$\varepsilon'/\varepsilon$中的同位旋破缺：$η_0$在2020年代初的影响
Isospin-breaking in $\varepsilon'/\varepsilon$: Impact of $η_0$ at the Dawn of the 2020s
摘要：
对于$K\toππ$衰变中的直接CP破坏，通常在百分比水平上的同位旋破缺效应被$ΔI=1/2$规则背后的动力学放大，并通常编码在$Ω_{\rm IB}$参数中。更新的预测$Ω_{\rm IB}^{(8)}=(15.9\pm 8.2)\times 10^{-2}$的手征微扰理论的强同位旋断裂由于$π_3-η_8$混合证实了这样的趋势，但相当敏感的理论输入值的低能量常数对应的味道单重$η_0$交换的贡献，在这个截断的八重态计划。相反，我们利用现象学的$η_8-η_0$混合作为探针的不可忽略的味道单重态分量的物理$η$极找到$Ω_{\rm IB}^{(9)}=(35\pm7)\times 10^{-2}$在一个完整的九重态计划。一个大的中心值，在九进制方案，从而取代了一个大的不确定性，在八位组之一。包括实验$π^+-π^0$质量差作为主导的电磁同位旋破缺，我们得到的有效参数进入比$ε'/ε$的改进结果$\hatΩ_{\rm eff}^{(9)}=(29\pm7)\times 10^{-2}$相比，$\hatΩ_{\rm eff}^{(8)}=(17\pm9)\times 10^{-2}$在最近的分析$ε'/ε$。相应地，我们得到从$(ε'/ε)_{\rm SM}^{(8)}=(17.4\pm 6.1)\times 10^{-4}$到$(ε'/ε)_{\rm SM}^{(9)}=(13.9\pm 5.2)\times 10^{-4}$的减少，从而有效地抑制$(ε'/ε)_{\rm SM}$的同位旋破缺修正大$40\%$相对于最近的RBC-UKQCD值。
英文摘要：
For direct CP-violation in $K\toππ$ decays, the usual isospin-breaking effects at the percent level are amplified by the dynamics behind the $ΔI=1/2$ rule and conventionally encoded in $Ω_{\rm IB}$ parameters. The updated prediction $Ω_{\rm IB}^{(8)}=(15.9\pm 8.2)\times 10^{-2}$ of the Chiral Perturbation Theory for the strong isospin-breaking due to $π_3-η_8$ mixing confirms such a tendency but is quite sensitive to the theoretical input value of the low-energy constant corresponding to the flavour-singlet $η_0$ exchange contribution in this truncated octet scheme. We rather exploit the phenomenological $η_8-η_0$ mixing as a probe for the non-negligible flavour-singlet component of the physical $η$ pole to find $Ω_{\rm IB}^{(9)}=(35\pm7)\times 10^{-2}$ in a complete nonet scheme. A large central value in the nonet scheme is thus substituted for a large uncertainty in the octet one. Including the experimental $π^+-π^0$ mass difference as the dominant electromagnetic isospin-breaking, we obtain for the effective parameter entering the ratio $ε'/ε$ an improved result $\hatΩ_{\rm eff}^{(9)}=(29\pm7)\times 10^{-2}$ to be compared with $\hatΩ_{\rm eff}^{(8)}=(17\pm9)\times 10^{-2}$ used in recent analyses of $ε'/ε$. Accordingly, we get a reduction from $(ε'/ε)_{\rm SM}^{(8)}=(17.4\pm 6.1)\times 10^{-4}$ to $(ε'/ε)_{\rm SM}^{(9)}=(13.9\pm 5.2)\times 10^{-4}$ and thereby an effective suppression of $(ε'/ε)_{\rm SM}$ by isospin-breaking corrections as large as $40\%$ relative to the recent RBC-UKQCD value.
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