Investment of the scalar unparticle and polarization at muon colliders through the leptonic and hadronic decays of W boson in the RS model

In this paper, by using Feynman diagram techniques we have evaluated the influence of the scalar unparticle and polarization at the muon colliders through the leptonic and hadronic decays of W boson in the RS model. The results show that with fixed collision energies, the total cross-sections for leptonic and hadronic productions in final states depend strongly on the parameters of the unparticle physics and muon beam polarization. The total cross-sections achieve the maximum value when both of muon beams polarize left or right and the minimum value when the μ⁻ beam polarizes left, the μ⁺ beam polarizes right and vice versa. In case of the different polarization, the cross-section increases as the collision energy increases and it changes insignificantly in case of the unpolarized muon beams. In particular, the cross-section for leptonic productions in final states is much larger than that of hadronic productions under same conditions. With the benchmark background (ΛU, dU) $= (1 $TeV$, 1.9)$, the cross-sections reach the maximum value. The integrated luminosity value is shown to correspond to a significance larger than 5σ.