Modified TM2 for Reproducing All Best-Fit Values of Neutrino Mixing Angles

TL;DR

This work introduces a unitarity-preserving modification of the TM$_2$ neutrino mixing framework by deforming the $(1,2)$ element with a real parameter $\epsilon$, yielding analytic relations that allow all three mixing angles to match their current best-fit values within $1\sigma$ and remain robust to future updates. The model supplies explicit formulas for $s^2_{12}$, $s^2_{23}$, $s^2_{13}$, and the Dirac phase $\delta$ as functions of $(\theta,\phi,\epsilon)$, and demonstrates benchmark points that achieve the desired fits for both normal and inverted mass ordering. It also analyzes Majorana CP phases, predicting $m_{\beta\beta}$ in a way that is independent of $\phi$ and compatible with existing 0νββ bounds, while outlining how future experiments could probe the inverted ordering region. Additionally, the authors examine the magic-texture structure and show that the deformation generically breaks this texture, with the degree of breaking related to the Majorana phase, thus tying texture features to CP-violating parameters. Overall, the modified TM$_2$ offers a precise, robust route to reproducing current neutrino mixing data and yields testable predictions for Majorana masses and texture symmetry breaking.

Abstract

As measurements of neutrino mixing angles continue to become more precise, it is increasingly likely that in the very near future a realistic neutrino mixing model will be required to precisely reproduce their best-fit values. In this study, a modified TM$_2$ mixing model which reproduces the best-fit values of all three neutrino mixing angles is proposed. The model reproduces the correct mixing angles within 1$σ$ of the current central values and is robust against any future changes of the best-fit values.

Figures (4)

• Figure 1: $s^2_{ij}$ vs $s^2_{jk}$ as predicted in the NO case by the modified TM$_2$ model for the ranges $\theta\in[\;2.96112,\:2.96468\:] \mathrm{\:rad}$, $\phi\in[\;4.88095,\:5.15905\:] \mathrm{\:rad}$, and $\epsilon\in[\;-0.0345881,\:-0.0297319\:]$. The $\pm1\sigma$ Eq. regions as in Eq. (7) are indicated by the red dotted lines.
• Figure 2: $s^2_{ij}$ vs $s^2_{jk}$ as predicted in the IO case by the modified TM$_2$ model for the ranges $\theta\in[\;2.96003,\:2.96389\:] \mathrm{\:rad}$, $\phi\in[\;4.04457,\:4.31543\:] \mathrm{\:rad}$, and $\epsilon\in[\;-0.0346311,\:-0.0297689\:]$. The $\pm1\sigma$ allowed regions as in Eq. (7) are indicated by the red dotted lines.
• Figure 3: $m_{\beta\beta}$ vs $\cos(2\alpha)$ in the NO(black, bottom) and IO(black, top) scenarios for the various combinations of the extreme values of $\theta$ and $\epsilon$ that still produce mixing angles within the $\pm1\sigma$ allowed region as in section 3.1. Also shown are the ranges on $m_{\beta\beta}$ from the full GERDAGERDA dataset(dashed magenta), the estimated range for the future XLZDXLZD experiment(dashed cyan), and from the full KamLAND-ZenKamLAND-Zen dataset(dashed dark blue) - all of which are at the 90% C.L..
• Figure 4: $\Delta S$ vs $\cos(2\alpha)$ in the NO(left figure, black) and IO(right figure, black) scenarios - many representative points have been calculated within the range of $\theta$, $\epsilon$, and $\phi$ which still produce mixing angles within the $\pm1\sigma$ allowed region as in section 3.1. Also shown are the calculations when $\epsilon = 0$ (red, both figures).