We compute the contributions to rare top decays $t\to cZ$ and $t\to c{h}_1$ from the scalar sector in the two Higgs doublet model type III with $CP$ violation, where $h_1$ is the Standard Model Higgs boson. The branching ratios for $\mathrm{BR}(t\to cZ)$ and $\mathrm{BR}(t\to c{h}_1)$ are obtained as a function of the model parameters. In particular, the $\mathrm{BR}(t\to cZ)$ can increase its value up to ${10}^{-3}$ for $\tan \beta =1$ and masses for the additional Higgs bosons of $m_{h_2,h_3,H^{\pm }}\sim 0.5\mathrm{TeV}$. Meanwhile $\mathrm{BR}(t\to c{h}_1)$ can reach values of the order of $\sim {10}^{-2}$. We constrain the model parameters (mixing angles of the neutral scalar fields in the $CP$ violation context and $\tan \beta$) using the reported values of the signal strengths $R_{XX}$ and $b\to s\gamma$ process.

• Received 7 November 2017

DOI:https://doi.org/10.1103/PhysRevD.98.035031

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Published by the American Physical Society