ATLAS Diboson Excess from Stueckelberg Mechanism

We discuss the diboson excess seen by the ATLAS detector around 2 TeV in the LHC run I at $\sqrt{s}=8$ TeV. We explore the possibility that such an excess can arise from a $Z'$ boson which acquires mass through a $U(1)_X$ Stueckelberg extension. The corresponding $Z'$ gauge boson is leptophobic with a mass of around 2 TeV and has interactions with $SU(2)_L$ Yang-Mills fields and gauge fields of the hypercharge. The analysis predicts $Z'$ decays into $WW$ and $ZZ$ as well as into $Z\gamma$. Further three-body as well as four-body decays of the $Z'$ such as $WWZ, WW\gamma, WWZZ$ etc are predicted. In the analysis we use the helicity formalism which allows us to exhibit the helicity structure of the $Z'$ decay processes in an transparent manner. In particular, we are able to show the set of vanishing helicity amplitudes in the decay of the massive $Z'$ into two vector bosons due to angular momentum conservation with a special choice of the reference momenta. The residual set of non-vanishing helicity amplitudes are identified. The parameter space of the model compatible with the diboson excess seen by the ATLAS experiment at $\sqrt s=8$ TeV is exhibited. Estimate of the diboson excess expected at $\sqrt s= 13$ TeV with 20 fb$^{-1}$ of integrated luminosity at LHC run II is also given. It is shown that the $WW$, $ZZ$ and $Z\gamma$ modes are predicted to be in the approximate ratio $1:\cos^2\theta_W (1+ \alpha \tan^2\theta_W)^2/2: (1-\alpha)^2\sin^2\theta_W/2$ where $\alpha$ is the relative strength of the couplings of hypercharge gauge fields to the couplings of the Yang-Mills gauge fields. Thus observation of the $Z\gamma$ mode as well as three-body and four-body decay modes of the $Z'$ will provide a definite test of the model and of a possible new source of interaction beyond the standard model.