发表机构
Pukyong National University; Korea University（釜山国立大学; 高丽大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种零点轨迹诊断方法，在FSI改进约定下通过局部二次恒等式识别$\phi\to\pi^+\pi^-\pi^0$中直接接触项的耦合常数，并验证了其数值稳定性，为全局拟合提供补充指导。
AI 中文摘要
我们在一个固定的 FSI 改进振幅约定内，为 $\phi\to\pi^+\pi^-\pi^0$ 中的直接接触项构建了一个零点轨迹诊断。共振 $\rho\pi$ 贡献通过复 Omnès 函数逐通道进行修饰，直接项乘以平均 Omnès 因子，并保留一个实常数背景作为平滑的残余振幅。在此约定下，$F^{\rm FSI}=R+c e^{i\delta_{\rm dir}}D$，其中 $c=g_{\phi3\pi}^{\rm eff}$，并且约化 Dalitz 密度的两个受约束不变质量梯度的差值在零轮廓上给出了关于 $c$ 的局部二次恒等式。该构造提供了一种与全局 Dalitz 图拟合互补的闭合性和稳定性诊断。对于基准输入 $g_{\phi3\pi}^{\rm eff}=-24.0~{\rm GeV}^{-3}$，我们在 $M_{+0}=0.460\pm0.025~{\rm GeV}$ 和 $M_{+-}\le0.560~{\rm GeV}$ 附近识别出一个数值稳定的零轮廓分支，其中紧轮廓中位数估计器重现了 $g_{\phi3\pi}^{\rm est}\simeq -24.0~{\rm GeV}^{-3}$，这是在所选 FSI 改进约定内对注入耦合的闭合恢复，而非独立提取。我们进一步改变该分支的质量窗口选择。在 $M_{+0}$ 窗口移动和其宽度适度变化下，中位数仍接近注入值，而均值和标准差对不稳定二次分支附近的离群点更为敏感。因此，该方法识别了 Dalitz 平面中直接项干涉局部良态的区域，并为未来全局拟合中的控制区域选择和系统变化提供了有用指导。
英文摘要
We formulate, within a fixed FSI-improved amplitude convention, a zero-locus diagnostic for the direct contact term in $ϕ\toπ^+π^-π^0$. The resonant $ρπ$ contribution is dressed channel by channel with the complex Omnès function, the direct term is multiplied by the averaged Omnès factor, and a real constant background is retained as a smooth residual amplitude. In this convention, $F^{\rm FSI}=R+c e^{iδ_{\rm dir}}D$ with $c=g_{\phi3π}^{\rm eff}$, and the difference of two constrained invariant-mass gradients of the reduced Dalitz density gives a local quadratic identity for $c$ on the zero-contour. The construction provides a closure and stability diagnostic complementary to a global Dalitz-plot fit. For the benchmark input $g_{\phi3π}^{\rm eff}=-24.0~{\rm GeV}^{-3}$, we identify a numerically stable zero-contour branch around $M_{+0}=0.460\pm0.025~{\rm GeV}$ and $M_{+-}\le0.560~{\rm GeV}$, where the tight-contour median estimator reproduces $g_{\phi3π}^{\rm est}\simeq -24.0~{\rm GeV}^{-3}$, a closure recovery of the injected coupling within the chosen FSI-improved convention rather than an independent extraction. We further vary the mass-window selection of the branch. The median remains close to the injected value under shifts of the $M_{+0}$ window and moderate changes of its width, while the mean and standard deviation are more sensitive to outlier points near unstable quadratic branches. The method therefore identifies Dalitz-plane regions where the direct-term interference is locally well-conditioned and provides useful guidance for control-region choices and systematic variations in future global fits.
Comments11 pages, 2 figures
