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

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(JP)=0(1+) udc¯b¯ tetraquark with mass in the range of 15 to 61 MeV below D¯B* threshold. Since this range includes the electromagnetic D¯Bγ 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 non-relativistic QCD (NRQCD) for the heavy quarks, simulating qq′b¯′b¯ and qq′b¯′b¯′ tetraquarks with q, q′=ud or ℓs and variable, unphysical mb′ 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 mb′=mc is reached, the results at higher mb′ clearly identify the udb¯′b¯ channel as the most likely to support a strong-interaction-stable tetraquark state at mb′=mc. This observation serves to motivate the direct udc¯b¯ simulation. Throughout we use dynamical nf=2+1 ensembles with pion masses mπ=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).