Li-Na Yan | Searcharxiv

arXiv2026

Lepton mixing from the $\Delta(96)$ Modular Littlest Seesaw

We perform the first comprehensive and model independent study of Modular Littlest Seesaw models based on the finite modular group $\Delta(96)$. We construct the vector-valued modular forms (VVMFs) for all irreducible representations of modular $\Delta(96)$, classify the inequivalent symmetry-preserving fixed points, and derive the corresponding alignments of the low-weight and next-to-lowest-weight triplet VVMFs. These results allow an exhaustive scan over the residual symmetries in the charged lepton, atmospheric neutrino, and solar neutrino sectors. We identify 35 phenomenologically viable and inequivalent breaking patterns, including 21 with normal ordering and 14 with inverted ordering. The resulting Dirac neutrino mass matrices go beyond the conventional CSD$(n)$ structure, yielding new fixed PMNS columns and novel correlations among the lepton mixing parameters beyond the TM$_1$ paradigm. The viable models are highly predictive, giving narrow ranges for neutrino masses, mixing parameters and CP phases, and can be stringently tested by upcoming experiments such as JUNO, DUNE and T2HK.

hep-ph↗

arXiv2025

Neutrino mixing parameters and masses from $\Delta(96)\rtimes H_{CP}$ in the tri-direct CP approach

We present a comprehensive model independent analysis of all breaking patterns resulting from $\Delta(96)\rtimes H_{CP}$ in the tri-direct CP approach of the minimal seesaw model with two right-handed neutrinos. The three generations of left-handed lepton doublets are assumed to transform as the irreducible triplet $\bm{3_{0}}$ of $\Delta(96)$, and the two right-handed neutrinos are assigned to singlets. In the case that both flavon fields $\phi_{\text{atm}}$ and $\phi_{\text{sol}}$ transform as triplet $\bm{\bar{3}_{0}}$, only one phenomenologically viable lepton mixing pattern is obtained for normal ordering neutrino masses. The lepton mixing matrix is predicted to be the TM1 pattern, with neutrino masses, mixing angles, and CP violation phases depending on only three real input parameters. When $\phi_{\text{sol}}$ is assigned to the $\bm{\bar{3}_{1}}$ representation, an additional real parameter $x$ must be included. Then we find 42 (12) independent phenomenologically interesting mixing patterns for normal (inverted) ordering neutrino masses, and the corresponding predictions for lepton mixing parameters and neutrino masses are obtained. Furthermore, we perform a detailed numerical analysis for five (one) example breaking patterns with some benchmark values of $x$ for normal (inverted) ordering. For the five normal examples, the absolute values of the first columns of the PMNS matrix are fixed to be $\left(\sqrt{\frac{2}{3}},\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}}\right)^{T}$, $\frac{1}{5}\left(\sqrt{17},2,2\right)^{T}$, $\frac{1}{\sqrt{38}}\left(5,2,3\right)^{T}$, $\frac{1}{\sqrt{57}}\left(\sqrt{37},\sqrt{10},\sqrt{10}\right)^{T}$ and $\frac{1}{3}\left(\sqrt{6},1,\sqrt{2}\right)^{T}$, respectively. For the inverted example, the absolute value of the third column of the PMNS matrix is $\frac{1}{2\sqrt{11}}\left(1,5,3\sqrt{2}\right)^{T}$.

hep-ph↗