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The flavor changing neutral current decays $t\to c X$ ($X=\gamma,\,g,\, Z,\,H$) and $t\to c\bar \ell\ell $ ($\ell=\mu,\,\tau$) are studied in arenormalizable scalar leptoquark (LQ) model with no proton decay, where ascalar $SU(2)$ doublet with hypercharge $Y=7/6$ is added to the standard model,yielding a non-chiral LQ $\Omega_{5/3}$. Analytical results for the one-loop(tree-level) contributions of a scalar LQ to the $f_i\to f_j X$ ($f_i\to f_j\bar f_m f_l$) decays, with $f_a=q_a, \ell_a$, are presented. We consider thescenario where $\Omega_{5/3}$ couples to the fermions of the second and thirdfamilies, with its right- and left-handed couplings obeying $\lambda_R^{\ellu_i}/\lambda_L^{\ell u_i}=O(\epsilon)$, where $\epsilon$ parametrizes therelative size between these couplings. The allowed parameter space is thenfound via the current constraints on the muon $(g-2)$, the $\tau\to \mu\gamma$decay, the LHC Higgs boson data, and the direct LQ searches at the LHC. For$m_{\Omega_{5/3}}=1$ TeV and $\epsilon=10^{-3}$, we find that the $t\to c X$branching ratios are of similar size and can be as large as $10^{-8}$ in a tinyarea of the parameter space, whereas ${\rm Br}(t\to c\bar \tau\tau)$ [${\rmBr}(t\to c\bar \mu\mu)$] can be up to $10^{-6}$ ($10^{-7}$).

Flavor changing neutral current decays $t\to c X$ ($X=\gamma,\,g,\, Z,\, H$) and $t\to c\bar \ell\ell $ ($\ell=\mu,\,\tau$) via scalar leptoquarks