2, 84, 30, 993, 560, 15456, 11962, 261485, ...: Higher dimension operators in the SM EFT

TL;DR

This paper systematically classifies higher dimension operators in the Standard Model Effective Field Theory up to dimension 12 using conformal algebra, revealing new operators beyond previous literature, especially for multiple fermion generations.

Contribution

It introduces a conformal algebra-based method to organize and count independent operators in the SM EFT up to dimension 12, including new operators not previously identified.

Findings

Identified additional operators at dimensions 7 and 8 for multiple fermion generations.

Provided a comprehensive count of independent operators up to dimension 12.

Demonstrated the utility of conformal algebra in effective field theory classification.

Abstract

In a companion paper, we show that operator bases for general effective field theories are controlled by the conformal algebra. Equations of motion and integration by parts identities can be systematically treated by organizing operators into irreducible representations of the conformal group. In the present work, we use this result to study the standard model effective field theory (SM EFT), determining the content and number of higher dimension operators up to dimension 12, for an arbitrary number of fermion generations. We find additional operators to those that have appeared in the literature at dimension 7 (specifically in the case of more than one fermion generation) and at dimension 8. (The title sequence is the total number of independent operators in the SM EFT with one fermion generation, including hermitian conjugates, ordered in mass dimension, starting at dimension 5.)