论文标题
hadronic真空极化的多级蒙特卡洛计算$（g_μ-2）$
Multi-level Monte Carlo computation of the hadronic vacuum polarization contribution to $(g_μ-2)$
论文作者
论文摘要
对于标准模型预测，必须在人均水平上确定对MUON异常磁矩$A_μ=（G_μ-2）/2 $的耐药贡献，以匹配正在进行的E989实验中预期的最终不确定性。这是分散方法的当前精度的3倍，比晶格QCD的纯粹理论确定的不确定性小5-15倍。到目前为止，绊脚石是对所需相关函数的蒙特卡洛评估中的巨大统计误差，而这些函数几乎无法被蛮力驯服。在这里，我们建议通过多级蒙特卡洛整合解决这个问题，该技术在田间距离内呈指数级降低相关器的方差。我们通过在线性延伸为3 fm，0.065 fm的间距和270 MeV的晶格上计算晶格上的辐射真空极化来测试我们的策略。实际上，两级集成通过通过模拟成本加速其反向缩放来忽略了长距离遗漏的统计误差的贡献。这些发现建立了多级蒙特卡洛，作为一种固体有效的方法，用于确定对$a_μ$的耐药贡献的精确晶格。由于该方法适用于受信噪比问题影响的其他计算，因此它有可能为核和粒子物理社区解锁许多开放问题。
The hadronic contribution to the muon anomalous magnetic moment $a_μ=(g_μ-2)/2$ has to be determined at the per-mille level for the Standard Model prediction to match the expected final uncertainty from the ongoing E989 experiment. This is 3 times better than the current precision from the dispersive approach, and 5-15 times smaller than the uncertainty on the purely theoretical determinations from lattice QCD. So far the stumbling-block is the large statistical error in the Monte Carlo evaluation of the required correlation functions which can hardly be tamed by brute force. Here we propose to solve this problem by multi-level Monte Carlo integration, a technique which reduces the variance of correlators exponentially in the distance of the fields. We test our strategy by computing the Hadronic Vacuum Polarization on a lattice with a linear extension of 3 fm, a spacing of 0.065 fm, and a pion mass of 270 MeV. Indeed the two-level integration makes the contribution to the statistical error from long-distances de-facto negligible by accelerating its inverse scaling with the cost of the simulation. These findings establish multi-level Monte Carlo as a solid and efficient method for a precise lattice determination of the hadronic contribution to $a_μ$. As the approach is applicable to other computations affected by a signal-to-noise ratio problem, it has the potential to unlock many open problems for the nuclear and particle physics community.
