论文标题
晶格QCD+QED模拟对Lepton $ G-2 $的耐药贡献的比率
Ratios of the hadronic contributions to the lepton $g-2$ from Lattice QCD+QED simulations
论文作者
论文摘要
使用lattice QCD+QCD+QCD+QED模拟计算，对电子，Muon和Tau-Lepton的异常磁矩（HVP）的比率对电子，Muon和Tau-Lepton的异常磁矩贡献，$ a _ {\ ell = e，μτ}^{hvp，lo} $计算。结果包括$ o（α_{em}^2）$的效果，以及在订单$ o（α_{em}^3）$和$ o（α__{em}^2（em}^2（m_u-m_d）$（m_u-m_d））$的电磁和强大的破坏issospin的校正，分别分别为$（m_u-m__-m__-m__d）$ - $ d $ n是$ nes $ nes $ nes $ nis $ nis $ - 我们采用由$ n_f = 2+1+1 $ dynamilical Quarks产生的量规配置，该量子的三个值（$ a \ simeq 0.062，0.082，0.089 $ fm），范围210-450 mev。我们表明，在电子比率的情况下，分子中的hadronic不确定性和分母中的hadronic不确定性在很大程度上取消了，而在电子-TAU和MUON-TAU比率的情况下，则不会发生这种取消。对于电子比率，我们得到$ r_ {e/μ} \ equiv（m_μ/m_e）^2（a_e^{hvp，lo}/a_μ^{hvp，lo}）= 1.1456〜（83）$，不关注$ \ simeq 0.7 \％$ $ $ \％\％\％$ \ simeq 0.7 \％。我们的结果代表了准确的标准模型（SM）预测，与使用实验$ E^+ E^ - \ to $ HADRONS数据的分散分析结果获得的估计非常吻合。取而代之的是，它与$ \ simeq 2.7 $的标准偏差不同于与当前的QED估计值减去当前的QED估算值后的预期价值（g-2）实验的价值。实验和QED对电子（g -2）的贡献提高了$ \ simeq 2 $的贡献，足以在显着性水平$ r_ {e/μ} $的SM值$ \ simeq 5 $标准偏差时达到张力。
The ratios among the leading-order (LO) hadronic vacuum polarization (HVP) contributions to the anomalous magnetic moments of electron, muon and tau-lepton, $a_{\ell=e,μτ}^{HVP,LO}$, are computed using lattice QCD+QED simulations. The results include the effects at order $O(α_{em}^2)$ as well as the electromagnetic and strong isospin-breaking corrections at orders $O(α_{em}^3)$ and $O(α_{em}^2(m_u-m_d))$, respectively, where $(m_u-m_d)$ is the $u$- and $d$-quark mass difference. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration with $N_f=2+1+1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082, 0.089$ fm) with pion masses in the range 210 - 450 MeV. We show that in the case of the electron-muon ratio the hadronic uncertainties in the numerator and in the denominator largely cancel out, while in the cases of the electron-tau and muon-tau ratios such a cancellation does not occur. For the electron-muon ratio we get $R_{e/μ} \equiv (m_μ/m_e)^2 (a_e^{HVP,LO} / a_μ^{HVP,LO}) = 1.1456~(83)$ with an uncertainty of $\simeq 0.7 \%$. Our result, which represents an accurate Standard Model (SM) prediction, agrees very well with the estimate obtained using the results of dispersive analyses of the experimental $e^+ e^- \to$ hadrons data. Instead, it differs by $\simeq 2.7$ standard deviations from the value expected from present electron and muon (g - 2) experiments after subtraction of the current estimates of the QED, electro-weak, hadronic light-by-light and higher-order HVP contributions, namely $R_{e/μ} = 0.575~(213)$. An improvement of the precision of both the experiment and the QED contribution to the electron (g - 2) by a factor of $\simeq 2$ could be sufficient to reach a tension with our SM value of the ratio $R_{e/μ}$ at a significance level of $\simeq 5$ standard deviations.
