Towards establishing the spin of warped gravitons

TL;DR

This work examines how to experimentally verify the spin-2 nature of the first Kaluza-Klein graviton in warped Randall-Sundrum models by analyzing the angular distribution of Z bosons in the graviton rest frame across multiple decay channels. It develops a spin-determination framework using Wigner D-matrices to link graviton spin to observable angular peaks and applies it to ZZ, WW, and KK-gauge-boson mediated final states, including realistic backgrounds and detector cuts. The study shows that the characteristic central-peaked angular distribution provides a robust spin signature and finds that, with 1000 fb^-1 of LHC data, RS gravitons up to about 2 TeV could be confirmed in ZZ→4ℓ and WWZ-like channels, while the newly considered W^{KK}(Z^{KK})W_L(Z_L) decays offer additional discovery avenues. Overall, the paper highlights practical channels and kinematic handles for validating the RS framework and mapping the structure of extra dimensions through spin-2 gravitons.

Abstract

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.

Figures (4)

• Figure 1: (a) Normalized angular distribution for the signal $\sigma(pp\to G_1 \to ZZ)$ cross-section due to the 1st KK graviton mode and (b) Normalized total (i.e. including SM background) angular distribution for the $\sigma(pp\to ZZ)$ cross-section for $m_1^G=1.5$ TeV (solid) and $m_1^G=3$ TeV (dashed) integrated in the $m_1^G\pm \Gamma_G$ ZZ invariant mass window with c$\equiv k/M_{Pl}=1$.
• Figure 2: (a) Total signal cross-section $\sigma(pp \to W_L W^{KK})\approx\sigma(pp \to Z_L Z^{KK})$ as a function of the 1st KK graviton mode mass integrated in the $m_1^G\pm \Gamma^G$$W_L W^{KK}$ mass window and with c=1.
• Figure 3: (a) Normalized angular distribution for the signal $\sigma(pp\to G_1 \to ZZH)$ cross-section due to the 1st KK graviton mode and (b) Normalized total angular distribution for $m_1^G=1.5$ TeV (solid) and $m_1^G=2$ TeV (dashed) with cuts as in Eq.\ref{['cuts']}.
• Figure 4: Normalized total angular distribution for $\sigma(pp\to WWZ)$ cross-section for $m_1^G=1.5$ TeV (solid) and $m_1^G=2$ TeV (dashed) with cuts as in Eq.\ref{['cuts1']} and Eq.\ref{['cuts2']}.