论文标题
围绕$ρ$共振的Pion Form-Factor数据的分析性和单位性测试
Test of analyticity and unitarity for the pion form-factor data around the $ρ$ resonance
论文作者
论文摘要
有关$ e^+e^ - \至π^+π^ - $横截面和旋转矢量形式的高统计数据已通过多个协作获得。不幸的是，到目前为止，不同数据集之间存在一些紧张关系，尤其是最精确的数据集之间尚未解决。因此，对数据的其他独立限制引起了人们的关注。我们考虑了最近提出的一种无参数性外推的方法，该方法基于混合阶段和模量极端问题，并将严格的上限和下限与数值模拟相结合，以说明输入和输出值的统计分布。关于区域中模量$（0.65-0.71）$ GEV的模量和测量值的空格数据被用作输入。在以前的作品中，形式主义被应用于将外形量推送到低能量。在目前的工作中，我们将其用作围绕$ρ$共振的高统计数据的一致性和分析性和单位性的一致性的严格和模型独立的测试。该研究揭示了一些不一致之处，尤其是低于$ρ$峰值的巴巴尔数据略高于外推值频段，而高于$ρ$峰的频段所有数据都位于频段的下边缘。简要讨论了结果对两杆真空偏振的贡献的影响。
High-statistics data on the $e^+e^-\to π^+π^-$ cross section and the pion vector form factor have been obtained recently by several collaborations. Unfortunately, there are some tensions between different datasets, especially the most precise ones, which have not been resolved so far. Additional independent constraints on the data are therefore of interest. We consider a parametrization-free method of analytic extrapolation proposed recently, which is based on a mixed phase and modulus extremal problem and combines rigorous upper and lower bounds with numerical simulations to account for the statistical distributions of the input and output values. Spacelike data on the form factor and measurements of the modulus in the region $(0.65-0.71)$ GeV are used as input. In previous works, the formalism was applied for extrapolating the form factor to low energies. In the present work, we use it as a stringent and model-independent test of consistency with analyticity and unitarity for the high-statistics data around the $ρ$ resonance. The study reveals some inconsistencies, in particular below the $ρ$ peak the BABAR data are slightly higher than the band of extrapolated values, while above the $ρ$ peak all the data are situated at the lower edge of the band. The implications of the results on the two-pion vacuuum polarization contribution to the anomalous magnetic moment of the muon are briefly discussed.
