格点量子色动力学中同位旋1/2 $Dπ$散射和最轻的$D_0^\ast$共振
Isospin-1/2 $Dπ$ scattering and the lightest $D_0^\ast$ resonance from lattice QCD
摘要：
用格点量子色动力学计算了1/2 $Dπ$散射的振幅，工作在一个体积约为$(3.6\; \mathrm{fm})^3$，轻夸克质量对应于$m_π\approx239$ MeV的情况下.计算了弹性$Dπ$能区的谱，得到20个能级。使用Lüscher有限体积量子化条件，这些能量被转化为对无限体积散射振幅的约束，从而使我们能够映射出弹性$Dπ$散射的能量依赖性。通过分析连续的散射振幅的范围内，$D_0^\ast$共振极点始终被发现强烈耦合到$S$波$Dπ$通道，具有质量$m\approx 2200$ MeV和宽度$Γ\approx400$ MeV。结合以前的工作调查的$D_{s0}^\ast$，和$D_0^\ast$与较重的轻夸克，类似的耦合之间的这些标量状态和它们的相关介子介子散射通道被确定。与目前报道的实验结果相反，始终发现$D_0^\ast$的质量远低于$D_{s0}^\ast$。
英文摘要：
Isospin-1/2 $Dπ$ scattering amplitudes are computed using lattice QCD, working in a single volume of approximately $(3.6\; \mathrm{fm})^3$ and with a light quark mass corresponding to $m_π\approx239$ MeV. The spectrum of the elastic $Dπ$ energy region is computed yielding 20 energy levels. Using the Lüscher finite-volume quantisation condition, these energies are translated into constraints on the infinite-volume scattering amplitudes and hence enable us to map out the energy dependence of elastic $Dπ$ scattering. By analytically continuing a range of scattering amplitudes, a $D_0^\ast$ resonance pole is consistently found strongly coupled to the $S$-wave $Dπ$ channel, with a mass $m\approx 2200$ MeV and a width $Γ\approx400$ MeV. Combined with earlier work investigating the $D_{s0}^\ast$, and $D_0^\ast$ with heavier light quarks, similar couplings between each of these scalar states and their relevant meson-meson scattering channels are determined. The mass of the $D_0^\ast$ is consistently found well below that of the $D_{s0}^\ast$, in contrast to the currently reported experimental result.
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