λ and ρ Regge trajectories for hidden bottom and charm tetraquarks (Qq)(Q¯q¯′)

Abstract

We propose the Regge trajectory relations for the heavy tetraquarks (Qq)(Q¯q¯′) (Q=b,c;q,q′=u,d,s) with hidden bottom and charm. By employing the new relations, both the λ-trajectories and the ρ-trajectories for the tetraquarks (Qq)(Q¯q¯′) can be discussed. The masses of the λ-mode excited states and the ρ-mode excited states are estimated, and they agree with other theoretical predictions. We show that the behaviors of the ρ-trajectories are different from those of the λ-trajectories. The ρ-trajectories behave as M∼xρ1/2 (xρ=nr,l) while the λ-trajectories behave as M∼xλ2/3 (xλ=Nr,L). Moreover, the Regge trajectory behaviors for other types of tetraquarks are investigated based on the spinless Salpeter equation. We show that both the λ-trajectories and the ρ-trajectories are concave downward in the (M2,x) plane. The Regge trajectories for the tetraquarks containing the light diquark and/or the light antidiquark also are concave in the (M2,x) plane when the masses of the light constituents are included and the confining potential is linear. Published by the American Physical Society 2024