AI 中文总结
该研究首次通过格点QCD直接计算θ诱导的CP破坏π-核子耦合$\tilde g_{\rm πNN}$，结合多种方法提升精度并完成外推，结果与间接确定一致，精度受海π质量外推限制。
AI 中文摘要
我们首次实现了θ诱导的CP破坏π-核子-核子耦合$\tilde g_{\rm πNN}$的格点QCD直接确定。在三个具有单一格点间距的2+1味畴壁费米子系综上，采用重叠价费米子，我们在θ真空下计算了等量赝标量密度的向前质子矩阵元，计算精度为$\barθ$的一阶。提取过程中计入了外部核子态的宇称混合效应，采用簇分解误差消减方法提升统计精度。通过对价π质量和海π质量同时外推，并基于赤池信息准则对7种形式进行模型平均，在物理点得到$\tilde g_{\rm πNN}=0.0306(56)(124)\barθ$，其中第一个不确定度包含统计和矩阵元拟合系统不确定度，第二个反映外推形式间的差异。在这些不确定度范围内，该结果与基于强中子-质子质量分裂的间接确定结果一致。当前精度主要受限于相对较重的海π质量外推。
英文摘要
We present the first direct lattice QCD determination of the $θ$-induced CP-violating pion-nucleon-nucleon coupling $\tilde g_{πNN}$. Using overlap valence fermions on three $2+1$-flavor domain-wall ensembles at a single lattice spacing, we calculate the forward proton matrix element of the isovector pseudoscalar density in the $θ$-vacuum to first order in $\barθ$. The parity-mixing effect in the external nucleon states is included in the extraction. The cluster-decomposition error-reduction method is used to improve the statistical precision. A simultaneous extrapolation in the valence- and sea-pion masses, with model averaging over 7 forms based on the Akaike information criterion, gives $\tilde g_{πNN}=0.0306(56)(124)\,\barθ$ at the physical point. The first uncertainty includes the statistical and matrix-element-fit systematic uncertainties, whereas the second reflects the spread among the extrapolation forms. Within these uncertainties, the result is consistent with the indirect determination based on the strong neutron-proton mass splitting. The present precision is limited primarily by the extrapolation from the relatively heavy sea-pion masses.
Comments9 pages, 3 figures
