Towards establishing the spin of warped gravitons

We study the possibility of experimental verification of the spin=2 nature of the Kaluza-Klein (KK) graviton which is predicted to exist in the extra-dimensional Randal-Sundrum (RS) warped models. The couplings of these gravitons to the particles located on or near the TeV brane is the strongest as the overlap integral of their profiles in the extra-dimension is large. Among them are unphysical Higgses ($W^{\pm}_L$ and $Z_L$) and KK excitations of the Standard Model (SM) gauge bosons. We consider the possibility to confirm the spin-2 nature of the first KK mode of the warped graviton ($G_1$) based on the angular distribution of the Z bozon in the graviton rest frame in the gg$\to G_1 \to W^{KK} (Z^{KK}) W (Z)\to WWZ$, gg$\to G_1\to ZZ$ and gg$\to G_1 \to Z^{KK} Z\to ZZH$ decay channels. Using Wigner D-matrix properties, we derive the relationship between the graviton spin, signal angular distribution peak value, and other theoretically calculable quantities. We then study the LHC signals for these decay modes and find that with 1000 fb$^{-1}$ of data, spin of the RS graviton up to $\sim$ 2 TeV may be confirmed in the $pp \to W^{KK} (Z^{KK}) W (Z) \to WWZ \to$ 3 leptons + jet + $\slashed{E}_T$ and $pp \to ZZ \to$ 4 leptons decay modes.