2025/11/21 by Shu Luo, Luo, Shu
Physics and Astronomy · #Dark Matter and Cosmic Phenomena #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Neutrino Physics Research #Particle physics theoretical and experimental studies
paper · pdf · doi:10.48550/arxiv.2511.16942
openalex publication_date 2025/11/21 · openalex created_date 2025/11/25 · openalex updated_date 2026/07/31
The field of neutrino physics has made significant progress in measuring the strength and frequency of neutrino and antineutrino oscillations in the past two decades. It is clear that the amplitudes involved in the neutrino oscillation probabilities are all rephaping invariants of the quartet forms of the elements of the PMNS mixing matrix. We show in this paper how these quartet observables can be directly linked to the rescaled leptonic unitarity triangles within the framework of three active neutrinos. We provide a systematic discussion of the nine CP-conserving quartets \cal Rγk ≡ \rm Re [ Vαi Vβj V*αj V*βi ] along with the universal Jarlskog invariant of CP violation \cal J ≡ ∑γεαβγ ∑k εijk \rm Im [ Vαi Vβj V*αj V*βi ], and place particular emphasis on the matter effect on these quartets. In addition to the well-known Naumov relation for the Jarlskog invariant \cal J, similar relations connecting \cal R in vacuum and its effective counterparts \widetilde\cal R in matter are introduced and examined in detail. We find that the effective CP-conserving invariants \widetilde\cal Rαi in matter can be regarded as linear combinations of their vacuum counterparts. With the latest global fit data of neutrino masses and mixing elements, numerical analyses are carried out to give an intuitive understanding of how these rephasing invariants evolve as the matter density increases.