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Quantum properties of vector boson scattering $V'_1V'_2\to V_1 V_2$, relatedto entanglement and violation of Bell inequalities, are explored in this paper.The analysis is based on the construction of the polarization density matrixassociated to the final state $V_1V_2$ by means of the computation of thecorresponding tree level amplitudes within the Standard Model. The aim of thiswork is to determine the regions of the phase space where the final vectorbosons after the scattering result entangled and if is it possible to test theBell inequalities in those regions. We found that in all cases the entanglementis present. The amount of it depends on the process and the Maximally Entangledstate is reached in some particular channels. Concerning the Bell inequality,it could be also tested in certain kinematical regions for some of theseprocesses. This work is a first step in the analysis of these quantumproperties for this kind of processes and it is postponed for future studiesthe reconstruction of the polarization density matrix and the related quantumparameters from experimental data through Monte-Carlo simulations using quantumtomography techniques.

Exploring Bell inequalities and quantum entanglement in vector boson scattering