发表机构
University of Edinburgh; CERN; DeepL SE; University of Cambridge; University of Cyprus（爱丁堡大学; 欧洲核子研究中心; DeepL公司; 剑桥大学; 塞浦路斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究完成SU(3)味对称格点QCD计算的第一部分，采用Wilson-clover规范系综与distillation框架，通过两种策略取连续极限，确定$D \to (Kπ)_{\mathbf{27}}$衰变的强相位，为完整衰变振幅分析奠定基础。
AI 中文摘要
我们呈现SU(3)味对称格点量子色动力学（QCD）计算的第一部分，该计算针对D介子衰变为Kπ末态的振幅，末态属于味对称群的27维不可约表示，记为$(Kπ)_{\mathbf{27}}$。本工作使用的Wilson-clover规范系综由OpenLat合作组生成，其参数调优至$M_π = M_K \approx 410\\,\mathrm{MeV}$。我们采用distillation框架，从投影到确定空间动量的单强子算符对构造欧几里得关联函数矩阵，通过求解广义本征值问题得到有限体积能谱，用于确定从阈值到$4 M_π \approx 1640\\,\mathrm{MeV}$的散射相移，该能量低于但合理处于$M_D^{\rm SU(3)} \simeq 1900\\,\mathrm{MeV}$的范围内。我们在三个格点间距下开展计算，并采用两种策略在计算的不同阶段取连续极限：（i）在提取的散射参数上取连续极限；（ii）在提取散射参数前，在固定物理体积的有限体积能谱上取连续极限。我们发现两种方法得到的散射相移作为质心系能量的函数$\delta_{\mathbf{27}}(E_{\sf cm})$结果一致。采用仅含散射长度的参数化，我们推导出弱衰变的强相位值为$\delta_{\mathbf{27}}(M_D^{\rm SU(3)})=-38.4(2.4)^\circ$。我们进一步描述使用相同算符基构造三点关联函数以提取$\langle (Kπ)_{\mathbf{27}}| H_W| D\rangle$的方法论，其中$H_W$为树图阶有效弱哈密顿量，以及将此类有限体积矩阵元与全衰变振幅关联的方法。后续手稿将呈现得到后者的完整分析。
英文摘要
We present part one of an SU(3)-flavour-symmetric lattice QCD calculation of the amplitude for a $D$-meson decaying to a $Kπ$ final state in the 27-dimensional irreducible representation of the flavour symmetry group, denoted $(Kπ)_{\mathbf{27}}$. The Wilson--clover gauge ensembles used in this work, generated by the OpenLat collaboration, are tuned such that $M_π= M_K \approx 410\,\mathrm{MeV}$. Using the distillation framework, we construct a matrix of Euclidean correlation functions from pairs of single-hadron operators projected to definite spatial momentum. Solving a generalised eigenvalue problem yields the finite-volume energy spectrum that is used to determine the scattering phase shift from threshold up to $4 M_π\approx 1640 \,\mathrm{MeV}$, which sits below but plausibly within reach of $M_D^{\rm SU(3)} \simeq 1900\,\mathrm{MeV}$. The calculation is performed across three lattice spacings, and we apply two strategies in which the continuum limit is taken at different stages of the computation: (i) on the extracted scattering parameters and (ii) on the finite-volume energies at fixed physical volume before extracting the scattering parameters. We find consistent results across these methods for the scattering phase shift as a function of the centre-of-mass energy, $δ_{\mathbf{27}}(E_{\sf cm})$. Taking a scattering-length-only parametrisation, we infer a value for the strong phase of the weak decay, $δ_{\mathbf{27}}(M_D^{\rm SU(3)})=-38.4(2.4)^\circ$. We further describe the methodology for using the same operator basis to compute three-point correlation functions to extract $\langle (Kπ)_{\mathbf{27}}| H_W| D\rangle$, for the tree-level effective weak Hamiltonian $H_W$, and for relating such finite-volume matrix elements to the full decay amplitude. The complete analysis leading to the latter will be presented in a forthcoming manuscript.
Comments41 pages, 15 figures, 6 tables
