Quantum orientation entanglement analysis of the interpolating helicity states between the instant form dynamics and the light-front dynamics

The interplay between quantum orientation entanglement and Wigner rotation is fundamental in understanding the behavior of spin angular momentum in the quantum states. Quantum orientation entanglement of the helicity states in the instant form dynamics (IFD) is well understood due to the Jacob-Wick helicity definition involving the rotation of the frame. However, understanding the quantum orientation entanglement of the helicity states in the light-front form dynamics (LFD) is highly nontrivial as the transverse rotations in LFD become dynamical. We discuss how one can achieve quantum orientation entanglement of the helicity states in LFD using the transverse light-front boost which is kinematical in LFD. In our analysis, we present a unique relationship for the spin orientation changes with the particle's momentum direction between IFD and LFD for the spin-1/2 and spin-1 spinors, as well as the spin-1 polarization vectors. From this analysis, we find that the interpolating helicity states between IFD and LFD can be understood as the rotated Jacob-Wick helicity states in terms of the Wigner d-functions. For the illustration, we compute interpolating helicity amplitudes of the scattering/annihilation processes which involve scalar and vector particles, and show the landscape of scattering angular distribution.