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 $\cos (2\phi )$ asymmetries in both Higgs Boson and top quark pair productions. The genesis of the $\cos (2\phi )$ correlation lies in the intricate quantum entanglement. Owing to the substantial $\cos (2\phi )$ effect, the NEEC observable in Higgs Boson and $t\bar{t}$ production emerges as a pivotal avenue for delving into quantum entanglement and scrutinizing the Bell inequality at high-energy colliders.