Emergent symmetry in a two-Higgs-doublet model from quantum information and nonstabiliserness

Abstract

Studies of scattering processes in scalar models with two Higgs doublets have recently hinted at a connection between the absence of flavour-space entanglement in ${\Phi }^{+}{\Phi }^0$ scattering and an emergent $\mathrm{SO}(8)$ symmetry in the scalar potential. We extend the analysis to all scattering channels with two particles in the external states by treating the process as a four-qubit system in the weak isospin and flavour subspaces of the $2$-particle state. We work with a generic quantum information-theoretic principle encoded by the commutativity of the initial state density matrix with the transition matrix (at leading order in perturbation theory). This yields a special case of the entanglement minimisation conditions previously derived in the literature, and we interpret the principle in terms of the conservation of non-stabiliserness (or magic). Working at leading order in the quartic couplings, we find a consistent set of conditions that implies an $\mathrm{SO}(8)$ symmetry on the quartic part of the potential for scattering an arbitrary initial state, but a smaller $\mathrm{SU}(2{)}_R$ symmetry when the initial state is chosen to have definite isospin. This follows by accounting for Bose symmetry in the initial state, which introduces entanglement between the isospin and flavour subspaces.

9 pages. Matches published version

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• Stabilizer Rényi entropy
• Variation of Entanglement Entropy in Scattering Process
• Minimal Entanglement and Emergent Symmetries in Low-energy QCD
• Entanglement in flavored scalar scattering
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Cited by in corpus (6)

• Operational interpretation of the Stabilizer Entropy
• Systematic analysis of 3HDM symmetries
• Qubit entanglement from forward scattering
• Gedanken Experiments of Entanglement in Particle Physics: Interactions, Operators and Bell Inequalities in Flavor Space
• Parameter Inference from Final-State Entanglement in Higgs Decays
• Van Hove singularities in stabilizer entropy densities