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⁺) udc̄b̄ tetraquark with mass in the range of 15 to 61 MeV below D̄B* threshold. Since this range includes the electromagnetic D̄Bγ 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^'b̄^'b̄ and qq^'b̄^'b̄^' tetraquarks with q, q^'=ud or s and variable, unphysical m_b^' 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^'=mc is reached, the results at higher m_b^' clearly identify the udb̄^'b̄ channel as the most likely to support a strong-interaction-stable tetraquark state at m_b^'=mc. This observation serves to motivate the direct udc̄b̄ simulation. Throughout we use dynamical nf=2+1 ensembles with pion masses m_π=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).