Effect on Jarlskog Determinant Above the GUT Scale Within Four Flavor Neutrino Framework

We study the Planck scale effects on Jarlskog determiant in the four flavor framework. On electroweak symmetry breaking, quantum gravitational effects lead to an effective SU(2) × U(1) invariant dimension-5 Lagrangian including neutrino and Higgs forces, which perturbed the neutrino mass term and produce an extra terms in the neutrino mass matrix. We consider that gravitational interaction is independent from flavor and compute the Jarlskog determiant due to Planck scale effects. In the case of leptonic sector, the strentgh of CP violation is measured by Jarlskog determiant. We applied our approach to study Jarlskog determinant in the four flavor neutrino mixing above the GUT scale.

The fate of hints: updated global analysis of three-flavor neutrino oscillations

Our herein described combined analysis of the latest neutrino oscillation data presented at the Neutrino2020 conference shows that previous hints for the neutrino mass ordering have significantly decreased, and normal ordering (NO) is favored only at the 1.6σ level. Combined with the χ2 map provided by Super-Kamiokande for their atmospheric neutrino data analysis the hint for NO is at 2.7σ. The CP conserving value δCP = 180° is within 0.6σ of the global best fit point. Only if we restrict to inverted mass ordering, CP violation is favored at the ∼ 3σ level. We discuss the origin of these results — which are driven by the new data from the T2K and NOvA long-baseline experiments —, and the relevance of the LBL-reactor oscillation frequency complementarity. The previous 2.2σ tension in ∆m221 preferred by KamLAND and solar experiments is also reduced to the 1.1σ level after the inclusion of the latest Super-Kamiokande solar neutrino results. Finally we present updated allowed ranges for the oscillation parameters and for the leptonic Jarlskog determinant from the global analysis.

Jarlskog determinant and data on flavor matrices

The essences of the weak [Formula: see text] violation, the quark and lepton Jarlskog invariants, are determined toward future model buildings beyond the Standard Model (SM). The equivalence of two calculations of Jarlskog invariants gives a bound on the [Formula: see text] phase in some parametrization. Satisfying the unitarity condition, we obtain the CKM and PMNS matrices from the experimental data, and present the results in matrix forms. The Jarlskog determinant [Formula: see text] in the quark sector is found to be [Formula: see text] while [Formula: see text] in the leptonic sector is [Formula: see text] in the normal hierarchy parametrization.