来自局域维度九算子的μ子到正电子转换：π极点改进的核多极矩
Muon-to-positron conversion from local dimension-nine operators: pion-pole-improved nuclear multipoles
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中文总结 AI 辅助
本文系统研究违反轻子数两个单位的无中微子μ子到正电子转换，为局域维度九算子构造π极点改进的核多极矩，并精确重耦合至双体核张量，适用于0+到0+跃迁。
中文摘要 AI 辅助
我们开始对无中微子μ子到正电子转换过程 $\mu^-+(A,Z)\to e^++(A,Z-2)$ 进行系统性研究，该过程违反轻子数两个单位并改变带电轻子味。本系列的第一篇论文为包含标量或赝标量轻子双线性以及两个收缩的矢量或轴矢量夸克流局域维度九相互作用构造核算子。协变核子流由全部六个矢量及轴矢量形状因子构建。对于实际使用的核算子，我们忽略第二类流，并采用π极点改进的约化方案：由所展示的单体流产生的非极点反冲项保留至逆核子质量的二阶，而π极点纵向轴矢量流在两条流收缩前保持完整。我们保留核子顶点处的两个独立动量转移以及出射正电子的库仑位移空间相位。从时空跃迁矩阵元出发，我们明确展示了相互作用坐标积分如何固定两条流动量之和而非其分配方式。不相等的形状因子参数随后产生在共同动量近似中不存在的相对坐标多极矩。我们给出了到双体核张量的精确重耦合，并将其专门应用于物理上重要的 $0^+\to0^+$ 跃迁。在这种情况下，外部核秩为零，所有磁和都坍缩，尽管有限动量的内部轨道和自旋张量仍然存在。结果以可直接与电荷交换双体跃迁密度收缩的形式表达。一般六形状因子流、任意核角动量以及幂次计数限定条件收集在附录中。
英文摘要
We begin a systematic study of neutrinoless muon-to-positron conversion, $μ^-+(A,Z)\to e^++(A,Z-2)$, which violates lepton number by two units and changes charged-lepton flavor. This first paper in a series constructs nuclear operators for local dimension-nine interactions containing a scalar or pseudoscalar lepton bilinear and two contracted vector or axial quark currents. The covariant nucleon currents are built with all six vector and axial form factors. For the working nuclear operator we neglect second-class currents and adopt a pion-pole-improved reduction: non-pole recoil terms generated by the displayed one-body currents are retained through second order in inverse nucleon mass, whereas the pion-pole longitudinal axial current is kept intact before the two currents are contracted. We preserve the two independent momentum transfers at the nucleon vertices and the Coulomb-shifted spatial phase of the outgoing positron. Starting from the spacetime transition element, we show explicitly how the interaction-coordinate integral fixes the sum, but not the sharing, of the two current momenta. Unequal form-factor arguments then generate relative-coordinate multipoles absent in the usually used common-momentum approximation. We give an exact recoupling into two-body nuclear tensors and specialize it to the phenomenologically important $0^+\to0^+$ transition. In this case the external nuclear rank is zero and all magnetic sums collapse, although finite-momentum internal orbital and spin tensors remain. The result is expressed in a form directly contractible with charge-changing two-body transition densities. General six-form-factor currents, arbitrary nuclear angular momenta, and power-counting qualifications are collected in appendices.
发表机构
- South China Normal University（华南师范大学）
- Guangdong Provincial Key Laboratory of Nuclear Science（广东省核科学重点实验室）
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