Investigation of the $l^{-}l^{+}ν\overlineν$ final state at multi-TeV muon colliders through the exclusive decay of ZZ/WW gauge bosons in the Randall-Sundrum model

TL;DR

The paper investigates the exclusive decay of WW/ZZ gauge bosons into the final state $l^{-}l^{+}\nu \overline{\nu}$ at multi-TeV muon colliders within the Randall-Sundrum framework that includes scalar unparticles and KK gravitons. It derives full transition amplitudes for $\mu^{+}\mu^{-} \to W^{+}W^{-}$ and $\mu^{+}\mu^{-} \to ZZ$, incorporating SM, radion, Higgs, unparticle, and KK-graviton exchanges, and computes cross-sections by combining production rates with leptonic decay BRs. Numerical analysis reveals strong dependence on the unparticle scale $\Lambda_U$, scaling dimension $d_U$, beam polarization, and anomalous couplings, with the WW channel generally dominating the $l^{-}l^{+}\nu \overline{\nu}$ rate and a pronounced energy/polarization dependence. The forward-backward asymmetry $A_{FB}$ emerges as a sensitive observable to polarization, suggesting that future muon colliders could substantially probe RS/unparticle dynamics through exclusive WW/ZZ decays.

Abstract

An attempt is made to present the effect of the exclusive decay of ZZ/WW gauge bosons at high energy colliders in the Randall-Sundrum (RS) model. In this paper, we investigate the $l^{-}l^{+}ν\overlineν$ final state at muon-TeV colliders through the exclusive decay of ZZ/WW gauge bosons in detail. The result shows that with fixed collision energies, cross-sections for $l^{-}l^{+}ν\overlineν$ production in final state depend strongly on the parameters of the unparticle physics, muon polarization coefficients, parameters on anomalous couplings and also KK-graviton propagators. With the benchmark background $(Λ_{U}, d_{U})$ $= (1 $TeV$, 1.9)$, the total cross-sections achieve the maximum value when both of muon beams polarize left or right. In case of the different polarization, the cross section increases as the collision energy increases. The numerical evaluation shows that the cross-section for $l^{-}l^{+}ν\overlineν$ final state through the exclusive decay of WW charged bosons is much larger than that of ZZ neutral bosons under the same conditions, which can be detected in the future muon collisions.

Figures (8)

• Figure 1: The total cross-section depends on the ($\Lambda_{U}, d_{U}$) in (a) $\mu^{+}\mu^{-} \rightarrow W^{+}W^{-} \rightarrow l^{-}l^{+}\nu \overline{\nu}$, (b) $\mu^{+}\mu^{-} \rightarrow ZZ \rightarrow l^{-}l^{+}\nu \overline{\nu}$ collisions. The parameters are chosen as $\sqrt{s} = 10$ TeV, $P_{\mu^{-}} = 0.8, P_{\mu^{+}} = -0.8$.
• Figure 2: The total cross-section in $\mu^{+}\mu^{-} \rightarrow W^{+}W^{-} \rightarrow l^{-}l^{+}\nu \overline{\nu}$ collision depends on the (a) ($\Delta k_{\gamma}, \lambda_{\gamma}$), (b) ($\Delta k_{Z}, \lambda_{Z}$). The parameters are chosen as $\sqrt{s} = 10$ TeV, $P_{\mu^{-}} = 0.8, P_{\mu^{+}} = -0.8$, $\Lambda_{U} = 1$ TeV, $d_{U} = 1.9$.
• Figure 3: The total cross-section in $\mu^{+}\mu^{-} \rightarrow ZZ \rightarrow l^{-}l^{+}\nu \overline{\nu}$ collision depends on the (a) ($f^{\gamma}_{4}, f^{\gamma}_{5}$), (b) ($f^{Z}_{4}, f^{Z}_{5}$). The parameters are chosen as $\sqrt{s} = 10$ TeV, $P_{\mu^{-}} = 0.8, P_{\mu^{+}} = -0.8$, $\Lambda_{U} = 1$ TeV, $d_{U} = 1.9$.
• Figure 4: The total cross-section as a function of the polarization coefficients of muon and antimuon beam in (a) $\mu^{+}\mu^{-} \rightarrow W^{+}W^{-} \rightarrow l^{-}l^{+}\nu \overline{\nu}$, (b) $\mu^{+}\mu^{-} \rightarrow ZZ \rightarrow l^{-}l^{+}\nu \overline{\nu}$ collisions. The parameters are chosen as $\sqrt{s} = 10$ TeV, $\Lambda_{U} = 1$ TeV, $d_{U} = 1.9$.
• Figure 5: The total cross-section depends on the collision energy in (a) $\mu^{+}\mu^{-} \rightarrow W^{+}W^{-} \rightarrow l^{-}l^{+}\nu \overline{\nu}$, (b) $\mu^{+}\mu^{-} \rightarrow ZZ \rightarrow l^{-}l^{+}\nu \overline{\nu}$ collisions in case of $(P_{\mu^{-}}, P_{\mu^{+}}) = (1, -1), (0.8, -0.8), (0.6, -0.6)$. The parameters are chosen as $\Lambda_{U} = 1$ TeV, $d_{U} = 1.9$.