Doubly heavy tetraquark bound and resonant states

We calculate the energy spectrum of the S-wave doubly heavy tetraquark systems, including the $QQ^{(\prime)}\bar q\bar q$, $QQ^{(\prime)}\bar s\bar q$, and $QQ^{(\prime)}\bar s\bar s$ ($Q^{(\prime)}=b,c$ and $q=u,d$) systems within the constituent quark model. We use the complex scaling method to obtain bound states and resonant states simultaneously, and the Gaussian expansion method to solve the complex-scaled four-body Schr\"odinger equation. With a novel definition of the root-mean-square radii, we are able to distinguish between meson molecules and compact tetraquark states. The compact tetraquarks are further classified into three different types with distinct spatial configurations: compact even tetraquarks, compact diquark-antidiquark tetraquarks and compact diquark-centered tetraquarks. In the $I(J^P)=0(1^+)$ $QQ\bar q\bar q$ system, there exists the $D^*D$ molecular bound state with a binding energy of $-14$ MeV, which is the candidate for $T_{cc}(3875)^+$. The shallow $\bar B^*\bar B$ molecular bound state is the bottom analog of $T_{cc}(3875)^+$. Moreover, we identify two resonant states near the $D^*D^*$ and $\bar B^*\bar B^*$ thresholds. In the $J^P=1^+$ $bb\bar q\bar q\,(I=0)$ and $bb\bar s\bar q$ systems, we obtain deeply bound states with a compact diquark-centered tetraquark configuration and a dominant $\chi_{\bar 3_c\otimes 3_c}$ component, along with resonant states with similar configurations as their radial excitations. These states are the QCD analog of the helium atom. We also obtain some other bound states and resonant states with ``QCD hydrogen molecule" configurations. Moreover, we investigate the heavy quark mass dependence of the $I(J^P)=0(1^+)$ $QQ\bar q\bar q$ bound states. We strongly urge the experimental search for the predicted states.