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arXiv 1404.0109hep-ph
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与跷跷板和轻子生成有关的轻子质量矩阵的交换子

Commutators of lepton mass matrices associated with seesaw and leptogenesis

Yikun Wang, Zhi-zhong Xing

备注：
LaTex 8 pages. Minor changes. Accepted for publication in Phys. Rev. D
发表信息：
Phys. Rev. D 89, 097301 (2014)
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摘要：

微中微子质量的起源和宇宙的重子数不对称性可以用正则的跷跷板机制和轻子生成机制来解释，其中包括重Majorana中微子质量矩阵$M_{\rm R}$、Dirac中微子质量矩阵$M_{\rm D}$、带电轻子质量矩阵$M_\ell$和有效（轻）中微子质量矩阵$M_ν$。我们发现，${\rm Im}\left(\det\left[ M^\dagger_{\rm D} M_{\rm D}, M^\dagger_{\rm R} M_{\rm R} \right]\right)$、${\rm Im}\left(\det\left[ M_\ell M^\dagger_\ell, M_νM^\dagger_ν\right]\right)$和${\rm Im}\left(\det\left[ M_\ell M^\dagger_\ell, M_{\rm D} M^\dagger_{\rm D} \right]\right)$可以分别作为与重中微子的轻子数违反衰变、轻中微子的味振荡和带电轻子的轻子味违反衰变相关的CP破坏的基无关测度.我们首先计算这些数量的帮助下，一个标准的参数化的$6\times 6$味混合矩阵，然后讨论它们的影响leptogenesis和CP破坏在低能量尺度。并与Branco { \it et al}提出的弱基不变量作了比较。

英文摘要：

The origin of tiny neutrino masses and the baryon number asymmetry of the Universe are naturally interpreted by the canonical seesaw and leptogenesis mechanisms, in which there are the heavy Majorana neutrino mass matrix $M_{\rm R}$, the Dirac neutrino mass matrix $M_{\rm D}$, the charged-lepton mass matrix $M_\ell$ and the effective (light) neutrino mass matrix $M_ν$. We find that ${\rm Im}\left(\det\left[ M^\dagger_{\rm D} M_{\rm D}, M^\dagger_{\rm R} M_{\rm R} \right]\right)$, ${\rm Im}\left(\det\left[ M_\ell M^\dagger_\ell, M_νM^\dagger_ν\right]\right)$ and ${\rm Im}\left(\det\left[ M_\ell M^\dagger_\ell, M_{\rm D} M^\dagger_{\rm D} \right]\right)$ can serve for a basis-independent measure of CP violation associated with lepton-number-violating decays of heavy neutrinos, flavor oscillations of light neutrinos and lepton-flavor-violating decays of charged leptons, respectively. We first calculate these quantities with the help of a standard parametrization of the $6\times 6$ flavor mixing matrix, and then discuss their implications on both leptogenesis and CP violation at low energy scales. A comparison with the weak-basis invariants of leptogenesis as proposed by Branco {\it et al} is also made.

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