INDIRECT MEASUREMENTS OF CROSS-SECTIONS IN COLLISIONS OF EQUAL MASS FERMIONS USING QUANTUM ENTANGLEMENT WITH A WITNESS PARTICLE
It is considered a QED scattering between two equal mass fermions (A,B) which are spin-entangled (total entanglement), or at least one of them (partial entanglement), with a witness particle (C) that does not participate directly in the collision. All the spin configurations are included in the formulation. The final C’s state is evaluated and, as a result, it is shown that it contains information of the AB scattering for some of these configurations. This is verifiable in the particular QED process electron+positron → muon+antimuon, by measuring the C’s spin expectation value on the z axis for a total entanglement; and both, on the x (eventually y) and z axis for a partial entanglement, being the remaining particle in a spin quantum overlapping. The von Neumann entropy as another argument is also calculated and plotted for these configurations.