| Summary: | Abstract We update the Standard Model (SM) predictions for the branching ratios of the rare top-quark decays $$t \rightarrow cg(g)$$ t → c g ( g ) , and evaluate the maximum rates that can be reached in the aligned as well as in the four conventional two-Higgs-doublet models (2HDMs) with $$\mathcal {Z}_2$$ Z 2 symmetries. Taking into account the relevant constraints on the model parameters resulting from a global fit obtained at the $$95.5\%$$ 95.5 % confidence level, we find that the branching ratios of $$t \rightarrow cg$$ t → c g and $$t \rightarrow cgg$$ t → c g g decays can reach up to $$3.36\times 10^{-9}$$ 3.36 × 10 - 9 and $$2.95\times 10^{-9}$$ 2.95 × 10 - 9 respectively, being therefore of the same order, in the aligned 2HDM (A2HDM). This is obviously different from the SM case, where the predicted branching ratio of the three-body decay $$t \rightarrow cgg$$ t → c g g is about two orders of magnitude larger than that of the two-body decay $$t \rightarrow cg$$ t → c g . On the other hand, compared with the SM predictions, no significant enhancements are observed in the four conventional 2HDMs with $$\mathcal {Z}_2$$ Z 2 symmetries for the branching ratios of these two decays. Nevertheless, the predicted branching ratios of $$t \rightarrow cg$$ t → c g and $$t \rightarrow cgg$$ t → c g g decays in the A2HDM are still out of the expected sensitivities of the future high-luminosity Large Hadron Collider and the Future Circular Collider in hadron-hadron mode.
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