Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.13363 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917130359799808 |
|---|---|
| author | Lu, Jianlong |
| author_facet | Lu, Jianlong |
| contents | We study basis-independent structures in the Type-I seesaw mechanism for light Majorana neutrinos, assuming the canonical scenario with three heavy right-handed (sterile) neutrinos. Let $m_ν$ denote the $3\times3$ mass matrix of light neutrinos, obtained at tree level from heavy Majorana singlets with diagonal mass matrix $D_N = \mathrm{diag}(M_1,M_2,M_3)$ and Dirac matrix $m_D$. We show that all right-actions $F$ on the seesaw matrix that leave $m_ν$ unchanged form the group $G = D_N^{1/2} O(3,\mathbb{C}) D_N^{-1/2}$. While oscillation data determine the PMNS matrix $U_{\rm PMNS}$ and the mass-squared splittings, they do not fix the $F$-class within $G$. We classify basis-invariant quantities into those that are class-blind (e.g.\ $\detη$) and class-sensitive (e.g. $\mathrm{Tr}\,η$, $\mathrm{Tr}\,η^2$, an alignment measure, and CP-odd traces relevant to leptogenesis), where $η$ denotes the non-unitarity matrix of the light sector. We provide explicit formulas and both high-scale and GeV-scale benchmark examples that illustrate these invariant fingerprints and their scaling with $D_N$. This converts the degeneracy at fixed $m_ν$ into measurable, basis-invariant fingerprints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13363 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $D_N$-Orthogonal Freedom in the Canonical Seesaw: Flavor Invariants and Physical Non-Equivalence of F-Classes Lu, Jianlong High Energy Physics - Phenomenology We study basis-independent structures in the Type-I seesaw mechanism for light Majorana neutrinos, assuming the canonical scenario with three heavy right-handed (sterile) neutrinos. Let $m_ν$ denote the $3\times3$ mass matrix of light neutrinos, obtained at tree level from heavy Majorana singlets with diagonal mass matrix $D_N = \mathrm{diag}(M_1,M_2,M_3)$ and Dirac matrix $m_D$. We show that all right-actions $F$ on the seesaw matrix that leave $m_ν$ unchanged form the group $G = D_N^{1/2} O(3,\mathbb{C}) D_N^{-1/2}$. While oscillation data determine the PMNS matrix $U_{\rm PMNS}$ and the mass-squared splittings, they do not fix the $F$-class within $G$. We classify basis-invariant quantities into those that are class-blind (e.g.\ $\detη$) and class-sensitive (e.g. $\mathrm{Tr}\,η$, $\mathrm{Tr}\,η^2$, an alignment measure, and CP-odd traces relevant to leptogenesis), where $η$ denotes the non-unitarity matrix of the light sector. We provide explicit formulas and both high-scale and GeV-scale benchmark examples that illustrate these invariant fingerprints and their scaling with $D_N$. This converts the degeneracy at fixed $m_ν$ into measurable, basis-invariant fingerprints. |
| title | $D_N$-Orthogonal Freedom in the Canonical Seesaw: Flavor Invariants and Physical Non-Equivalence of F-Classes |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2509.13363 |