AI 中文总结
该论文围绕强子结构、散射及衰变展开研究，开发晶格量子色动力学方法，利用Mathematica包构建算符，通过量子化条件关联有限与无限体积谱，研究多强子共振，给出相关预测并建立程序，还研究粲介子衰变，为强子共振研究提供新成果与见解。
AI 中文摘要
本论文开发了用于研究强子结构、散射和衰变的晶格量子色动力学方法，特别关注多强子共振。开发了Mathematica包OpTion以自动构建晶格多强子算符。通过量子化条件将有限体积谱与无限体积振幅联系起来。对于耦合通道Dπ散射，确定了极点轨迹和散射长度的π介子质量依赖性，结果支持D0*(2300)的双极结构。接着研究了ω(782)的三π衰变，计算了两体和三体谱，开发了三体量子化条件和有效场论描述。提取的共振极点外推到物理点，给出与实验一致的质量和宽度，为相互作用的三体系统建立了实用的第一性原理程序。这些方法进一步应用于π(1300)，首次给出了其在多个π介子质量下的共振极点的第一性原理预测，揭示了显著的三体效应。最后研究了粲介子的辐射和半轻子衰变，开发了一种与模型无关的方法来更精确地提取跃迁形状因子。这些结果推进了耦合通道和三体强子共振的第一性原理研究，并为其结构和衰变提供了新见解。
英文摘要
This thesis develops lattice-QCD methods for studying hadron structure, scattering, and decays, with particular emphasis on multi-hadron resonances. The \texttt{Mathematica} package \texttt{OpTion} is developed to automate the construction of lattice multi-hadron operators. Finite-volume spectra are related to infinite-volume amplitudes through quantization conditions. For coupled-channel $Dπ$ scattering, the pion-mass dependence of the pole trajectories and the scattering length are determined, and the results support a two-pole structure for the $D_0^*(2300)$. The thesis then studies the three-pion decay of the $ω(782)$. Two- and three-body spectra are calculated, and three-body quantization conditions and effective field theory descriptions are developed. The extracted resonance pole, extrapolated to the physical point, gives a mass and width consistent with experiment and establishes a practical first-principles procedure for interacting three-body systems. These methods are further applied to the $π(1300)$, providing, for the first time, first-principles predictions of its resonance pole at several pion masses and revealing significant three-body effects. Finally, radiative and semileptonic decays of charmed mesons are investigated, and a model-independent method is developed to extract transition form factors with improved precision. These results advance the first-principles study of coupled-channel and three-body hadron resonances and provide new insight into their structure and decays.
CommentsPh.D. thesis, Peking University, 2026. English translation of the original Chinese version
