Kavli Affiliate: Marcela Carena
| First 5 Authors: Marcela Carena, Guglielmo Coloretti, Wanqiang Liu, Mira Littmann, Ian Low
| 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 $Phi_a$, $a=1,2$, can
be viewed as a qubit: $Phi_1=|0rangle$ and $Phi_2=|1rangle$. More
specifically, we compute the scattering amplitudes for $Phi_a Phi_b to
Phi_c Phi_d$ and require the outgoing flavor entanglement to be maximal for a
full product basis such as the computational basis, which consists of
${|00rangle,|01rangle,|10rangle,|11rangle}$. 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 $mathrm{Z}_2$ 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 $mathrm{Z}_2$ symmetry.
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