Modified Tri-bimaximal neutrino mixing confronted by JUNO $\theta_{12}$ measurement

The JUNO collaboration has released its first measurement of reactor neutrino oscillations results, obtaining $\sin^2\theta_{12} = 0.3092\pm 0.0087$, an improvement in precision by a factor of 1.6 over previous combined results. We confront the minimally modified tri-bimaximal mixing pattern with the new data. Before the measurement of a non-zero $\theta_{13}$ mixing angle, the tri-bimximal mixing pattern is one of the most popular simple mixing scheme for neutrinos. Modifications have been proposed to keep some features of tri-bimaximal mixing and make it to be consistent with data. Minimal modifications preserving one column of the tri-bimaximal mixing matrix, yielding three patterns: a) unchanged third, b) unchanged second and c) unchanged first column. Pattern a) is excluded since it keeps $\theta_{13}=0$. Pattern b) predicts $V_{e2} = 1/\sqrt{3}$ and specific CP phase correlations, but JUNO's smaller $|V_{e2}|$ disfavors it at more than 3.5$\sigma$. Pattern c), predicting $V_{e2} = \cos\tau/\sqrt{3}$, can be in agreement with current data within 1$\sigma$, and implies $\sin^2\theta_{12} = (1-3\sin^2\theta_{13})/3(1-\sin^2\theta_{13})$ and CP violating quantity $\sin \theta = \pm 0.998$. The negative sign favors the inverted neutrino mass hierarchy. Upcoming experiments can further test this scenario.