标题： 在格点QCD中，浅层$\bar{b}\bar{c}ud$四夸克束缚态和宽$\bar{b}\bar{c}ud$四夸克共振态在$B$-$D$和$B^*$-$D$散射中的证据 显示英文标题

标题： Evidence for shallow $\bar{b}\bar{c}ud$ tetraquark bound states and broad $\bar{b}\bar{c}ud$ tetraquark resonances in $B$-$D$ and $B^*$-$D$ scattering from lattice QCD

摘要： 我们首次利用格点QCD确定了$B$-$D$和$B^*$-$D$自旋为0的$S$-波散射振幅的能量依赖性，分别在阈值上下进行研究，这使我们能够严格检验混合底- charm$\bar{b}\bar{c}ud$四夸克是否存在作为束缚态或共振态。 通过Lüscher方法，从两种不同体积的能量谱中得到了散射相移。 为了确保不遗漏任何相关的能级，我们使用大而对称的$7 \times 7$和$8 \times 8$相关矩阵，这些矩阵在源和汇处包括$B^{(*)}$-$D$散射算符，以及最低的三或四个可能的背对背动量，此外还包括局部的$\bar{b}\bar{c}ud$算符。我们使用有效范围展开式来拟合提取的散射相移的能量依赖性。 我们在$B^{(*)}$-$D$的散射速率中观察到接近阈值的尖峰，这些尖峰与浅束缚态有关，无论是真实的还是虚拟的，均位于$B^{(*)}$-$D$阈值以下几 MeV 或更少。 此外，我们发现了质量约为$100$MeV 高于阈值的共振以及衰变宽度约为$200$MeV 的证据。 显示英文摘要

摘要： We present the first determination of the energy dependence of the $B$-$D$ and $B^*$-$D$ 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, $B^{(*)}$-$D$ 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 $B^{(*)}$-$D$ scattering rates close to the thresholds, which are associated with shallow bound states, either genuine or virtual, a few MeV or less below the $B^{(*)}$-$D$ thresholds. In addition, we find evidence for resonances with masses of order $100$ MeV above the thresholds and decay widths of order $200$ MeV.