标题： 窗口量用于计算μ子异常磁矩中的强子真空极化贡献，包括空间-like区域和时间-like区域 显示英文标题

标题： Window quantities for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment in spacelike and timelike domains

摘要： 强子真空极化对μ子异常磁矩贡献的窗口量在时空中和时间中关系的研究 $a^{\text{HVP}}_{\mu}$在时空和时间中区域被研究。 讨论了两种类型的窗口函数（突变和光滑）以及两种类型的运动学区间（相对于时空/时间中翻转对称和不对称）。 研究表明，如果考虑到窗口边缘效应的附加贡献，并推导出这些贡献的明确表达式，那么用强子真空极化函数、阿德勒函数和电子正电子湮灭成强子的$R$比率表示的$a^{\text{HVP}}_{\mu}$的窗口量评估是相互等价的。 所得结果使得能够准确比较基于 MUonE 或格点数据的$a^{\text{HVP}}_{\mu}$窗口量与基于$R$比率数据的窗口量，即使窗口函数覆盖的时空和时间中区域的运动学范围不同。 显示英文摘要

摘要： The relations between the window quantities for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment $a^{\text{HVP}}_{\mu}$ in spacelike and timelike domains are studied. Two types of window functions (abrupt and smooth) as well as two kinds of kinematic intervals (symmetric and asymmetric with respect to the spacelike/timelike flip) are addressed. It is shown that the evaluations of the window quantities for $a^{\text{HVP}}_{\mu}$ represented in terms of the hadronic vacuum polarization function, the Adler function, and the $R$-ratio of electron-positron annihilation into hadrons are mutually equivalent only if the additional contributions due to the window edge effects are properly taken into account and the explicit expressions for such contributions are derived. The obtained results enable one to accurately compare the window quantities for $a^{\text{HVP}}_{\mu}$ based, e.g., on MUonE or lattice data with the ones based on $R$-ratio data, even if the window function covers different kinematic ranges in spacelike and timelike domains.