We report a lattice QCD study of the heavy-light meson-meson interactions with an explicitly exotic flavor content $bc\overline{u}\overline{d}$, isospin $I=0$, and axial-vector $J^P=1^{+}$ quantum numbers in search of possible tetraquark bound states. The calculation is performed at four values of lattice spacing, ranging from $\sim 0.058$ to $\sim 0.12\mathrm{fm}$, and at five different values of valence light quark mass $m_{u/d}$, corresponding to pseudoscalar meson mass $M_{\mathrm{ps}}$ of about 0.5, 0.6, 0.7, 1.0, and 3.0 GeV. The energy eigenvalues in the finite volume are determined through a variational procedure applied to correlation matrices built out of two-meson interpolating operators as well as diquark-antidiquark operators. The continuum limit estimates for $D{\overline{B}}^{*}$ elastic $S$-wave scattering amplitude are extracted from the lowest finite-volume eigenenergies, corresponding to the ground states, using amplitude parametrizations supplemented by a lattice spacing dependence. Light quark mass $m_{u/d}$ dependence of the $D{\overline{B}}^{*}$ scattering length ($a_0$) suggests that at the physical pion mass $a_0^{\mathrm{phys}}=+0.57{(}_{-5}^{+4})(17)\mathrm{fm}$, which clearly points to an attractive interaction between the $D$ and ${\overline{B}}^{*}$ mesons that is strong enough to host a real bound state $T_{bc}$, with a binding energy of $-43{(}_{-7}^{+6}){(}_{-24}^{+14})\mathrm{MeV}$ with respect to the $D{\overline{B}}^{*}$ threshold. We also find that the strength of the binding decreases with increasing $m_{u/d}$ and the system becomes unbound at a critical light quark mass $m_{u/d}^{*}$ corresponding to $M_{\mathrm{ps}}^{*}=2.73(21)(19)\mathrm{GeV}$.

中文翻译：

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使用二介子和双夸克-反夸克变分基础从晶格 QCD 得到束缚等标量轴向矢量 bcu´d´ 四夸克 Tbc

我们报告了重-轻介子-介子相互作用与明确的异国风味含量的晶格 QCD 研究$乙C\stackrel{￣}{你}\stackrel{￣}{d}$, 同位旋$我=0$，和轴向矢量$J^{磷}=1^{+}$寻找可能的四夸克束缚态的量子数。计算是在四个晶格间距值下进行的，范围为$～0.058$到$～0.12\mathrm{调频}$，以及五个不同价态轻夸克质量值${米}_{你/d}$，对应于赝标量介子质量${\mathrm{中号}}_{\mathrm{附注}}$约0.5、0.6、0.7、1.0和3.0GeV。有限体积中的能量特征值是通过应用于由双介子插值算子以及双夸克-反双夸克算子构建的相关矩阵的变分过程来确定的。连续统极限估计为$D{\stackrel{￣}{乙}}^{*}$松紧带$S$使用由晶格间距依赖性补充的振幅参数化，从对应于基态的最低有限体积本征能中提取波散射振幅。轻夸克质量${米}_{你/d}$的依赖性$D{\stackrel{￣}{乙}}^{*}$散射长度（$A_0$）表明在物理π介子质量$A_0^{\mathrm{物理}}=+0.57{（}_{-5}^{+4}）（\mathrm{17\; 号}）\mathrm{调频}$，这清楚地表明了之间有吸引力的相互作用$D$和${\stackrel{￣}{乙}}^{*}$介子的强度足以容纳真实的束缚态${\mathrm{时间}}_{乙C}$，结合能为$-43{（}_{-7}^{+6}）{（}_{-24}^{+14}）\mathrm{兆伏}$相对于该$D{\stackrel{￣}{乙}}^{*}$临界点。我们还发现，结合强度随着增加而降低${米}_{你/d}$并且系统在临界轻夸克质量处变得不受约束${米}_{你/d}^{*}$对应于${\mathrm{中号}}_{\mathrm{附注}}^{*}=2.73（21）（19）\mathrm{GeV}$。