Leptonic first-row correlation and non-unitarity waiting for direct JUNO and Daya Bay precision tests
Zhi-zhong Xing
TL;DR
The paper investigates potential non-unitarity of the PMNS matrix arising from the canonical seesaw mechanism and proposes a robust first-row correlation, $|U_{e1}|^2 = 2(|U_{e2}|^2+|U_{e3}|^2)$, as a non-unitary generalization of a TM1-inspired relation between $ heta_{12}$ and $ heta_{13}$. Using the Euler-like seesaw parametrization $U = A U_0$, it shows the first-row normalization satisfies $|U_{e1}|^2+|U_{e2}|^2+|U_{e3}|^2 = (c_{14} c_{15} c_{16})^2$, with current bounds $s_{14}^2+s_{15}^2+s_{16}^2 \,<\, ext{a few} imes 10^{-3}$ implying near-unitarity. The correlation ties directly to the TM1 pattern, yielding $ an^2 heta_{12} = ig| rac{U_{e2}}{U_{e1}}ig|^2$ and $ an^2 heta_{13} = rac{|U_{e3}|^2}{|U_{e1}|^2+|U_{e2}|^2}$, and predicts $ ext{sin}^2 heta_{12} = rac{1}{3}(1-2 an^2 heta_{13})$; current data are broadly consistent, and upcoming JUNO and Daya Bay precision measurements offer a direct test. The work also discusses RG corrections, supports the TM1 flavor-symmetry origin, and provides an indirect benchmark for the soon-to-be-available direct unitarity tests.
Abstract
We conjecture that there exists a remarkable correlation among the three elements in the first row of the $3\times 3$ lepton flavor mixing matrix $U$: $|U^{}_{e1}|^2 = 2 \left(|U^{}_{e2}|^2 + |U^{}_{e3}|^2\right)$, which holds even though $U$ is non-unitary in the canonical seesaw mechanism. This ``first-row correlation" is fully consistent with $\sin^2θ^{}_{12} = \left(1 - 2\tan^2θ^{}_{13}\right)/3$ for the two active neutrino mixing angles derived from the TM1 flavor mixing pattern, and it will be {\it directly} tested by the upcoming JUNO precision data combined with the Daya Bay precision measurement.