Abstract
In a companion paper [1], 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.)
Highlights
Into short multiplets of the conformal group. (2) The IBP removes operators that are total derivatives, which can be regarded as descendants in a conformal field theory
In a companion paper [1], we show that operator bases for general effective field theories are controlled by the conformal algebra
We find additional operators to those that have appeared in the literature at dimension 7 and at dimension 8. (The title sequence is the total number of independent operators in the standard model effective field theory (SM EFT) with one fermion generation, including hermitian conjugates, ordered in mass dimension, starting at dimension 5.)
Summary
Into short multiplets of the conformal group. (2) The IBP removes operators that are total derivatives, which can be regarded as descendants in a conformal field theory. Note that we regard the SM with only the kinetic terms as the zeroth order Lagrangian, where all fields are massless and the theory is (classically) conformal. The we classify additional higher-dimension operators as perturbation to the system. This technique is a natural generalization of what we studied in 1D QFT in our previous paper [11]. In this paper we aim to present the method with a minimal amount of technical details, but to the level at which it can be reproduced and applied to other phenomenological Lagrangians of interest. The method is outlined in section 2; details beyond those needed for the present purpose can be found in [1].
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