Regge trajectories for the triply heavy triquarks

We attempt to apply the Regge trajectory approach to the triply heavy triquarks $((Q{Q}^{\mathrm{\prime }}){\bar{Q}}^{\mathrm{\prime }\mathrm{\prime }})$ $(Q,Q^{\mathrm{\prime }},Q^{\mathrm{\prime }\mathrm{\prime }}=b,c)$. We present the triquark Regge trajectory relations, and then employ them to crudely estimate the spectra of the triquarks $((cc)\bar{c})$, $((cc)\bar{b})$, $((bc)\bar{c})$, $((bc)\bar{b})$, $((bb)\bar{c})$, and $((bb)\bar{b})$. The $\lambda$-trajectories and the $\rho$-trajectories are discussed. The triquark Regge trajectory becomes a new and very simple approach for estimating the spectra of triquarks. Moreover, the spin-averaged masses of the ground states of pentaquarks $(\bar{c}(cc))(cc)$, $(\bar{b}(cc))(cc)$ and $(\bar{c}(bb))(cc)$ are estimated, which are consistent with other theoretical predictions.