Reply to "Comment on `Unified neutrino mixing and approximate $\mu-\tau$ reflection symmetry'[arXiv:2603.00885]''

TL;DR

This paper responds to critiques of a neutrino mixing model, clarifying overlooked conditions and discussing the viability of Inverted Ordering in light of recent data and constraints.

Contribution

The authors address specific points raised about their previous work, emphasizing the importance of real-value conditions and clarifying the status of Inverted Ordering.

Findings

Inverted Ordering is still constrained by the sum of neutrino masses.

The overlooked real-value condition related to $$-$$ reflection symmetry is acknowledged.

Inverted Ordering remains compatible with $|M_{ee}|$ data but is in tension with $ u$ mass bounds.

Abstract

Huang and Li [arXiv:2603.00885] have raised the following two points regarding our previous work [arXiv:2502.18029]:(1) The real-value conditions associated with $\mu$-$\tau$ reflection symmetry were overlooked. (2) Inverted Ordering (IO) remains viable when the latest experimental data are taken into account. As they have pointed out, we overlooked an important real-value condition. However, with regard to point (2), we believe that there may be a misunderstanding. In our original study, we excluded IO based on the constraint on the sum of neutrino masses, $\sum m_\nu$. In contrast, they argue that IO remains viable when considering the effective neutrino mass, $|M_{ee}|$. While IO may indeed remain allowed in light of the latest $|M_{ee}|$ data, it is still in tension with the experimental bounds on $\sum m_\nu$ under approximate $\mu-\tau$ symmetry within the discussed model parameter space.