基于群代数的轻子混合模式研究

轻子的味混合模式及其物理解释是中微子理论研究中的基本问题。对此问题，流行的分立味对称性方案需要引入人工调节参数或复杂高阶群，否则难以满足近来中微子振荡实验结果的严格约束。本项目寻求超越流行方案的新型数学结构描述轻子味对称性。基于源自低阶群的群代数、味对称破缺、新近的中微子振荡数据，我们拟系统地研究群代数表达的味对称性及其对轻子味混合模式的预言。具体研究内容包括：二维群代数的不同构建方式、基于低阶群的可行群代数、基于可行群代数的轻子混合模式景观与混合模型。通过这些研究，我们期望获得满足实验约束的群代数构建方案，弄清楚群代数参数在味对称破缺中的作用，揭示轻子混合模式的决定机制。这些成果可以为轻子味对称性的实现提供简洁、有效的新方法，为轻子混合模式的物理起源研究提供启发性的新思路。

How to obtain lepton flavor mixing patterns and explain their physical origins is a fundamental question in theoretical researches on neutrinos. With respect to this question, fine-tuning parameters or complex large groups are introduced in the popular framework of discrete flavor symmetries. Otherwise, the results from it cannot satisfy the stringent constraints of the recent neutrino oscillation experiments. In order to overcome the shortcomings of the popular framework, this project intends to search for a new mathematical structure to describe flavor symmetries of leptons. On the basis of group algebras from small groups, flavor symmetry breaking, and the new recent neutrino oscillation data, flavor symmetries expressed by group algebras and their predictions on lepton mixing patterns will be studied systematically. The specific contents include constructions of 2-dimensional group algebras, viable group algebras based on small groups, lepton mixing pattern landscapes and mixing models based on viable group algebras. Through these researches, we expect to obtain experiments compatible construction frameworks of group algebras, clarify behaviors of the group algebra parameter in flavor symmetry breaking, and reveal the mechanism for lepton mixing patterns. Our results may provide new simple and useful methods for the realization of lepton flavor symmetries and a new inspiring thought for researches on physical origins of lepton mixing patterns.