The influence of the scalar unparticle and polarization on the exclusive W boson hadronic decays in the final state at muon colliders in the Randall-Sundrum model

TL;DR

The paper investigates how scalar unparticles and Higgs-radion mixing in a Randall-Sundrum framework, together with muon beam polarization, influence exclusive hadronic decays of the W boson at high-energy muon colliders. It constructs the RS-based theoretical setup, derives the W pair production amplitudes including unparticle contributions, and computes cross sections for the rare decays $W^{\pm}\rightarrow \pi^{\pm}\gamma$, $W^{\pm}\rightarrow K^{\pm}\gamma$, and $W^{\pm}\rightarrow \rho^{\pm}\gamma$, factoring in polarization and anomalous couplings. The results show a strong dependence on unparticle parameters $\Lambda_U$ and $d_U$, with maximal cross sections at $(\Lambda_U,d_U)=(1\ \text{TeV}, 1.9)$ and $(P_{\mu^{-}}, P_{\mu^{+}})=(1,1)$; statistical significance, though small in the SM baseline, can be significantly enhanced in the RS plus unparticle scenario, indicating promising sensitivity for future high-energy muon colliders. These findings highlight the potential of muon colliders to probe scalar unparticles and RS-induced new physics via rare W decays.

Abstract

An attempt is made to present the effect of unparticle physics and polarization on the exclusive decays of W boson at high energy colliders in the Randall-Sundrum (RS) model. By using Feynman diagram techniques we have evaluated the influence of the scalar unparticle and polarization on the exclusive W boson hadronic decays of $W^{\pm} \rightarrow π^{\pm}γ$, $W^{\pm} \rightarrow K^{\pm}γ$ and $W^{\pm} \rightarrow ρ^{\pm}γ$ at the high energy muon colliders in the RS model. The result shows that with fixed collision energies, the total cross-section for hadronic productions in the final state depends strongly on the parameters of the unparticle physics and muon beam polarizes. With a center-of-mass energy of 10 TeV, the total cross-sections achieve the maximum value when the benchmark signal point as $(Λ_{U}, d_{U})$ $= (1 \text{TeV}, 1.9)$ and the polarization coefficient as $(P_{μ^{-}}, P_{μ^{+}} )= (1,1)$. The numerical evaluation for the statistical significance is given in detail which indicates that the effect is greatly enhanced in the future experiments with moderately high energy colliders.

Figures (6)

• Figure 1: Feynman diagrams for $\mu^{+}\mu^{-} \rightarrow W^{+}W^{-} \rightarrow \pi^{-}\pi^{+}\gamma\gamma/K^{-}K^{+}\gamma\gamma/\rho^{-}\rho^{+}\gamma\gamma$ collisions. $M^{\pm}$ stands for the $\pi^{\pm}, K^{\pm}, \rho^{\pm}$ .
• Figure 2: The total cross-section depends on the ($\Lambda_{U}, d_{U}$) in the reactions of (a) $\mu^{+}\mu^{-} \rightarrow W^{+}W^{-} \rightarrow \pi^{+}\pi^{-}\gamma\gamma$, (b) $\mu^{+}\mu^{-} \rightarrow W^{+}W^{-} \rightarrow K^{+}K^{-}\gamma\gamma$ and (c) $\mu^{+}\mu^{-} \rightarrow W^{+}W^{-} \rightarrow \rho^{+}\rho^{-}\gamma\gamma$, respectively. The parameters are chosen as $\sqrt{s} = 10$ TeV, $(P_{\mu^{-}}, P_{\mu^{+}} )= (0.8,-0.8)$, $(\Delta k_{\gamma},\lambda_{\gamma}) = (0.190, 0.061)$, $(\Delta k_{Z},\lambda_{Z}) = (-0.061,-0.062)$.
• Figure 3: The total cross-section depends on the ($\Delta k_{\gamma}, \lambda_{\gamma}$). The benchmark signal point are taken to be $(\Lambda_{U}, d_{U})$$= (1 \text{TeV}, 1.9)$. The other parameters are chosen as in Fig.\ref{['Fig.2']}.
• Figure 4: The total cross-section depends on the ($\Delta k_{Z}, \lambda_{Z}$). The benchmark signal point are taken to be $(\Lambda_{U}, d_{U})$$= (1 \text{TeV}, 1.9)$. The parameters are chosen as in Fig.\ref{['Fig.2']}.
• Figure 5: The total cross-section as a function of the polarization coefficients ($P_{\mu^{-}}, P_{\mu^{+}}$). The parameters are chosen as $\sqrt{s} = 10$ TeV, $(\Lambda_{U}, d_{U})$$= (1 \text{TeV}, 1.9)$, $(\Delta k_{\gamma},\lambda_{\gamma}) = (0.190, 0.061)$, $(\Delta k_{Z},\lambda_{Z}) = (-0.061,-0.062)$.