Bell inequalities with top quark pairs with the ATLAS Detector at the LHC

This work is a feasibility study for the detection of a violation of Bell inequalities using top spin correlations at the LHC. Bell inequalities are a model-independent test of non-classical behavior; in a theory where observables are local and have definite values ahead of measurement, one can put an upper bound on how correlated two systems can be. A violation of such limits (i.e. of Bell inequalities) has been observed in many quantum systems, such as pairs of entangled photons. We are able to cast Bell inequalities in a form that is usable for tt~ pairs produced in hadron colliders, in what would be the first test at the TeV scale. In particular, top quark pairs emitted perpendicular to the proton beam at v ∼ c have their spin maximally entangled as a consequence of conservation of angular momentum. In this regime our proposed experimental setup is identical (in spirit) to the one used in quantum optics. We simulate the measurement starting from event generation at parton level, fully showering hard partons, simulating the response of the ATLAS detector, reconstructing the event kinematics, and unfolding the distributions obtained. We show that a violation of Bell inequalities is expected. The statistical significance for a violation is small if considering the upcoming LHC Run 3 luminosity, but should grow after the next High-Luminosity run, reaching, conservatively, ∼ 90% CL.