Leptonic first-row correlation and unitarity waiting for further JUNO 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 $\sin^2\theta^{}_{12} = \left(1 - 2\tan^2\theta^{}_{13}\right)/3$ in the unitarity limit of $U$, as supported by the latest JUNO and Daya Bay precision measurements at a confidence level close to $1\sigma$.