Extending trinity to the scalar sector through discrete flavoured symmetries
Abstract We conjecture the existence of a relation between elementary scalars and fermions, making it plausible the existence of three Higgs doublets. We introduce a Trinity Principle (TP) which, given the fact that there are no massless quarks, requires the existence of a minimum of three Higgs dou...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-08-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-020-8265-3 |
| _version_ | 1828794430589501440 |
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| author | João M. Alves Francisco J. Botella Gustavo C. Branco Miguel Nebot |
| author_facet | João M. Alves Francisco J. Botella Gustavo C. Branco Miguel Nebot |
| author_sort | João M. Alves |
| collection | DOAJ |
| description | Abstract We conjecture the existence of a relation between elementary scalars and fermions, making it plausible the existence of three Higgs doublets. We introduce a Trinity Principle (TP) which, given the fact that there are no massless quarks, requires the existence of a minimum of three Higgs doublets. The TP states that each row of the mass matrix of a quark of a given charge should receive the contribution from one and only one scalar doublet and furthermore a given scalar doublet should contribute to one and only one row of the mass matrix of a quark of a given charge. This principle is analogous to the Natural Flavour Conservation (NFC) of Glashow and Weinberg with the key distinction that NFC required the introduction of a flavour blind symmetry, while the TP requires a flavoured symmetry, to be implemented in a natural way. We provide two examples which satisfy the Trinity Principle based on $${\mathbb {Z}}_3$$ Z3 and $${\mathbb {Z}}_2\times {\mathbb {Z}}_2'$$ Z2×Z2′ flavoured symmetries, and show that they are the minimal multi-Higgs extensions of the Standard Model where CP can be imposed as a symmetry of the full Lagrangian and broken by the vacuum, without requiring soft-breaking terms. We show that the vacuum phases are sufficient to generate a complex CKM matrix, in agreement with experiment. The above mentioned flavoured symmetries lead to a strong reduction in the number of parameters in the Yukawa interactions, enabling a control of the Scalar Flavour Changing Neutral Couplings (SFCNC). We analyse some of the other physical implications of the two models, including an estimate of the enhancement of the Baryon Asymmetry of the Universe provided by the new sources of CP violation, and a discussion of the strength of their tree-level SFCNC. |
| first_indexed | 2024-12-12T03:45:21Z |
| format | Article |
| id | doaj.art-90ff986e708345b9abc3d96598db2a8d |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-12-12T03:45:21Z |
| publishDate | 2020-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-90ff986e708345b9abc3d96598db2a8d2022-12-22T00:39:34ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522020-08-0180811410.1140/epjc/s10052-020-8265-3Extending trinity to the scalar sector through discrete flavoured symmetriesJoão M. Alves0Francisco J. Botella1Gustavo C. Branco2Miguel Nebot3Departamento de Física and Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico (IST), U. de Lisboa (UL)Departament de Fìsica Teòrica and Instituto de Física Corpuscular (IFIC), Universitat de València-CSICDepartamento de Física and Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico (IST), U. de Lisboa (UL)Departamento de Física and Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico (IST), U. de Lisboa (UL)Abstract We conjecture the existence of a relation between elementary scalars and fermions, making it plausible the existence of three Higgs doublets. We introduce a Trinity Principle (TP) which, given the fact that there are no massless quarks, requires the existence of a minimum of three Higgs doublets. The TP states that each row of the mass matrix of a quark of a given charge should receive the contribution from one and only one scalar doublet and furthermore a given scalar doublet should contribute to one and only one row of the mass matrix of a quark of a given charge. This principle is analogous to the Natural Flavour Conservation (NFC) of Glashow and Weinberg with the key distinction that NFC required the introduction of a flavour blind symmetry, while the TP requires a flavoured symmetry, to be implemented in a natural way. We provide two examples which satisfy the Trinity Principle based on $${\mathbb {Z}}_3$$ Z3 and $${\mathbb {Z}}_2\times {\mathbb {Z}}_2'$$ Z2×Z2′ flavoured symmetries, and show that they are the minimal multi-Higgs extensions of the Standard Model where CP can be imposed as a symmetry of the full Lagrangian and broken by the vacuum, without requiring soft-breaking terms. We show that the vacuum phases are sufficient to generate a complex CKM matrix, in agreement with experiment. The above mentioned flavoured symmetries lead to a strong reduction in the number of parameters in the Yukawa interactions, enabling a control of the Scalar Flavour Changing Neutral Couplings (SFCNC). We analyse some of the other physical implications of the two models, including an estimate of the enhancement of the Baryon Asymmetry of the Universe provided by the new sources of CP violation, and a discussion of the strength of their tree-level SFCNC.http://link.springer.com/article/10.1140/epjc/s10052-020-8265-3 |
| spellingShingle | João M. Alves Francisco J. Botella Gustavo C. Branco Miguel Nebot Extending trinity to the scalar sector through discrete flavoured symmetries European Physical Journal C: Particles and Fields |
| title | Extending trinity to the scalar sector through discrete flavoured symmetries |
| title_full | Extending trinity to the scalar sector through discrete flavoured symmetries |
| title_fullStr | Extending trinity to the scalar sector through discrete flavoured symmetries |
| title_full_unstemmed | Extending trinity to the scalar sector through discrete flavoured symmetries |
| title_short | Extending trinity to the scalar sector through discrete flavoured symmetries |
| title_sort | extending trinity to the scalar sector through discrete flavoured symmetries |
| url | http://link.springer.com/article/10.1140/epjc/s10052-020-8265-3 |
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