New rephasing invariants and CP violation built from the trios of the CKM or PMNS matrix elements

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Luo, Shu, Xing, Zhi-zhong
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