Symmetry in Neutrino Oscillation in Matter: New Picture and the <i>ν</i>SM–Non-Unitarity Interplay
We update and summarize the present status of our understanding of the reparametrization symmetry with an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mo>↔</mo><mi&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/12/2581 |
| _version_ | 1797455198662164480 |
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| author | Hisakazu Minakata |
| author_facet | Hisakazu Minakata |
| author_sort | Hisakazu Minakata |
| collection | DOAJ |
| description | We update and summarize the present status of our understanding of the reparametrization symmetry with an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mo>↔</mo><mi>j</mi></mrow></semantics></math></inline-formula> state exchange in neutrino oscillation in matter. We introduce a systematic method called <i>“Symmetry Finder”</i> (SF) to uncover such symmetries, demonstrate its efficient hunting capability, and examine their characteristic features. Apparently they have a local nature: the 1–2 and 1–3 state exchange symmetries exist at around the solar and atmospheric resonances, respectively, with the level-crossing states exchanged. However, this view is not supported, to date, in the globally valid Denton et al. (DMP) perturbation theory, which possesses the 1–2, but not the 1–3, exchange symmetry. This is probably due to our lack of understanding, and we find a clue for a larger symmetry structure than we know of. In the latter part of this article, we introduce non-unitarity, or unitarity violation (UV), into the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>SM neutrino paradigm, a low-energy description of beyond <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>SM new physics at a high (or low) scale. Based on the analyses of UV extended versions of the atmospheric resonance and the DMP perturbation theories, we argue that the reparametrization symmetry has a diagnostic capability for the theory with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>SM and UV sectors. Speculation is given on the topological nature of the identity, which determines the transformation property of the UV <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> parameters. |
| first_indexed | 2024-03-09T15:48:05Z |
| format | Article |
| id | doaj.art-d4dfc02f412e4274ba202ef7025ccb94 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T15:48:05Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-d4dfc02f412e4274ba202ef7025ccb942023-11-24T18:19:31ZengMDPI AGSymmetry2073-89942022-12-011412258110.3390/sym14122581Symmetry in Neutrino Oscillation in Matter: New Picture and the <i>ν</i>SM–Non-Unitarity InterplayHisakazu Minakata0Center for Neutrino Physics, Department of Physics, Virginia Tech, Blacksburg, VA 24061, USAWe update and summarize the present status of our understanding of the reparametrization symmetry with an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mo>↔</mo><mi>j</mi></mrow></semantics></math></inline-formula> state exchange in neutrino oscillation in matter. We introduce a systematic method called <i>“Symmetry Finder”</i> (SF) to uncover such symmetries, demonstrate its efficient hunting capability, and examine their characteristic features. Apparently they have a local nature: the 1–2 and 1–3 state exchange symmetries exist at around the solar and atmospheric resonances, respectively, with the level-crossing states exchanged. However, this view is not supported, to date, in the globally valid Denton et al. (DMP) perturbation theory, which possesses the 1–2, but not the 1–3, exchange symmetry. This is probably due to our lack of understanding, and we find a clue for a larger symmetry structure than we know of. In the latter part of this article, we introduce non-unitarity, or unitarity violation (UV), into the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>SM neutrino paradigm, a low-energy description of beyond <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>SM new physics at a high (or low) scale. Based on the analyses of UV extended versions of the atmospheric resonance and the DMP perturbation theories, we argue that the reparametrization symmetry has a diagnostic capability for the theory with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula>SM and UV sectors. Speculation is given on the topological nature of the identity, which determines the transformation property of the UV <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> parameters.https://www.mdpi.com/2073-8994/14/12/2581reparametrization symmetryneutrino oscillationnon-unitarity |
| spellingShingle | Hisakazu Minakata Symmetry in Neutrino Oscillation in Matter: New Picture and the <i>ν</i>SM–Non-Unitarity Interplay Symmetry reparametrization symmetry neutrino oscillation non-unitarity |
| title | Symmetry in Neutrino Oscillation in Matter: New Picture and the <i>ν</i>SM–Non-Unitarity Interplay |
| title_full | Symmetry in Neutrino Oscillation in Matter: New Picture and the <i>ν</i>SM–Non-Unitarity Interplay |
| title_fullStr | Symmetry in Neutrino Oscillation in Matter: New Picture and the <i>ν</i>SM–Non-Unitarity Interplay |
| title_full_unstemmed | Symmetry in Neutrino Oscillation in Matter: New Picture and the <i>ν</i>SM–Non-Unitarity Interplay |
| title_short | Symmetry in Neutrino Oscillation in Matter: New Picture and the <i>ν</i>SM–Non-Unitarity Interplay |
| title_sort | symmetry in neutrino oscillation in matter new picture and the i ν i sm non unitarity interplay |
| topic | reparametrization symmetry neutrino oscillation non-unitarity |
| url | https://www.mdpi.com/2073-8994/14/12/2581 |
| work_keys_str_mv | AT hisakazuminakata symmetryinneutrinooscillationinmatternewpictureandtheinismnonunitarityinterplay |