Long Range Azimuthal Correlation, Entanglement and Bell Inequality Violation by Spinning Gluons at the LHC

We apply the recently developed concept of the nucleon energy-energy correlator (NEEC) for the gluon sector to investigate the long-range azimuthal angular correlations in proton-proton collisions at the LHC. The spinning gluon in these collisions will introduce a significant nonzero (2) asymmetries in both Higgs Boson and top quark pair productions. The genesis of the (2) correlation lies in the intricate quantum entanglement. Owing to the substantial (2) effect, the NEEC observable in Higgs Boson and t t production emerges as a pivotal avenue for delving into quantum entanglement and scrutinizing the Bell inequality at high-energy colliders.