Production of Magic States via $Z$ Bosons and Dark Photons

Abstract

The production of magic states is studied in two settings. The first is the electroweak (EW) sector of the Standard Model (SM). The second is an extension featuring a new broken $U(1)$ gauge symmetry and a Dirac fermion charged under it. This setup resembles a dark $U(1)$ scenario, with the additional fermion playing the role of a dark matter candidate that annihilates into SM particles through its coupling to the new gauge boson. In the EW sector, the low-energy regime reproduces earlier magic production results obtained for Quantum Electrodynamics, whereas the high-energy and $Z$-resonance regimes generate new magic distribution functions and non-trivially reorganize the stabilizer state classes, with Bhabha scattering exhibiting the strongest sensitivity to electroweak effects. Also, a subset of fixed stabilizer states is identified, for which the magic distributions remain unchanged across the different energy regimes. In the dark sector, the main effect of the new massive mediator is the appearance of new magic distributions functions for Moller-like, Bhabha-like, and inverse pair-annihilation processes in the low-energy limit. These reach the maximal magic value at the SM-to-dark fermion mass ratios $m_f/m_χ\to 0$ and $m_f/m_χ\to 1.83929$.