利用背景电场通过晶格量子色动力学计算中子电偶极矩
The Neutron Electric Dipole Moment from Lattice QCD using a Background Electric Field
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中文总结 AI 辅助
该研究利用2 + 1味域壁费米子系综，通过背景电场引起的能量位移计算中子电偶极矩。采用单时间切片拓扑电荷采样提高精度，构建变形核子基态消除污染，外推到物理点得到结果，为研究中子电偶极矩提供新方法。
中文摘要 AI 辅助
我们展示了使用具有固定晶格间距\(a\approx0.11\,\text{fm}\)和340、420及576 MeV 三种π介子质量的2 + 1味域壁费米子系综来计算中子电偶极矩（nEDM）\(d_n\)。在存在 CP 破坏的 QCD θ项\(\bar\theta Q_{top}\)时，中子电偶极矩可从静态均匀外部背景电场引起的能量位移中提取。受费曼 - 海尔曼定理启发，我们在单个时间切片上对拓扑电荷\(q_{top}(t)\)进行采样，而非全局拓扑电荷\(Q_{top}=\int q_{top}(t) \, dt\)，显著提高了θ诱导nEDM的统计精度。我们的方法关键在于计算背景电场使核子变形时拓扑电荷密度的前向矩阵元。发现传统正宇称投影核子算符计算受大激发态污染，通过求解非厄米广义特征值问题构建变形核子基态来消除污染。采用此方法，使用不同核子插值算符时nEDM值一致。最后外推到物理点，得到\(d_n=-0.0050(4)^\text{stat}(8)^\text{sys}\bar{\theta}\) \(e\) fm，未来工作将处理如离散化、有限体积和手征外推效应等传统系统误差。
英文摘要
We present the calculation of the neutron electric dipole moment (nEDM) $d_n$ using 2+1 flavor domain wall fermion ensembles with fixed lattice spacing $a\approx 0.11\,\text{fm}$ and pion masses of 340, 420, and 576 MeV. We show that the neutron electric dipole moment can be extracted from the energy shift induced by a static uniform external background electric field in the presence of the CP-violating QCD theta-term, $\barθQ_{top}$. Motivated by the Feynman-Hellmann theorem, we employ sampling of the topological charge $q_\text{top}(t)$ on a single time-slice rather than the global topological charge $Q_\text{top}=\int q_\text{top}(t) \, dt$, which dramatically improves the statistical precision of the $θ$-induced nEDM. Key to our method is to calculate the forward matrix element of the topological charge density in the nucleon deformed by a background electric field. We find that calculation with the traditional positive parity-projected nucleon operator is subject to large excited-state contamination. To remove the contamination, we construct the ground state of the deformed nucleon by solving a non-Hermitian generalized eigenvalue problem. With this approach, we find consistent values for the nEDM when using different nucleon interpolating operators, regardless of whether they are covariant or non-covariant under chiral transformations. Finally, after extrapolating to the physical point, we obtain $d_n=-0.0050(4)^\text{stat}(8)^\text{sys}\barθ$ $e$ fm, where the systematic uncertainty includes excited-state effects estimated as variation with the Euclidean-time fits and the dependence on the strength of the electric field applied to the neutron. Conventional systematic errors like discretization, finite-volume, and chiral extrapolation effects will be addressed in future work.
