Entanglement Maximization and Symmetry Selection in Composite Higgs Models

Recent developments suggest that the extremization of quantum entanglement may provide a useful organizing principle for strong dynamics. While entanglement suppression characterizes low-energy QCD, we investigate the role of entanglement maximization in the electroweak symmetry breaking sector. Focusing on the Composite Higgs Model, we analyze the process $hh \to t\bar{t}$ by treating the fermionic helicity space as a bipartite quantum system. Maximal entanglement imposes nontrivial constraints on the fermionic effective theory and leads to two simple symmetry structures in the top sector. One is the Maximal Symmetry branch, characterized by the vanishing of the Higgs-dependent form factor $\Pi_1$ and the finiteness of the Higgs potential. The other is a generalized $Z_2$-matching branch relating the left- and right-handed top sectors. Our results establish a quantitative connection between entanglement structure and the naturalness of electroweak symmetry breaking, and suggest that the symmetry patterns of the strong sector may be understood from the perspective of entanglement extremization.