudes of wea
k gauge bosons at the tree level (unitarity sum rules). It is shown that the unitarity sum rules require the tree level $rho$ parameter to be 1, without explicitly invoking the custodial symmetry arguments. The one-loop finiteness of the electroweak oblique corrections is automatically guaranteed once these unitarity sum rules are imposed among Higgs couplings. Severe constraints on the lightest Higgs coupling (125GeV Higgs coupling) and the mass of the second lightest Higgs boson are obtained from the unitarity and the results of the electroweak precision tests (oblique parameter measurements). These results are compared with the effective theory of the light Higgs boson, and we find simple relationships between the mass of the second lightest Higgs boson in our framework and the ultraviolet cutoff in the effective theory framework.
