New rephasing invariants and CP violation built from the trios of the CKM or PMNS matrix elements
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914000310108160 |
|---|---|
| author | Luo, Shu Xing, Zhi-zhong |
| author_facet | Luo, Shu Xing, Zhi-zhong |
| contents | Given the $3\times 3$ Cabibbo-Kobayashi-Maskawa (CKM) quark flavor mixing matrix $V$, we define a new set of rephasing invariants in terms of the "trios" of its nine elements: $\lozenge^{ijk}_{αβγ} \equiv (V^{}_{αi} V^{}_{βj} V^{}_{γk})/\det V$ with $α\neq β\neq γ$ and $i \neq j \neq k$ running respectively over $(u, c, t)$ and $(d, s, b)$. We find that ${\rm Im} \lozenge^{ijk}_{αβγ} = - {\cal J}$ holds, where ${\cal J}$ is the well-known Jarlskog invariant of weak CP violation. Analogous rephasing invariants $\blacklozenge^{ijk}_{αβγ} \equiv (U^{}_{αI} U^{}_{βj} U^{}_{γk})/\det U$ can be defined for the $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) lepton flavor mixing matrix $U$, where $α\neq β\neq γ$ and $i \neq j \neq k$ run respectively over $(e, μ, τ)$ and $(1, 2, 3)$. Taking into account small non-unitarity of $U$ based on the canonical seesaw mechanism for neutrino mass generation, we calculate ${\rm Im} \blacklozenge^{ijk}_{αβγ}$ with the help of a full Euler-like block parametrization of the seesaw flavor structure and demonstrate that their leading terms converge to a universal invariant ${\cal J}^{}_ν$ in the unitarity limit of $U$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New rephasing invariants and CP violation built from the trios of the CKM or PMNS matrix elements Luo, Shu Xing, Zhi-zhong High Energy Physics - Phenomenology High Energy Physics - Experiment Given the $3\times 3$ Cabibbo-Kobayashi-Maskawa (CKM) quark flavor mixing matrix $V$, we define a new set of rephasing invariants in terms of the "trios" of its nine elements: $\lozenge^{ijk}_{αβγ} \equiv (V^{}_{αi} V^{}_{βj} V^{}_{γk})/\det V$ with $α\neq β\neq γ$ and $i \neq j \neq k$ running respectively over $(u, c, t)$ and $(d, s, b)$. We find that ${\rm Im} \lozenge^{ijk}_{αβγ} = - {\cal J}$ holds, where ${\cal J}$ is the well-known Jarlskog invariant of weak CP violation. Analogous rephasing invariants $\blacklozenge^{ijk}_{αβγ} \equiv (U^{}_{αI} U^{}_{βj} U^{}_{γk})/\det U$ can be defined for the $3\times 3$ Pontecorvo-Maki-Nakagawa-Sakata (PMNS) lepton flavor mixing matrix $U$, where $α\neq β\neq γ$ and $i \neq j \neq k$ run respectively over $(e, μ, τ)$ and $(1, 2, 3)$. Taking into account small non-unitarity of $U$ based on the canonical seesaw mechanism for neutrino mass generation, we calculate ${\rm Im} \blacklozenge^{ijk}_{αβγ}$ with the help of a full Euler-like block parametrization of the seesaw flavor structure and demonstrate that their leading terms converge to a universal invariant ${\cal J}^{}_ν$ in the unitarity limit of $U$. |
| title | New rephasing invariants and CP violation built from the trios of the CKM or PMNS matrix elements |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment |
| url | https://arxiv.org/abs/2508.15662 |