Comments on "Unified neutrino mixing and approximate $\mu-\tau$ reflection symmetry" (Mod. Phys. Lett. A, 40 (2025) 26, 2550097 [arXiv:2502.18029 [hep-ph]])

Abstract

Resolving mass ordering is an important issue in the neutrino physics. In Ref.\cite{yt} the authors investigate the phenomenology of a unified neutrino mixing framework and reveal that the predicted sum of neutrino masses derived from an approximate $\mu-\tau$ reflection symmetric flavor neutrino mass matrix based on the unified neutrino mixing with an inverted mass ordering, is excluded from DESI2024 and Supernova Ia luminosity distance data. We note that in Ref.\cite{yt} an error is present in Eq.(20), {\it i.e.}, the expression for $ M_{23}^{\mu-\tau} $, a similar error also appears in Eq.(26) for $M_{13}^{\mu-\tau}$. That is, the condition that $M_{ee}$ and $M_{\mu\tau}$ are real is omitted. We impose this condition and analyze its consequences. Using the newest data\cite{azz}, it is obtained that the predicted sm derived from the approximate $\mu-\tau$ reflection symmetric neutrino mass matrices $M_{23}$ for both NO and IO are allowed. We note also that their conclusion is invalid, as it is based on outdated data.