Neutrino amplitude decomposition, $S$ matrix rephasing invariance, and reparametrization symmetry
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917563668103168 |
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| author | Minakata, Hisakazu |
| author_facet | Minakata, Hisakazu |
| contents | The $S$ matrix rephasing invariance is one of the fundamental principles of quantum mechanics that originates in its probabilistic interpretation. For a given $S$ matrix which describes neutrino oscillation, one can define the two different rephased amplitudes $S_{αβ}^{ \text{Reph-1} } \equiv e^{ i (λ_{1} / 2E) x} S_{αβ}$ and $S_{αβ}^{ \text{Reph-2} } \equiv e^{ i (λ_{2} / 2E) x} S_{αβ}$, which are physically equivalent to each other, where $λ_{k} / 2E$ denotes the energy eigenvalue of the $k$-th mass eigenstate. We point out that the transformation of the reparametrization (Rep) symmetry obtained with ``Symmetry Finder'' maps $S_{αβ}^{ \text{Reph-1} }$ to $S_{αβ}^{ \text{Reph-2} }$, and vice versa, providing a local and manifest realization of the $S$ matrix rephasing invariance by the Rep symmetry of the 1-2 state exchange type. It is strongly indicative of quantum mechanical nature of the Rep symmetry. The rephasing and Rep symmetry relation, though its all-order treatment remains incomplete, is shown to imply absence of the pure 1-3 exchange symmetry in Denton~{\it et al.}~perturbation theory. It then triggers a study of convergence of perturbation series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_14501 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Neutrino amplitude decomposition, $S$ matrix rephasing invariance, and reparametrization symmetry Minakata, Hisakazu High Energy Physics - Phenomenology High Energy Physics - Theory The $S$ matrix rephasing invariance is one of the fundamental principles of quantum mechanics that originates in its probabilistic interpretation. For a given $S$ matrix which describes neutrino oscillation, one can define the two different rephased amplitudes $S_{αβ}^{ \text{Reph-1} } \equiv e^{ i (λ_{1} / 2E) x} S_{αβ}$ and $S_{αβ}^{ \text{Reph-2} } \equiv e^{ i (λ_{2} / 2E) x} S_{αβ}$, which are physically equivalent to each other, where $λ_{k} / 2E$ denotes the energy eigenvalue of the $k$-th mass eigenstate. We point out that the transformation of the reparametrization (Rep) symmetry obtained with ``Symmetry Finder'' maps $S_{αβ}^{ \text{Reph-1} }$ to $S_{αβ}^{ \text{Reph-2} }$, and vice versa, providing a local and manifest realization of the $S$ matrix rephasing invariance by the Rep symmetry of the 1-2 state exchange type. It is strongly indicative of quantum mechanical nature of the Rep symmetry. The rephasing and Rep symmetry relation, though its all-order treatment remains incomplete, is shown to imply absence of the pure 1-3 exchange symmetry in Denton~{\it et al.}~perturbation theory. It then triggers a study of convergence of perturbation series. |
| title | Neutrino amplitude decomposition, $S$ matrix rephasing invariance, and reparametrization symmetry |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2308.14501 |