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arXiv 2410.03350hep-ph
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关于Majorana中微子Yukawa相互作用Casas-Ibarra参数化中的正交矩阵

On the orthogonal matrix in the Casas-Ibarra parametrization for the Yukawa interactions of Majorana neutrinos

Zhi-zhong Xing

AI总结:

本文推广了Majorana中微子的Casas-Ibarra参数化,考虑精确seesaw关系与PMNS矩阵非幺正性,推导出正交矩阵的解析表达式,揭示了其特定模式等价于对seesaw参数空间施加特殊条件。

摘要:

通过考虑精确的seesaw关系并包含 $3 \times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) 味混合矩阵的非幺正性,Majorana中微子Yukawa耦合矩阵的Casas-Ibarra (CI) 参数化被推广。借助seesaw机制味结构的完整 $6 \times 6$ 类Euler块描述,我们发现CI参数化中的正交矩阵 $\mathbb{O}$ 可表示为 $\mathbb{O}^{}_{ij} = \sqrt{M^{}_j/m^{}_i} \hspace{0.05cm} F^{}_{ij}$,其中 $m^{}_i$ 和 $M^{}_j$ 分别为轻和重Majorana中微子的质量,$F^{}_{ij}$ 由PMNS和活性-惰性味混合参数构成(对于 $i, j = 1, 2, 3$)。因此,假设 $\mathbb{O}$ 的特定模式等价于对seesaw参数空间施加某些特殊条件。

英文摘要:

The Casas-Ibarra (CI) parametrization of the Yukawa coupling matrix of Majorana neutrinos is generalized by considering the exact seesaw relation and including non-unitarity of the $3 \times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) flavor mixing matrix. With the help of a full $6 \times 6$ Euler-like block description of the flavor structure for the seesaw mechanism, we find that the orthogonal matrix $\mathbb{O}$ in the CI parametrization can be expressed as $\mathbb{O}^{}_{ij} = \sqrt{M^{}_j/m^{}_i} \hspace{0.05cm} F^{}_{ij}$ with $m^{}_i$ and $M^{}_j$ being the masses of light and heavy Majorana neutrinos and $F^{}_{ij}$ consisting of the PMNS and active-sterile flavor mixing parameters (for $i, j = 1, 2, 3$). Assuming a specific pattern of $\mathbb{O}$ is therefore equivalent to imposing some special conditions on the seesaw parameter space.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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