$P$-wave states $T_{bb}^{-}$ from diquarks

Abstract

We investigate the $P$-wave states $T_{bb}^{-}$ in the isospin singlet and three excited modes [excitation occurring in the diquark $[bb{]}_{c_1}^{s_1}$ ($\rho$-mode), antidiquark $[\bar{u}\bar{d}{]}_{c_2}^{s_2}$ ($r$-mode) or between them ($\lambda$-mode)] from diquarks in a quark model. We analyze the dynamical behaviors of the diquark $[bb{]}_{c_1}^{s_1}$, antidiquark $[\bar{u}\bar{d}{]}_{c_2}^{s_2}$ and their correlations in the states $T_{bb}^{-}$ by decomposing the interactions from various sources in the model. The absolute dominant color-spin configuration, more than $99\%$, in the $\rho$-mode with $1^1{P}_1$ is $[bb{]}_{\bar{3}}^0[\bar{u}\bar{d}{]}_3^0$. Its energy is lower by about $18$ MeV than the threshold $\bar{B}\bar{B}$ so that it can establish a compact bound state. The chromomagnetic and meson-exchange interactions in the antidiquark $[\bar{u}\bar{d}{]}_3^0$ are responsible for its binding mechanism. Two other excited modes are higher than their respective threshold. The color configuration $6\otimes \bar{6}$ need to be handled discreetly in the tetraquark states.

Comments: 7 pages, 1 figures, 4 tables, to be published in Phys. Rev. D