标题： 浅束缚态和夸克成分$\bar{b}\bar{c}ud$在格点QCD的$B$-$\bar{D}$和$B^*$-$\bar{D}$散射中的宽共振线索 显示英文标题

标题： Shallow Bound States and Hints for Broad Resonances with Quark Content $\bar{b}\bar{c}ud$ in $B$-$\bar{D}$ and $B^*$-$\bar{D}$ Scattering from Lattice QCD

摘要： 我们首次利用格点QCD确定了能量依赖关系，包括同位旋为0的$B$-$\bar{D}$和$B^*$-$\bar{D}$波散射振幅，以及$S$波散射振幅，这些振幅既在阈值以下也在阈值以上。这使我们能够严格检验是否存在作为束缚态或共振态的混合底夸克-粲夸克四夸克态$\bar{b}\bar{c}ud$。散射相移是通过Lüscher方法从两个不同体积中的能谱中得到的。 为了确保没有相关的能级被遗漏，我们使用了大型的、对称的包含源和湮没点的$7 \times 7$和$8 \times 8$相关矩阵，其中除了局域的$\bar{b}\bar{c}ud$算符外，还包括具有最低三个或四个可能的背对背动量的$B^{(*)}$至$\bar{D}$散射算符。 我们利用有效范围展开式来拟合提取出的散射相移的能量依赖性。 我们观察到，在阈值附近，$B^{(*)}$-$\bar{D}$散射率出现尖锐的峰值，这些峰值与浅束缚态有关，无论是真实的还是虚拟的，束缚态的能量比$B^{(*)}$-$\bar{D}$阈值低几兆电子伏或更低。 此外，我们还发现了一些迹象表明，在阈值上方约$100$兆电子伏处存在共振态，其衰变宽度约为$200$兆电子伏。 显示英文摘要

摘要： We present the first determination of the energy dependence of the $B$-$\bar{D}$ and $B^*$-$\bar{D}$ isospin-0, $S$-wave scattering amplitudes both below and above the thresholds using lattice QCD, which allows us to investigate rigorously whether mixed bottom-charm $\bar{b}\bar{c}ud$ tetraquarks exist as bound states or resonances. The scattering phase shifts are obtained using L\"uscher's method from the energy spectra in two different volumes. To ensure that no relevant energy level is missed, we use large, symmetric $7 \times 7$ and $8 \times 8$ correlation matrices that include, at both source and sink, $B^{(*)}$-$\bar{D}$ scattering operators with the lowest three or four possible back-to-back momenta in addition to local $\bar{b}\bar{c}ud$ operators. We fit the energy dependence of the extracted scattering phase shifts using effective-range expansions. We observe sharp peaks in the $B^{(*)}$-$\bar{D}$ scattering rates close to the thresholds, which are associated with shallow bound states, either genuine or virtual, a few MeV or less below the $B^{(*)}$-$\bar{D}$ thresholds. In addition, we find hints for resonances with masses of order $100$ MeV above the thresholds and decay widths of order $200$ MeV.