[论文解读] Theoretical Prediction and Impact of Fundamental Electric Dipole Moments

Sebastian A. R. Ellis, Gordon Kane|arXiv (Cornell University)|May 29, 2014

Particle physics theoretical and experimental studies参考文献 11被引用 5

一句话总结

本文在紧化M理论框架下预测了电子和中子电偶极矩（EDM）的上限，表明EDM源于标准模型Yukawa相位在电弱尺度的跑动。尽管存在新物理，EDM仍被约束在电子的$5 \times 10^{-30}~e\text{cm}$以下、中子的$5 \times 10^{-29}~e\text{cm}$以下，为无任意CP相位的M理论启发模型提供了关键检验。

ABSTRACT

The predicted Standard Model (SM) electric dipole moments (EDMs) of electrons and quarks are tiny, providing an important window to observe new physics. Theories beyond the SM typically allow relatively large EDMs. The EDMs depend on the relative phases of terms in the effective Lagrangian of the extended theory, which are generally unknown. Underlying theories, such as string/M-theories compactified to four dimensions, could predict the phases and thus EDMs in the resulting supersymmetric (SUSY) theory. Earlier one of us, with collaborators, made such a prediction and found, unexpectedly, that the phases were predicted to be zero at tree level in the theory at the unification or string scale $\sim\mathcal{O}(10^{16}$ GeV). Electroweak (EW) scale EDMs still arise via running from the high scale, and depend only on the SM Yukawa couplings that also give the CKM phase. Here we extend the earlier work by studying the dependence of the low scale EDMs on the constrained but not fully known fundamental Yukawa couplings. The dominant contribution is from two loop diagrams and is not sensitive to the choice of Yukawa texture. The electron EDM should not be found to be larger than about $ 5 imes 10^{-30} e$ cm, and the neutron EDM should not be larger than about $5 imes 10^{-29}e$ cm. These values are quite a bit smaller than the reported predictions from Split SUSY and typical effective theories, but much larger than the Standard Model prediction. Also, since models with random phases typically give much larger EDMs, it is a significant testable prediction of compactified M-theory that the EDMs should not be above these upper limits. The actual EDMs can be below the limits, so once they are measured they could provide new insight into the fundamental Yukawa couplings of leptons and quarks. We comment also on the role of strong CP violation. EDMs probe fundamental physics near the Planck scale.

研究动机与目标

• 在基于紧化M理论的物理学基础理论中，约束电子和中子的电偶极矩（EDM）。
• 确定超势Yukawa耦合中的CP破坏相位（负责CKM相位）如何通过量子修正在低能下生成EDM。
• 为EDM提供可检验的预测，其值显著小于通用有效场论或Split SUSY模型的预测，从而探测底层Yukawa结构。
• 评估强CP破坏在EDM可观测量中的作用，并将其与弱尺度CP破坏区分开来。

提出的方法

• 使用两圈Barr-Zee图和一圈SUSY图计算EDM，主要贡献来自圈中第三代标量夸克（stop和sbottom）。
• 从统一尺度（~10¹⁶ GeV）到电弱尺度应用跑动方程，追踪高能Yukawa耦合的相位演化。
• 推导EDM的表达式，其依赖于三线耦合和软对称性破缺质量的虚部，相位依赖关系与超势Yukawa耦合相关。
• 考虑多种Yukawa结构情形，并表明主导的两圈贡献对结构选择不敏感。
• 使用两圈函数$ F(r) $及其导数$ F'(r) $计算Barr-Zee贡献的振幅，涉及质量尺度$ M_A $、$ m_{\tilde{q}} $和$ m_f $。
• 忽略Barr-Zee贡献（因其数值过小），转而聚焦于主导的两圈和次主导的一圈图。

实验结果

研究问题

• RQ1 在无任意CP相位的紧化M理论中，电子和中子EDM的上限是多少？
• RQ2 源自超势的Yukawa耦合中的CP破坏相位如何通过量子修正在低能下生成EDM？
• RQ3 为何预测的EDM显著小于通用有效场论或Split SUSY模型的预测？
• RQ4 这些EDM预测在不同Yukawa结构选择下有多稳健？主导贡献是否对结构细节敏感？
• RQ5 未来的EDM测量能否约束夸克和轻子的基本Yukawa耦合？

主要发现

• 电子EDM预测值不超过$ 5 \times 10^{-30}~e\text{cm} $，远低于典型Split SUSY和有效场论的预测值。
• 中子EDM预测值不超过$ 5 \times 10^{-29}~e\text{cm} $，为M理论紧化提供了严格检验。
• EDM的主要贡献来自涉及第三代标量夸克的两圈图，且对Yukawa结构的具体形式不敏感。
• 一圈贡献为次主导，不改变整体上限。
• 结果源于高能超势中CP破坏相位对齐而非任意，导致EDM被抑制。
• 预测具有可检验性：若未来EDM实验测得值超过这些上限，将排除本文研究的特定M理论紧化框架。