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).
Highlights
Many theoretical efforts since the formulation of QCD have hypothesized the existence of exotic states containing four or more quarks and/or antiquarks
We perform a study at fixed pion mass, with non-relativistic QCD (NRQCD) for the heavy quarks, simulating qq0b 0band qq0b 0b 0 tetraquarks with q, q0 1⁄4 ud or ls and variable, unphysical mb0 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 mb0 1⁄4 mc is reached, the results at higher mb0 clearly identify the udb 0bchannel as the most likely to support a strong-interaction-stable tetraquark state at mb0 1⁄4 mc
Summary
Many theoretical efforts since the formulation of QCD have hypothesized the existence of exotic states containing four or more quarks and/or antiquarks (for a recent review see [1] and references therein). In this work we use lattice QCD to investigate configurations of two light quarks and two heavy antiquarks in channels expected to be favorable to the formation of bound, exotic tetraquark states. The increase with decreasing heavy-quark mass of the net residual light-heavy spin-dependent attraction in the two-meson (vector-pseudoscalar) threshold will reduce the tetraquark binding relative to this threshold and produce binding corrections proportional to the inverse of the heavy quark mass These qualitative expectations can be tested by extending our previous study to include unphysical values of the masses of one or both of the two heavy antiquarks. For the variable-heavy-mass study, we will focus our attention on the ensemble with mπ 1⁄4 299 MeV and study the heavy anti-diquark mass dependence for unphysical tetraquark candidates qq0Q Q 0, with q 1⁄4 u, q0 1⁄4 d, s, and either Q 0 ≠ Qor Q 0 1⁄4 Q
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