Abstract
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 cos(2ϕ) asymmetries in both Higgs boson and top quark pair productions, where ϕ is the azimuthal angle between the forward and backward energy correlators in the NEEC observables. The genesis of the cos(2ϕ) correlation lies in the intricate quantum entanglement. Owing to the substantial cos(2ϕ) effect, the NEEC observable in Higgs boson and tt¯ production emerges as a pivotal avenue for delving into quantum entanglement and scrutinizing the Bell inequality at high-energy colliders.