论文标题
对Muonic $（G-2）$的领先HVP贡献中有限体积和热效应
Finite-volume and thermal effects in the leading-HVP contribution to muonic $(g-2)$
论文作者
论文摘要
主要的有限体积和热效应，是在数值晶格QCD计算中产生的，$ a^{\ text {hvp，lo}}_μmequiv（g-2）^{\ equiv（g-2）^{\ text {hvp，lo}} _μ/2 $都确定了与互动相关性的依据。与基于有限体积哈密顿量的早期工作相反，此处介绍的结果是通过正式求和的所有有助于欧几里得电磁电流的两点功能的Feynman图，并具有任何数量的内部斜向loop和交互作用。正如我们先前出版物中已经发现的那样，领先的有限体积校正对$ a^{\ text {hvp，lo}} _μ$比例为$ \ exp [ - m l] $，其中$ m $是the pion smos，$ l $是三个周期空间方向的长度。在这项工作中，我们还控制两个子领先的指数，将缩放为$ \ exp [ - \ sqrt {2} m l] $和$ \ exp [ - \ sqrt {3} m l] $。与前术语一样，它们的系数由亲核的前向综合幅度给出，这意味着有效理论的所有细节都退出了最终结果。还考虑了热效应，并且发现对于典型的晶格计算是次级级别。所有有限体积校正均以$ a^{\ text {hvp，lo}} _μ$的形式呈现，并且每次两点功能的每次切片，后者有望在纠正小到中间的电流分离方面特别有用，因此，一系列的Expients均表现出良好的转换。
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.
