Chiral perturbative solution for the type-I seesaw mechanism in next-to-leading order
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909093349818368 |
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| author | Yang, Masaki J. S. |
| author_facet | Yang, Masaki J. S. |
| contents | In this letter, we perform chiral perturbative diagonalization of the type-I seesaw mechanism by hierarchical singular values $λ_{i}$ of the Dirac mass matrix $m_{D}$ up to the next-to-leading order (NLO). Since the mass matrix of right-handed neutrinos $M_{R}$ has parity symmetries under $λ_{i} \leftrightarrow - λ_{i}$, the singular values $M_{i}$ and mixing angles of diagonalization of $M_{R}$ are written by only even and odd orders of $λ_{i}$ respectively.
We confirm this fact by specific perturbative expansions of the third- and the fourth-order by $λ_{i}$. As a result, as long as the chiral perturbation theory is valid, the NLO contributions are generally suppressed by $O(λ_{i}^{2} / \labmda_{j}^{2}) \lesssim 1\%$ compared to the leading-order expressions that have sufficient accuracies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02767 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chiral perturbative solution for the type-I seesaw mechanism in next-to-leading order Yang, Masaki J. S. High Energy Physics - Phenomenology In this letter, we perform chiral perturbative diagonalization of the type-I seesaw mechanism by hierarchical singular values $λ_{i}$ of the Dirac mass matrix $m_{D}$ up to the next-to-leading order (NLO). Since the mass matrix of right-handed neutrinos $M_{R}$ has parity symmetries under $λ_{i} \leftrightarrow - λ_{i}$, the singular values $M_{i}$ and mixing angles of diagonalization of $M_{R}$ are written by only even and odd orders of $λ_{i}$ respectively. We confirm this fact by specific perturbative expansions of the third- and the fourth-order by $λ_{i}$. As a result, as long as the chiral perturbation theory is valid, the NLO contributions are generally suppressed by $O(λ_{i}^{2} / \labmda_{j}^{2}) \lesssim 1\%$ compared to the leading-order expressions that have sufficient accuracies. |
| title | Chiral perturbative solution for the type-I seesaw mechanism in next-to-leading order |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2402.02767 |