发表机构
University of Edinburgh（爱丁堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种直接从位置空间欧几里得关联函数获取复动量形状因子的方法，无需解析延拓或逆问题求解，可扩展解析域并改进电荷半径测定，并在二维O(3)模型中验证。
AI 中文摘要
我们证明，在复值动量下评估的形状因子可以直接从位置空间的欧几里得关联函数中获取，而无需对后者进行解析延拓，也无需解决逆问题。该方法直接将双边拉普拉斯变换应用于格点数据，从而在收敛域内提供解析延拓后的形状因子。聚焦于量子色动力学（QCD）中的π介子形状因子，这使得我们能够在扩展的解析域内，即所有实部大于-4m_π^2的复数Q^2，将可观测量作为不变量Q^2的函数进行访问。例如，这可用于改进电荷半径的测定，或为基于共形映射的数据拟合提供更完整的数据。在开发了适用于无穷体积关联函数的方法之后，我们讨论了适用于实际计算的有限体积估计器的各种选项，包括位置空间拟合或应用由具有虚扭转角的边界条件表示的空间化学势。最后，我们使用蒙特卡洛数据在二维O(3)非线性σ模型中测试了该方法。
英文摘要
We demonstrate that form factors evaluated at complex-valued momenta can be directly accessed from position-space Euclidean correlators without analytically continuing the latter and without solving an inverse problem. The approach directly applies a bilateral Laplace transform to the lattice data, which provides the analytically continued form factor wherever it converges. Focusing on the pion form factor in Quantum Chromodynamics (QCD), this gives access to the observable as a function of invariant \(Q^2\) throughout an extended analytic domain consisting of all complex \(Q^2\) with real part larger than \(-4m_π^2\). This could, for example, be used to improve charge-radius determinations or provide more complete data for fits based on conformal mapping of the data. After developing the approach for infinite-volume correlators, we discuss various options for finite-volume estimators suitable for realistic calculations, including position-space fits or application of a spatial chemical potential represented by boundary conditions with an imaginary twist angle. Finally, we test the method in the two-dimensional \(O(3)\) nonlinear sigma model using Monte Carlo data.
Comments40 pages, 11 figures
