论文标题
$ρ-ω$混合在亲矢量形式及其对$（g-2）_μ$的影响的动量依赖性
Momentum-dependence of $ρ-ω$ mixing in the pion vector form factor and its effect on $(g-2)_μ$
论文作者
论文摘要
$ρ-ω$混合效果的包含对于精确描述了对Pion电磁形式的描述$ E e^+E^ - \rightArrowπ^+π^ - $过程，该过程量化了对MUON $a_μ$ $a_μ$的两个速度贡献的两种速度贡献。在本文中，我们通过在共鸣性手性理论框架内以$ 1/n_c $扩展的方式考虑$ρ-ω$混合的动量依赖性。我们重新审视[Y. H. Chen，D。L。Yao和H. Q. Zheng，Commun。理论。物理。 69（2018）1]，考虑到Kaon循环中的Kaon质量分裂和最新的实验数据产生的贡献。我们执行两种拟合（与动量无关或动量有关的$ρ-ω$混合振幅）来描述$ e^+e^ - \rightarrowπ^+π^ - $和$τ\rightArrowν_τ2π$在能源区域内的600 $ $ \ sim $ 900 mev and $ 900 $ \ $ und的$ \ $^y和pright的能源区域中比较他们的结果。我们的发现表明，动量无关和动量依赖性$ρ-ω$混合方案都提供了适当的数据描述。但是，考虑到获得的混合矩阵元素的合理虚构部分$π_{ρΩ} $，该动量依赖性方案表现出更大的自洽性。 Regarding the contribution to the anomalous magnetic moment of the muon, $a_μ^{ππ}|_{[0.6,0.9]\text{GeV}}$, the results obtained from the fits considering the momentum-dependent $ρ-ω$ mixing amplitude agree well with those obtained without incorporating the momentum dependence of the $ρ-ω$ mixing, within the margin of errors.此外，基于相关参数的拟合值，我们观察到$ω\rightarrowπ^+π^ - $的衰减宽度主要受$ρ-ω$混合效应的影响。
The inclusion of the $ρ-ω$ mixing effect is essential for a precise description of the pion electromagnetic form factor in the $e^+e^- \rightarrow π^+π^-$ process, which quantifies the two-pion contribution to the anomalous magnetic moment of the muon $a_μ$. In this paper, we analyse the momentum dependence of the $ρ-ω$ mixing by considering loop contributions at the next-to-leading order in the $1/N_C$ expansion within the framework of resonance chiral theory. We revisit the work [Y. H. Chen, D. L. Yao, and H. Q. Zheng, Commun. Theor. Phys. 69 (2018) 1], considering the contribution arising from the kaon mass splitting in the kaon loops and the latest experimental data. We perform two kinds of fits (with momentum-independent or momentum-dependent $ρ-ω$ mixing amplitude) to describe the $e^+e^-\rightarrow π^+π^-$ and $τ\rightarrow ν_τ2π$ data within the energy region of 600$\sim$900 MeV and the decay width of $ω\rightarrow π^+π^-$, and compare their results. Our findings indicate that both the momentum-independent and momentum-dependent $ρ-ω$ mixing schemes provide appropriate descriptions of the data. However, the momentum-dependent scheme exhibits greater self-consistency, considering the reasonable imaginary part of the mixing matrix element $Π_{ρω}$ obtained. Regarding the contribution to the anomalous magnetic moment of the muon, $a_μ^{ππ}|_{[0.6,0.9]\text{GeV}}$, the results obtained from the fits considering the momentum-dependent $ρ-ω$ mixing amplitude agree well with those obtained without incorporating the momentum dependence of the $ρ-ω$ mixing, within the margin of errors. Furthermore, based on the fitted values of the relevant parameters, we observe that the decay width of $ω\rightarrow π^+π^-$ is predominantly influenced by the $ρ-ω$ mixing effect.
