Most general EFTs from spurion analysis Hilbert series and minimal lepton flavor violation
Abstract We derive a saturation theorem for general Effective Field Theories (EFTs) constructed using spurion analysis. Let S be a set of spurion fields introduced to organize the breaking of a global symmetry G f , and H S be the subgroup of G f that remains unbroken under a generic vacuum expectat...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2025)259 |
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| author | Benjamín Grinstein Xiaochuan Lu Carlos Miró Pablo Quílez |
| author_facet | Benjamín Grinstein Xiaochuan Lu Carlos Miró Pablo Quílez |
| author_sort | Benjamín Grinstein |
| collection | DOAJ |
| description | Abstract We derive a saturation theorem for general Effective Field Theories (EFTs) constructed using spurion analysis. Let S be a set of spurion fields introduced to organize the breaking of a global symmetry G f , and H S be the subgroup of G f that remains unbroken under a generic vacuum expectation value ⟨S⟩; we show that the EFT Lagrangian constructed from the spurion analysis saturates the EFT Lagrangian without the spurions but restricted to H S invariance, provided that arbitrary powers of the spurion fields are allowed. As examples, we study several implementations of the Minimal Lepton Flavor Violation (MLFV) principle, corresponding to various origins of the neutrino masses. In each scenario, we compute the Hilbert series to obtain the numbers of independent lepton flavor covariants that appear in the corresponding EFT at mass dimension 6. These numbers agree with the number of H S invariants in the EFT without the spurions, demonstrating the saturation theorem. Motivated by phenomenological connections, we provide linearly independent spurion polynomials for selected lepton flavor covariants. A supplementary material file supplies , a Mathematica notebook that provides functions for computing general Hilbert series of invariants and covariants of compact classical groups. It presents examples demonstrating the use of the code, including the Hilbert series for our MLFV scenarios. |
| format | Article |
| id | doaj-art-affbd0c5b96e4fff8eb1507e9097da80 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-affbd0c5b96e4fff8eb1507e9097da802025-08-20T04:01:47ZengSpringerOpenJournal of High Energy Physics1029-84792025-07-012025714110.1007/JHEP07(2025)259Most general EFTs from spurion analysis Hilbert series and minimal lepton flavor violationBenjamín Grinstein0Xiaochuan Lu1Carlos Miró2Pablo Quílez3Department of Physics, University of California, San DiegoDepartment of Physics, University of California, San DiegoDepartament de Física Teòrica and Instituto de Física Corpuscular (IFIC), Universitat de València — CSICDepartment of Physics, University of California, San DiegoAbstract We derive a saturation theorem for general Effective Field Theories (EFTs) constructed using spurion analysis. Let S be a set of spurion fields introduced to organize the breaking of a global symmetry G f , and H S be the subgroup of G f that remains unbroken under a generic vacuum expectation value ⟨S⟩; we show that the EFT Lagrangian constructed from the spurion analysis saturates the EFT Lagrangian without the spurions but restricted to H S invariance, provided that arbitrary powers of the spurion fields are allowed. As examples, we study several implementations of the Minimal Lepton Flavor Violation (MLFV) principle, corresponding to various origins of the neutrino masses. In each scenario, we compute the Hilbert series to obtain the numbers of independent lepton flavor covariants that appear in the corresponding EFT at mass dimension 6. These numbers agree with the number of H S invariants in the EFT without the spurions, demonstrating the saturation theorem. Motivated by phenomenological connections, we provide linearly independent spurion polynomials for selected lepton flavor covariants. A supplementary material file supplies , a Mathematica notebook that provides functions for computing general Hilbert series of invariants and covariants of compact classical groups. It presents examples demonstrating the use of the code, including the Hilbert series for our MLFV scenarios.https://doi.org/10.1007/JHEP07(2025)259Effective Field TheoriesFlavour SymmetriesSMEFT |
| spellingShingle | Benjamín Grinstein Xiaochuan Lu Carlos Miró Pablo Quílez Most general EFTs from spurion analysis Hilbert series and minimal lepton flavor violation Journal of High Energy Physics Effective Field Theories Flavour Symmetries SMEFT |
| title | Most general EFTs from spurion analysis Hilbert series and minimal lepton flavor violation |
| title_full | Most general EFTs from spurion analysis Hilbert series and minimal lepton flavor violation |
| title_fullStr | Most general EFTs from spurion analysis Hilbert series and minimal lepton flavor violation |
| title_full_unstemmed | Most general EFTs from spurion analysis Hilbert series and minimal lepton flavor violation |
| title_short | Most general EFTs from spurion analysis Hilbert series and minimal lepton flavor violation |
| title_sort | most general efts from spurion analysis hilbert series and minimal lepton flavor violation |
| topic | Effective Field Theories Flavour Symmetries SMEFT |
| url | https://doi.org/10.1007/JHEP07(2025)259 |
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