Spectroscopy, Regge trajectories and decay properties of the \(bc\bar q\bar q\) and \(bq\bar c\bar q\) tetraquark systems

Abstract

Bottom-charm tetraquarks probe the interplay of heavy-quark dynamics, light-quark correlations, color structure and nearby hadronic thresholds. We investigate the spectroscopy and strong-rearrangement properties of the $bc\bar q\bar q$ and $bq\bar c\bar q$ ($q=u,d$) systems in a Cornell-type diquark--antidiquark framework with nonrelativistic (NR) and semirelativistic (SR) kinetics. Scalar and axial-vector cluster configurations are treated explicitly, and model-parameter uncertainties are propagated into state-dependent mass errors. For the $\bar{3}_c\otimes 3_c$ axial-axial ground states, the $0^+$ masses are $7530.1\pm75.4$ MeV (NR) and $7720.7\pm78.8$ MeV (SR) for $bc\bar q\bar q$, and $7307.6\pm90.5$ MeV (NR) and $7523.5\pm93.6$ MeV (SR) for $bq\bar c\bar q$. The multiplets follow $0^+<1^+<2^+$, and radial spacings decrease with excitation. In the $bq\bar c\bar q$ sector several low-lying configurations approach the $B^*D^*$ threshold: the axial-axial $0^+$ state lies $25.7$ MeV below it in NR but $190.2$ MeV above it in SR, so its threshold assignment is model sensitive and not evidence of robust strong-interaction stability. Spin and color wavefunctions are recoupled independently, giving configuration-dependent $PP$, $PV$, $VP$ and $VV$ rearrangement strengths and distinct color-singlet projections for the $\bar{3}_c\otimes 3_c$ and $6_c\otimes\bar{6}_c$ sectors. The strong short-distance attraction of the sextet coefficient $k_s=-10/3$ makes the finite SR expansion unreliable in that branch, so quantitative masses are restricted to the antitriplet sector. The results provide experimentally useful signatures and a baseline for coupled-channel and color-mixing studies.