One-loop contributing for $A\to ZZ\gamma$ in the Two-Higgs-Doublet Model with Vector-Like Quarks

In this paper, we present the first results for the one-loop decay $A\to ZZ\gamma$ in the Two-Higgs-Doublet Model and its extension with Vector-Like Quarks. We calculate the one-loop partial decay widths and branching ratios for both unpolarized and polarized final-state $Z$ bosons. The effects of Vector-Like Quarks propagating in the loop are also examined in our phenomenological analysis. We find that the branching ratios can reach ${10}^{-5}-{10}^{-4}$ for several benchmark points within the viable parameter space of the considered models. The contributions from Vector-Like Quarks can modify the total rates by approximately $5\mathrm{\%}$. With the high luminosities expected at future multi-TeV muon colliders, these effects may be experimentally accessible.