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

TL;DR

This paper explores how quantum information principles reveal an emergent SO(8) symmetry in a two-Higgs-doublet model's scalar potential through analysis of scattering processes as a four-qubit system.

Contribution

It extends previous work by analyzing all scattering channels with quantum information theory, revealing symmetry conditions and the role of entanglement and non-stabiliserness in the model.

Findings

Emergent SO(8) symmetry in the scalar potential for arbitrary initial states.

Smaller SU(2)_R symmetry when initial states have definite isospin.

Entanglement between isospin and flavour subspaces due to Bose symmetry.

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.