Electromagnetic finite-size effects to the hadronic vacuum polarization
Electromagnetic finite-size effects to the hadronic vacuum polarization
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DOI：
10.1103/physrevd.100.014508
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发表时间：
2019-07-24
影响因子：
5
通讯作者：
Portelli, A.
中科院分区：
文献类型：
--
作者：
Bijnens, J.;Harrison, J.;Portelli, A.
为了减少当前强子在理论预测中对μ子异常磁矩的不确定性，晶格计算需要在强子-真空极化贡献上达到低于百分之一的精度。这需要包含（α）电磁校正。已知在晶格模拟中包含电磁相互作用会产生潜在的大有限尺寸效应，仅由逆空间范围的幂抑制。本文导出了标量QED中电磁耦合下阶强子真空极化的双介子贡献的QED(L)有限体积修正的解析表达式。发现首项的阶为1/L-3，其中L为空间范围。1/L-2项不存在，因为电流是中性的，因此远处的光子看不到电荷，我们证明这个结果是普遍的。我们的分析结果与环积分的数值计算结果以及随机产生光子场的晶格标量U(1)规范理论的模拟结果一致。在后一种情况下，该协议取决于指数抑制的有限体积效应。为了完整起见，我们还利用双环主积分的基础计算了无限体积中的强子真空极化。
In order to reduce the current hadronic uncertainties in the theory prediction for the anomalous magnetic moment of the muon, lattice calculations need to reach subpercent accuracy on the hadronic-vacuum-polarization contribution. This requires the inclusion of (alpha) electromagnetic corrections. The inclusion of electromagnetic interactions in lattice simulations is known to generate potentially large finite-size effects suppressed only by powers of the inverse spatial extent. In this paper we derive an analytic expression for the QED(L) finite-volume corrections to the two-pion contribution to the hadronic vacuum polarization at next-to-leading order in the electromagnetic coupling in scalar QED. The leading term is found to be of order 1/L-3 where L is the spatial extent. A 1/L-2 term is absent since the current is neutral and a photon far away thus sees no charge and we show that this result is universal. Our analytical results agree with results from the numerical evaluation of loop integrals as well as simulations of lattice scalar U(1) gauge theory with stochastically generated photon fields. In the latter case the agreement is up to exponentially suppressed finite-volume effects. For completeness we also calculate the hadronic vacuum polarization in infinite volume using a basis of 2-loop master integrals.