Entanglement suppression for $ΩΩ$ scattering

TL;DR

This work uses entanglement suppression to extract emergent symmetries from hadron-hadron scattering, focusing on $\Omega\Omega$ with spin $3/2$ where FD statistics restrict to antisymmetric spin channels. Treating the $S$-matrix as a spin operator, the authors compute entanglement power and identify two minimal-EP phase-shift configurations: $|\delta_{02}|=0$ yielding an identity-like, SU(4)-symmetric antisymmetric subspace, and $|\delta_{02}|=\pi/2$ yielding a ${\rm SWAP}_{\rm A}$-type structure associated with nonrelativistic conformal symmetry. A key result is that the $2\delta_{02}$-dependent terms cancel due to a specific Clebsch–Gordan structure of the $3/2\otimes3/2$ system, leaving a clean $\cos(4\delta_{02})$ dependence with minimal entanglement. The linear entropy analysis shows the normalized antisymmetric state has a constant entropy of $1/2$, and at the two minimal-EP points the entanglement power is also $1/2$, making these regimes directly identifiable from the CG relations. Overall, the paper connects entanglement properties to emergent symmetries in hadronic scattering and aligns with lattice QCD hints of large scattering lengths in the $J=2$ channel.

Abstract

We study entanglement suppression in $s$-wave $ΩΩ$ scattering, where each baryon has spin $3/2$. By treating the $S$-matrix as a quantum operator acting on the spin states, we quantify its ability to generate entanglement and identify the conditions on the phase shifts of the spin channels that minimize entanglement generation in the system. In $ΩΩ$ scattering, only antisymmetric spin channels are allowed due to Fermi-Dirac statistics. Applying the entanglement-suppression framework to $ΩΩ$ scattering, we find two solutions for the phase shifts: one leading to a spin SU(4) symmetry and the other to a nonrelativistic conformal symmetry. We show that the solution associated with the nonrelativistic conformal symmetry originates from the specific structure of the Clebsch-Gordan coefficients in the $3/2 \otimes 3/2$ system.