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We present an efficient algorithm for determining the Hilbert series of an effective theory and provide a companion code called ECO (Efficient Counting of Operators) in FORM. For example, the Hilbert series for the dimension 15 operators in the Standard Model Effective Theory (SMEFT) can be obtained in a minute on a single CPU core. While our implementation focusses on SMEFT, we allow for a flexible user input of the light degrees of freedom. Furthermore, gravity, as well as additional U(1) global or gauge symmetries can be included.
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Cited by 2 Pith papers
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Chiral Effective Field Theories for Strong and Weak Dynamics
The paper constructs complete and minimal relativistic operator bases for nucleon-nucleon, pion-nucleon-nucleon, and three-nucleon sectors up to p6, and a spurion-based leptonic sector up to p4, using Hilbert series a...
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Fingerprinting New Physics with Effective Field Theories
A thesis compiling published SMEFT global fits, automated UV-model constraints, and ML-based unbinned observables, with projections for HL-LHC, FCC-ee, and CEPC.
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