Connect discreteness to continuousness in leptonic flavor symmetries
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914955936137216 |
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| author | Xu, Ding-Hui Rong, Shu-Jun |
| author_facet | Xu, Ding-Hui Rong, Shu-Jun |
| contents | Discrete groups are widely used in the expression of flavor symmetries of leptons. In this paper, we employ a novel mathematical object called group-algebra (GA) to describe symmetries of the leptonic mass matrices. A GA element is constructed by a discrete group with continuous parameters. For a GA element, there is an equivalent symmetry which can be continuous, discrete, and hybrid. According to the equivalence between a GA element and other symmetries, we perform a classification of 198 nontrivial elements of the GA generated by the group $S_{4}$. Based on the results of the classification, the phenomenological consequences of the $S_{4}$ GA are illustrated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15871 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Connect discreteness to continuousness in leptonic flavor symmetries Xu, Ding-Hui Rong, Shu-Jun High Energy Physics - Phenomenology Discrete groups are widely used in the expression of flavor symmetries of leptons. In this paper, we employ a novel mathematical object called group-algebra (GA) to describe symmetries of the leptonic mass matrices. A GA element is constructed by a discrete group with continuous parameters. For a GA element, there is an equivalent symmetry which can be continuous, discrete, and hybrid. According to the equivalence between a GA element and other symmetries, we perform a classification of 198 nontrivial elements of the GA generated by the group $S_{4}$. Based on the results of the classification, the phenomenological consequences of the $S_{4}$ GA are illustrated. |
| title | Connect discreteness to continuousness in leptonic flavor symmetries |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2409.15871 |