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arXiv 1810.00007hep-phhep-exhep-latnucl-th
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双π介子对强子真空极化的贡献

Two-pion contribution to hadronic vacuum polarization

Gilberto Colangelo, Martin Hoferichter, Peter Stoffer

备注：
40 pages, 16 figures, 13 tables; version published in JHEP
发表信息：
JHEP 1902 (2019) 006
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摘要：

我们提出了一个详细的分析$e^+e^-\toπ^+π^-$数据$\sqrt{s}=1\,\text{GeV}$的分散关系的框架。从$ππ$ $P$ -波相移族出发，根据先前对$ππ$散射的Roy方程分析，我们用几个自由参数写出了π矢量形状因子的扩展Omnès表示，并研究了现代高统计数据集在多大程度上可以由遵循QCD一般原理的拟合函数来描述。我们发现，统计上可接受的拟合成为可能，只要考虑到能量校准中的潜在不确定性，提供一个强大的交叉检查的数据集的内部一致性，但更喜欢的质量的$ω$介子显着低于目前的PDG平均值。除了一个完整的治疗的统计和系统误差传播的数据，我们进行了全面的分析的系统误差的色散表示，并得出的后果为两π介子贡献强子真空极化。在一个全球性的适合时间和空间的数据集，我们发现$a_μ^{ππ}|_{\leq 1\,\text{GeV}}=495.0(1.5)(2.1)\times 10^{-10}$和$a_μ^{ππ}|_{\leq 0.63\,\text{GeV}}=132.8(0.4)(1.0)\times 10^{-10}$。虽然限制，因此最严格的低能量，我们得到的不确定性估计在整个能量范围内，应该证明有价值的证实相应的贡献异常磁矩的μ子。作为副产品，我们得到改进的约束$ππ$ $P$波，有价值的输入，为未来的全球分析的低能量$ππ$散射，以及确定的π电荷半径，$\langle r_π^2 \rangle = 0.429(1)(4)\,\text{fm}^2$。

英文摘要：

We present a detailed analysis of $e^+e^-\toπ^+π^-$ data up to $\sqrt{s}=1\,\text{GeV}$ in the framework of dispersion relations. Starting from a family of $ππ$ $P$-wave phase shifts, as derived from a previous Roy-equation analysis of $ππ$ scattering, we write down an extended Omnès representation of the pion vector form factor in terms of a few free parameters and study to which extent the modern high-statistics data sets can be described by the resulting fit function that follows from general principles of QCD. We find that statistically acceptable fits do become possible as soon as potential uncertainties in the energy calibration are taken into account, providing a strong cross check on the internal consistency of the data sets, but preferring a mass of the $ω$ meson significantly lower than the current PDG average. In addition to a complete treatment of statistical and systematic errors propagated from the data, we perform a comprehensive analysis of the systematic errors in the dispersive representation and derive the consequences for the two-pion contribution to hadronic vacuum polarization. In a global fit to both time- and space-like data sets we find $a_μ^{ππ}|_{\leq 1\,\text{GeV}}=495.0(1.5)(2.1)\times 10^{-10}$ and $a_μ^{ππ}|_{\leq 0.63\,\text{GeV}}=132.8(0.4)(1.0)\times 10^{-10}$. While the constraints are thus most stringent for low energies, we obtain uncertainty estimates throughout the whole energy range that should prove valuable in corroborating the corresponding contribution to the anomalous magnetic moment of the muon. As side products, we obtain improved constraints on the $ππ$ $P$-wave, valuable input for future global analyses of low-energy $ππ$ scattering, as well as a determination of the pion charge radius, $\langle r_π^2 \rangle = 0.429(1)(4)\,\text{fm}^2$.

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