arXiv 1607.081742016-07hep-lathep-ph

π介子跃迁形状因子$π^0 \to γ^* γ^*$的晶格计算

Lattice calculation of the pion transition form factor $π^0 \to γ^* γ^*$

Antoine Gérardin, Harvey B. Meyer, Andreas Nyffeler

备注：: 31 pages - Minor text improvements. Published version
发表信息：: Phys. Rev. D 94, 074507 (2016)
DOI：: 10.1103/PhysRevD.94.074507

摘要：

我们计算了两种夸克的格点QCD中的$π^0\to γ^*γ^*$跃迁形状因子${\cal F}_{π^0γ^*γ^*}(q_1^2,q_2^2)$。我们的主要动机是提供输入计算的$π^0$极的贡献强子光的光散射的μ子$(g-2)$，$a_μ^{\rm HLbL;π^0}$。因此，我们集中在该地区的两个光子是类空的虚拟约$1.5~$ GeV $^2$，这是迄今为止还没有实验访问。结果得到的物理π介子质量的连续相结合的外推。我们再现了手征异常的预测，实际光子的精度约为$8-9\%$。我们还比较了各种最近提出的模型，并找到合理的协议，其中一些模型的参数与它们的唯象值。最后，我们使用这些模型的晶格数据的参数化来计算$a_μ^{\rm HLbL;π^0}$。

英文摘要：

We calculate the $π^0\to γ^*γ^*$ transition form factor ${\cal F}_{π^0γ^*γ^*}(q_1^2,q_2^2)$ in lattice QCD with two flavors of quarks. Our main motivation is to provide the input to calculate the $π^0$-pole contribution to hadronic light-by-light scattering in the muon $(g-2)$, $a_μ^{\rm HLbL;π^0}$. We therefore focus on the region where both photons are spacelike up to virtualities of about $1.5~$GeV$^2$, which has so far not been experimentally accessible. Results are obtained in the continuum at the physical pion mass by a combined extrapolation. We reproduce the prediction of the chiral anomaly for real photons with an accuracy of about $8-9\%$. We also compare to various recently proposed models and find reasonable agreement for the parameters of some of these models with their phenomenological values. Finally, we use the parametrization of our lattice data by these models to calculate $a_μ^{\rm HLbL;π^0}$.

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