INDIRECT MEASUREMENTS OF CROSS-SECTIONS IN COLLISIONS OF EQUAL MASS FERMIONS USING QUANTUM ENTANGLEMENT WITH A WITNESS PARTICLE
We consider a general QED scattering process between two fermions with the same mass, A and B, one of which is initially entangled with a witness particle, C. The latter does not participate in the collision. The final state of C is evaluated usaing standard S matrix formalism and we show that for certain configurations of spin entanglement, it contains information about the dynamics of the AB scattering. As an illustration we use electron, positron -> muon, antimuon (inelastic scattering), as well as the elastic processes Bhabha and Moeller scatterings. We show that spin measurements on the particle C can be effected to deleiver information on the cross section. We verify how such measurements are related by an observer in the center-of-mass frame and another moving perpendicularly to the the direction before the collision through Wigner rotations. The quantum correlations are evaluated considering a unitary process to this order in perturbation theory via the von Neumann entropy.