Kavli Affiliate: Marcela Carena
| Summary:
We consider 2-to-2 scatterings of Higgs bosons in a CP-conserving two-Higgs-doublet model (2HDM) and study the implication of maximizing the entanglement in the flavor space, where the two doublets $Φ_a$, $a=1,2$, can be viewed as a qubit: $Φ_1=|0rangle$ and $Φ_2=|1rangle$. More specifically, we compute the scattering amplitudes for $Φ_a Φ_b to Φ_c Φ_d$ and require the outgoing flavor entanglement to be maximal for a full product basis such as the computational basis, which consists of $$. In the unbroken phase and turning off the gauge interactions, entanglement maximization results in the appearance of an $U(2)times U(2)$ global symmetry among the quartic couplings, which in general is broken softly by the mass terms. Interestingly, once the Higgs bosons acquire vacuum expectation values, maximal entanglement enforces an exact $U(2) times U(2)$ symmetry, which is spontaneously broken to $U(1)times U(1)$. As a byproduct, this gives rise to Higgs alignment as well as to the existence of 6 massless Nambu-Goldstone bosons. The $U(2)times U(2)$ symmetry can be gauged to lift the massless Goldstones, while maintaining maximal entanglement demands the presence of a discrete $mathrmZ_2$ symmetry interchanging the two gauge sectors. The model is custodially invariant in the scalar sector, and the inclusion of fermions requires a mirror dark sector, related to the standard one by the $mathrmZ_2$ symmetry.
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