Finite-volume and thermal effects in the leading-HVP contribution to muonic $(g-2)$
Maxwell T. Hansen, Agostino Patella
备注：
74 pages, 7 figures, 3 tables, CERN-TH-2020-053, HU-EP-20/08; v2: added missing references and included more detailed numerical comparison, corrected factor of (-1/3) in finite-T results, leading to a change in table 3
在$a^{\text{HVP,LO}}_μ\equiv (g-2)^{\text{HVP,LO}}_μ/2$的数值格点量子色动力学计算中，有限体积效应和热效应被确定为π介子的相对论有效场论相互作用的所有阶数。与基于有限体积哈密顿量的早期工作相比，这里给出的结果是通过正式总结所有费曼图对欧几里得电磁流两点函数的贡献而得出的，具有任何数量的内部π环和相互作用顶点。正如我们在以前的出版物中已经发现的那样，对$a^{\text{HVP,LO}}_μ$的主要有限体积修正标度为$\exp[- m L]$，其中$m$是π介子质量，$L$是三个周期性空间方向的长度。在这项工作中，我们还控制两个子领先的指数，缩放为$\exp[- \sqrt{2} m L]$和$\exp[- \sqrt{3} m L]$。与首项一样，这些项的系数由π介子的前向康普顿振幅给出，这意味着有效理论的所有细节都从最终结果中消失。热效应被另外考虑，并发现是典型的晶格计算的子百分比水平。所有的有限体积校正都为$a^{\text{HVP,LO}}_μ$和每个时间片的两点函数，后者预计将是特别有用的，在纠正小到中等电流分离，一系列的指数表现出良好的收敛。
英文摘要：
The leading finite-volume and thermal effects, arising in numerical lattice QCD calculations of $a^{\text{HVP,LO}}_μ\equiv (g-2)^{\text{HVP,LO}}_μ/2$, are determined to all orders with respect to the interactions of a generic, relativistic effective field theory of pions. In contrast to earlier work based in the finite-volume Hamiltonian, the results presented here are derived by formally summing all Feynman diagrams contributing to the Euclidean electromagnetic-current two-point function, with any number of internal pion loops and interaction vertices. As was already found in our previous publication, the leading finite-volume corrections to $a^{\text{HVP,LO}}_μ$ scale as $\exp[- m L]$ where $m$ is the pion mass and $L$ is the length of the three periodic spatial directions. In this work we additionally control the two sub-leading exponentials, scaling as $\exp[- \sqrt{2} m L]$ and $\exp[- \sqrt{3} m L]$. As with the leading term, the coefficient of these is given by the forward Compton amplitude of the pion, meaning that all details of the effective theory drop out of the final result. Thermal effects are additionally considered, and found to be sub-percent-level for typical lattice calculations. All finite-volume corrections are presented both for $a^{\text{HVP,LO}}_μ$ and for each time slice of the two-point function, with the latter expected to be particularly useful in correcting small to intermediate current separations, for which the series of exponentials exhibits good convergence.
Hadronic vacuum polarization contribution to the muon $g-2$ with 2+1 flavor lattice QCD on a larger than (10 fm$)^4$ lattice at the physical point
研究了格点量子色动力学计算强子真空极化对μ子$g-2$贡献的系统不确定性。我们调查三个系统的影响，有限体积（FV）的效果，截止效应，和集成方案的依赖性。我们使用PACS 10组态在相同的截止尺度下评估了两种不同体积的（5.4 fm $)^4$和（10.8 fm $)^4$）在物理π质量下的FV效应。对于截止效应，我们比较了两种类型的晶格矢量运营商，这是本地和保守（点分裂）电流，通过改变截止尺度大于（10 fm $)^4$晶格的物理点。对于积分方案的依赖性，我们比较了在（10.8 fm $)^4$）晶格上的物理点处的坐标-和动量-空间积分方案之间的结果。在连续极限下，我们的结果是由$g-2$给出的，其中第一个误差是统计的，第二个误差是系统的.
