通过Kähler $R$-宇称破坏恢复最小模中微子质量

中文摘要 AI 辅助

重新分析了在模对称框架中通过单个模形式多重态描述中微子质量的可能性。实现这一点的最小模型是Feruglio基于模$A_4$对称性的模型，该模型包含一个手征flavon三重态$\phi$，所有中微子质量和混合都由模形式超场三重态$Y(\tau)$决定。我们指出，在局域超对称中，这些超场本身允许来自模型Kähler势的额外$R$-宇称破坏对中微子质量的贡献。$R$破坏通过有效超势中的双线性项$\epsilon_i L_i H_u$体现，其中参数$\epsilon_i$由$Y(\tau)$及其导数确定。Kähler势还将中微子与$\phi$的费米子分量混合，当这些费米子有质量时导致跷跷板中微子质量。我们分析了两种独立情况，中微子分别通过Weinberg算子或$\phi$诱导的跷跷板机制获得质量。与原始模型不同，加入$R$破坏贡献后，在两种情况下都能准确再现正常和倒置顺序的中微子混合角和质量比，其中Weinberg算子预测的中微子质量总和接近宇宙学极限，而跷跷板机制预测的质量总和舒适地低于该极限。

英文摘要

The possibility of describing neutrino masses through a single multiplet of modular forms in a modular symmetric framework is reanalysed. The minimal model achieving this is Feruglio's model based on modular $A_4$ symmetry, which contains a chiral flavon triplet $ϕ$, with all neutrino masses and mixing determined by a superfield triplet of modular forms $Y(τ)$. We point out that, in local supersymmetry, these superfields by themselves allow an additional $R$-parity-violating contribution to neutrino masses originating from the Kähler potential of the model. The $R$ violation manifests through a bilinear term $ε_i L_i H_u$ in the effective superpotential, with parameters $ε_i$ determined in terms of $Y(τ)$ and its derivatives. The Kähler potential also mixes neutrinos with the fermionic component of $ϕ$, leading to seesaw neutrino masses when these fermions are massive. Two separate cases are analysed, with neutrinos obtaining mass through the Weinberg operator or through the $ϕ$-induced seesaw. Unlike the original model, adding the $R$-violating contribution allows accurate reproduction of neutrino mixing angles and mass ratios for both the normal and inverted orderings in either case, with the Weinberg operator predicting a sum of neutrino masses close to the cosmological limit and the seesaw mechanism predicting ones comfortably below it.

发表机构

• Theoretical Physics Division, Physical Research Laboratory（物理研究实验室理论物理部）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

备注

12 pages + appendices