Leptonic first-row correlation and unitarity waiting for further JUNO tests

TL;DR

This paper proposes a specific correlation among the elements of the lepton flavor mixing matrix that remains valid even if the matrix is non-unitary, and discusses its consistency with recent experimental measurements from JUNO and Daya Bay.

Contribution

It introduces a novel first-row correlation in the lepton mixing matrix that holds beyond the unitarity assumption, supported by current experimental data.

Findings

The correlation is consistent with JUNO and Daya Bay measurements.

The correlation holds even if the mixing matrix is non-unitary.

Supports the potential for future tests of unitarity.

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 $1\sigma$.