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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.18702 |
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| _version_ | 1866914967573233664 |
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| author | Fujikawa, Kazuo Tureanu, Anca |
| author_facet | Fujikawa, Kazuo Tureanu, Anca |
| contents | The commonly used pseudo-C symmetry $(ν_{L})^{c}=C\overline{ν_{L}}^{T}$ is not defined in Lagrangian field theory. In general, there exist two classes of Majorana fermions; the first is associated with the Dirac-type fermion with the conventional C and P symmetries, and the second is associated with the Weyl-type fermion defined by CP symmetry only and formally characterised by the pseudo-C symmetry. Taking the seesaw model as an example, it is shown that a generalized Pauli--Gürsey (or Bogoliubov-type) canonical transformation converts the neutrino defined by the Weyl-type fermion to the neutrino defined by the Dirac-type fermion and thus to the conventional Majorana fermion, while preserving the canonical anti-commutation relations. The mixing angles in the weak lepton sector are not modified by this generalized Pauli--Gürsey transformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18702 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two classes of Majorana neutrinos in the seesaw model Fujikawa, Kazuo Tureanu, Anca High Energy Physics - Phenomenology The commonly used pseudo-C symmetry $(ν_{L})^{c}=C\overline{ν_{L}}^{T}$ is not defined in Lagrangian field theory. In general, there exist two classes of Majorana fermions; the first is associated with the Dirac-type fermion with the conventional C and P symmetries, and the second is associated with the Weyl-type fermion defined by CP symmetry only and formally characterised by the pseudo-C symmetry. Taking the seesaw model as an example, it is shown that a generalized Pauli--Gürsey (or Bogoliubov-type) canonical transformation converts the neutrino defined by the Weyl-type fermion to the neutrino defined by the Dirac-type fermion and thus to the conventional Majorana fermion, while preserving the canonical anti-commutation relations. The mixing angles in the weak lepton sector are not modified by this generalized Pauli--Gürsey transformation. |
| title | Two classes of Majorana neutrinos in the seesaw model |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2405.18702 |