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  • Open Access

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

Giorgio Busoni*, John Gargalionis†, Ewan N. V. Wallace‡, and Martin J. White§

  • University of Adelaide, ARC Centre of Excellence for Dark Matter Particle Physics and CSSM, Department of Physics, Adelaide, South Australia 5000, Australia

  • *Contact author: giorgio.busoni@adelaide.edu.au
  • †Contact author: john.gargalionis@adelaide.edu.au
  • ‡Contact author: ewan.n.wallace@adelaide.edu.au
  • §Contact author: martin.white@adelaide.edu.au
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Phys. Rev. D 112, 035022 – Published 15 August, 2025

DOI: https://doi.org/10.1103/r5ps-pmh3

Abstract

Studies of scattering processes in scalar models with two Higgs doublets have recently hinted at a connection between the absence of flavor-space entanglement in Φ+Φ0 scattering and an emergent 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 flavor subspaces of the two-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 minimization conditions previously derived in the literature, and we interpret the principle in terms of the conservation of nonstabilizerness (or “magic”). Working at leading order in the quartic couplings, we find a consistent set of conditions that implies an SO(8) symmetry on the quartic part of the potential for scattering an arbitrary initial state but a smaller 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 flavor subspaces.

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Phys. Rev. D 112, 035022– Published 15 August, 2025
  • Received 11 June 2025
  • Accepted 25 July 2025
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