CP asymmetries of $t \to c \gamma$ and $t \to cg$ decays in the aligned two-Higgs-doublet model

We study the CP asymmetries of the rare top-quark decays $t \to c \gamma$ and $t \to cg$ in the aligned two-Higgs-doublet model (A2HDM), which is generically characterized by new sources of CP violation beyond the Standard Model (SM). Specifically, the branching ratios and CP asymmetries of these rare top-quark decays are explicitly formulated, with an emphasis on the origins of weak and strong phases in the A2HDM. Taking into account the most relevant constraints on this model, we evaluate the variations of these observables with respect to the model parameters. It is found that the branching ratios of $t \to c \gamma$ and $t \to cg$ decays can maximally reach up to $1.47\times10^{-10}$ and $4.86\times10^{-9}$ respectively, which are about four and three orders of magnitude higher than the corresponding SM predictions. While the branching ratios are almost independent of the relative phase $\varphi$ between the two alignment parameters $\varsigma_u$ and $\varsigma_d$ within the allowed parameter space, the CP asymmetries are found to be very sensitive to $\varphi$. When the two alignment parameters are complex with a non-zero $\varphi$ varied within the range $[50^\circ,150^\circ]$, the magnitudes of the CP asymmetries can be significantly enhanced relative to both the SM and the real case. In particular, the maximum absolute values of the CP asymmetries can even reach up to $\mathcal{O}(1)$ for these two decay modes, in the range $\varphi \in [70^\circ,100^\circ]$. These interesting observations could be utilized to discriminate the SM and the different scenarios of the A2HDM.