Regge trajectories for the hidden bottom tetraquarks in the diquark picture

We apply the newly proposed Regge trajectory relation for the heavy-light diquarks alongside the Regge trajectory formula for the heavy-heavy systems to investigate the hidden bottom tetraquarks (bq)(b̄q̄') $(q,\,q'=u,\,d,\,s)$. The Regge trajectory formulas for the hidden bottom tetraquarks are obtained. The masses of the λ-mode excited states and the ρ-mode excited states of the hidden bottom tetraquarks are estimated. Additionally, the λ-trajectories and the ρ-trajectories of the tetraquarks with hidden bottom are discussed. We find that the behavior of the ρ-trajectories is different from that of the λ-trajectories. The ρ-trajectories behave as M~xρ1/2 (xρ=nᵣ,\,l) because the ρ-mode excitations are in diquark and antidiquark, with both the diquark $(bq)$ and antidiquark (b̄q̄') being the heavy-light systems. Conversely, the λ-trajectories behave as M~xλ2/3 (xλ=Nᵣ,\,L) because the λ-mode excitations occure between diquark $(bq)$ and antidiquark (b̄q̄'), with the the diquark $(bq)$ and antidiquark (b̄q̄') forming a heavy-heavy system (bq)(b̄q̄'). Moreover, not only the λ-trajectories but also the ρ-trajectories for the hidden bottom tetraquarks are concave downwards in the (M²,\,x) plane.