$T^+_{cc}$ and its partners

Inspired by the $T^+_{cc}$ signal discovered by the LHCb Collaboration, we systematically investigate the doubly heavy tetraquark states with the molecule configuration $[Q_1\bar{q}_2][Q_3\bar{q}_4]$ ($Q=c$ and $b$, $q=u$, $d$ and $s$) in a nonrelativistic quark model. The model involves a color screening confinement potential, meson-exchange interactions and one-gluon-exchange interactions. The $T^+_{cc}$ state with $IJ^P=01^+$ is a very loosely bound deuteron-like state with a binding energy around 0.34 MeV and a huge size of 4.32 fm. Both the meson exchange force and the coupled channel effect play a pivotal role. Without the meson exchange force, there does not exist the $T^+_{cc}$ molecular state. In strong contrast, the QCD valence bond forms clearly in the $T^+_{bb}$ system when we turn off the meson-exchange force, which is very similar to the hydrogen molecule in QED. Moreover, the $T^+_{bb}$ becomes a helium-like QCD-atom if we increase the bottom quark mass by a factor of three. Especially, the $T^+_{bb}$ states with $01^+$, $T^+_{bc}$ with $00^+$ and $01^+$ and the $V$-spin antisymmetric states $T^+_{bbs}$ with $\frac{1}{2}1^+$, $T^+_{bcs}$ with $\frac{1}{2}0^+$ and $\frac{1}{2}1^+$ can form a compact, hydrogen molecule-like or deuteron-like bound state with different binding dynamics. The high-spin states $T^+_{bc}$ with $02^+$ and $T^+_{bcs}$ with $\frac{1}{2}2^+$ can decay into $D$-wave $\bar{B}D$ and $\bar{B}_sD$ although they are below the thresholds $\bar{B}^*D^*$ and $\bar{B}^*_sD^*$, respectively. The isospin and $V$-spin symmetric states are unbound. We also calculate their magnetic moments and axial charges.