$\mathcal{O} \,(\theta)$ Feynman rules for quadrilinear gauge boson couplings in noncommutative standard model

We examine the electroweak gauge sector of noncommutative standard model and in particular, obtain the $\mathcal{O} \,(\theta)$ Feynman rules for all quadrilinear gauge boson couplings. Surprisingly, an electroweak-chromodynamics mixing appears in the gauge sector of noncommutative standard model, where photon as well as the neutral weak boson are coupled directly to three gluons. The phenomenological perspectives of the model in $W^-W^+ \rightarrow Z Z$ scattering are studied and it is shown that there is a characteristic oscillatory behaviour in azimuthal distribution of scattering cross sections which can be interpreted as a direct signal of noncommutative standard model. Assuming the integrated luminosity 100 $\mathrm{fb}^{-1}$, the number of $W^-W^+ \rightarrow Z Z$ subprocesses are estimated for some values of noncommutative scale $\Lambda_{\mathrm{NC}}$ at different center of mass energies and the results are compared with predictions of the standard model.