发表机构
University of Tennessee（田纳西大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于生成函数方法的微扰计算框架，用于超允许β衰变中同位旋破缺修正$\delta_C$，以克服标准形式违反核子基独立性的系统误差，满足卡比玻幺正性检验的精度需求。
AI 中文摘要
当前从$J^P=0^+$、$T=1$原子核的超允许β衰变高精度确定$|V_{ud}|$，在很大程度上建立在费米矩阵元同位旋破缺修正$\delta_C$的“标准”计算之上，该计算假设$\delta_C=\delta_{C1}+\delta_{C2}$，其中$\delta_{C1}$和$\delta_{C2}$分别代表“同位旋混合”修正和“径向失配”修正。本文表明，该形式违反了核子基独立性规则，类似于量子场论中的规范不变性要求，因此其结果不可避免地受到不受控制的系统误差的影响。我进一步论证，微扰形式是唯一能够在卡比玻幺正性检验所需精度水平下计算$\delta_C$的方法。在现有文献的基础上，我发展了完整的“生成函数方法”来微扰计算$\delta_C$，并以核质量劈裂和核电荷半径中的同位旋破缺作为理论基准。
英文摘要
The present high precision determination of $|V_{ud}|$ from superallowed beta decays of $J^P=0^+$, $T=1$ nuclei is largely built on top of the ``standard'' calculation of the isospin breaking correction $δ_C$ to the Fermi matrix element, which assumes the splitting $δ_C=δ_{C1}+δ_{C2}$, where $δ_{C1}$ and $δ_{C2}$ represent the ``isospin mixing'' correction and the ``radial mismatch'' correction, respectively. In this paper I show that this formalism violates the rule of nucleon basis independence, similar to the gauge invariance requirement in quantum field theory, therefore its outcome is inevitably subject to uncontrolled systematic errors. I further argue that the perturbative formalism is the only approach that allows the computation of $δ_C$ at the precision level required for the test of the Cabibbo unitarity. Advancing from existing literature, I develop the full ``generating function approach'' to compute $δ_C$ perturbatively, with connections to nuclear mass splittings and the isospin breaking in nuclear charge radii as theory benchmarks.
Comments40 pages, 1 figure
