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<p>We derive a saturation theorem for general Effective Field Theories (EFTs) constructed using spurion analysis. Let <i>S</i> be a set of spurion fields introduced to organize the breaking of a global symmetry <i>G</i><sub><i>f</i></sub>, and <i>H</i><sub><i>S</i></sub> be the subgroup of <i>G</i><sub><i>f</i></sub> that remains unbroken under a generic vacuum expectation value ⟨<i>S</i>⟩; we show that the EFT Lagrangian constructed from the spurion analysis <i>saturates</i> the EFT Lagrangian without the spurions but restricted to <i>H</i><sub><i>S</i></sub> 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 <i>H</i><sub><i>S</i></sub> 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 <InlineMediaObject> <ImageObject Color="Color" FileRef="MediaObjects/13130_2025_26835_Figa_HTML.png" Format="PNG" Height="38" Rendition="HTML" Resolution="300" Type="Halftone" Width="222" /> </InlineMediaObject>, 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.</p>

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Most general EFTs from spurion analysis Hilbert series and minimal lepton flavor violation

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  • 发表日期：

    2025年7月28日

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  • Benjamín Grinstein,
  • Xiaochuan Lu,
  • Carlos Miró,
  • Pablo Quílez

摘要

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 Gf, and HS be the subgroup of Gf 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 HS 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 HS 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.