Evidence for charm-bottom tetraquarks and the mass dependence of heavy-light tetraquark states from lattice QCD

Abstract: We continue our study of heavy-light four-quark states and find evidence from lattice QCD for the existence of a strong-interaction-stable $I(J^P)=0(1^+)$ $ud\bar{c}\bar{b}$ tetraquark with mass in the range of 15 to 61 MeV below $\bar{D}B^*$ threshold. Since this range includes the electromagnetic $\bar{D}B\gamma$ decay threshold, current uncertainties do not allow us to determine whether such a state would decay electromagnetically, or only weakly. We also perform a study at fixed pion mass, with NRQCD for the heavy quarks, simulating $qq^\prime \bar{b}^\prime \bar{b}$ and $q q^\prime \bar{b}^\prime\bar{b}^\prime$ tetraquarks with $q,\, q^\prime =ud$ or $\ell s$ and variable, unphysical $m_{b^\prime}$ in order to investigate the heavy mass-dependence of such tetraquark states. We find that the dependence of the binding energy follows a phenomenologically-expected form and that, though NRQCD breaks down before $m_{b^\prime}=m_c$ is reached, the results at higher $m_{b^\prime}$ clearly identify the $ud\bar{b}^\prime \bar{b}$ channel as the most likely to support a strong-interaction-stable tetraquark state at $m_{b^\prime}=m_c$. This observation serves to motivate the direct $ud\bar{c}\bar{b}$ simulation. Throughout we use dynamical $n_f=2+1$ ensembles with pion masses $m_\pi=$415, 299, and 164 MeV reaching down almost to the physical point, a relativistic heavy quark prescription for the charm quark, and NRQCD for the bottom quark(s).