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Most general EFTs from spurion analysis: Hilbert series and Minimal Lepton Flavor Violation by Grinstein, Benjamín; Lu, Xiaochuan; Miró, Carlos; Quílez, Pablo is a scholarly article available to read on EtoBox.

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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 $\langle S\rangle$; 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. An ancillary file is supplied at https://github.com/Hilbert

Author

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

Published

2024

Language

EN