论文标题
HVP对MUON $ G-2 $的有限尺寸效果与C $^{\ Star} $边界条件
Finite-Size Effects of the HVP Contribution to the Muon $g-2$ with C$^{\star}$ Boundary Conditions
论文作者
论文摘要
MUON $ G-2 $是由于实验平均值，数据驱动的理论结果和晶格结果的当前站立张力而引人注目的数量。匹配Fermilab和J-Parc实验的最终目标准确性将构成未来几年的Lattice社区的重大挑战。因此，值得考虑不同的选择来控制系统错误。在此程序中，我们讨论了在存在C $^{\ Star} $边界条件下，领先的强子真空极化（HVP）贡献对MUON $ G-2 $的有限效应。在考虑对HVP的均质校正时，C $^{\ star} $边界条件在有限体积中提供了$ \ mathrm {qcd+qed} $的一致公式。即使可以在领先的HVP贡献的计算中避免这些边界条件，但我们发现有趣的结果是它们去除了领先的指数有限体积校正。实际上，与周期性情况相比，c $^{\ star} $边界条件将有限尺寸的效果切成一半，在物理大小$m_πl= 4 $的晶格上，几乎为$m_πl= 8 $的百分之十。我们讨论了这种减少的起源以及对计算效率的影响。
The muon $g-2$ is a compelling quantity due to the current standing tensions among the experimental average, data-driven theoretical results, and lattice results. Matching the final target accuracy of the experiments at Fermilab and J-PARC will constitute a major challenge for the lattice community in the coming years. For this reason, it is worthwhile to consider different options to keep the systematic errors under control. In this proceedings, we discuss finite-volume effects of the leading Hadron Vacuum Polarization (HVP) contribution to the muon $g-2$ in the presence of C$^{\star}$ boundary conditions. When considering isospin-breaking corrections to the HVP, C$^{\star}$ boundary conditions provide a possible consistent formulation of $\mathrm{QCD+QED}$ in finite volume. Even though these boundary conditions can be avoided in the calculation of the leading HVP contribution, we find the interesting result that they remove the leading exponential finite-volume correction. In practice, compared to the periodic case, C$^{\star}$ boundary conditions cut the finite-size effects in half on a lattice of physical size $M_πL=4$ and by a factor of almost ten for $M_πL=8$. We discuss the origin of this reduction and implications for computational efficiency.
