The contribution of new physics on the exclusive W boson hadronic decays in the final state at muon colliders in the Randall-Sundrum model

Abstract

An attempt is made to present the effect of new physics in 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, polarization and anomalous couplings on the exclusive W boson hadronic decays of $W^{\pm} \rightarrow \pi^{\pm}\gamma$, $W^{\pm} \rightarrow K^{\pm}\gamma$ and $W^{\pm} \rightarrow \rho^{\pm}\gamma$ 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, muon beam polarizes and also anomalous couplings. With a center-of-mass energy of 10 TeV, the total cross-sections achieve the maximum value when the benchmark signal point as $(\Lambda_{U}, d_{U})$ $= (1 \text{TeV}, 1.9)$ and the polarization coefficient as $(P_{\mu^{-}}, P_{\mu^{+}} )= (1,1)$. The numerical evaluation shows that with the contribution of new physics in the RS model, the effect is greatly enhanced at high energy colliders. The statistical significance can reach $1\sigma - 7\sigma$ in case of using the W branching ratio at the experimental bounds of $\mathcal{O} (10^{-6})$. To clarify the contribution of new physics, we use a $\chi^{2}$ analysis with systematic errors to determine the sensitivities of the new contributions. The result indicates that the sensitivities on the anomalous coupling $WW\gamma$ are much larger than that on the anomalous coupling $WW Z$ under the same conditions.