Chiral effective theory of scalar and vector diquarks is formulated according to the linear sigma model. The main application is to describe the ground and excited states of singly heavy baryons with a charm or bottom quark. Applying the potential quark model between the diquark and the heavy quark ($Q=c, b$), we construct a heavy-quark--diquark model. The spectra of the positive- and negative-parity states of $Lambda_Q$, $Sigma_Q$, $Xi^{()}_Q$ and $Omega_Q$ are obtained. The masses and interaction parameters of the effective theory are fixed partly from the lattice QCD data and also from fitting low-lying heavy baryon masses. We find that the negative parity excited states of $Xi_Q$ (flavor $bar{bf 3}$) are different from those of $Lambda_Q$, because of the inverse hierarchy of the pseudoscalar diquark. On the other hand, $Sigma_Q, Xi_Q$ and $Omega_Q$ (flavor ${bf 6}$) baryons have similar spectra. We compare our results of the heavy-quark--diquark model with experimental data as well as the quark model.
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