Long-Range Azimuthal Correlation, Entanglement, and Bell Inequality Violation by Spinning Gluons at the Large Hadron Collider.

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 Large Hadron Collider. The spinning gluon in these collisions will introduce substantial nonzero asymmetries in both Higgs boson and top quark pair productions, where is the azimuthal angle between the forward and backward energy correlators in the NEEC observables. The genesis of the correlation lies in the intricate quantum entanglement. Owing to the substantial effect, the NEEC observable in Higgs boson and production emerges as a pivotal avenue for delving into quantum entanglement and scrutinizing the Bell inequality at high-energy colliders.