Complete Set of Dimension-8 Operators in the Standard Model Effective Field Theory

Understand

We present a complete list of the dimension 8 operator basis in the standard model effective field theory using group theoretic techniques in a systematic and automated way.

• We adopt a new form of operators in terms of the irreducible representations of the Lorentz group, and identify the Lorentz structures as states in a $SU(N)$ group.
• In this way, redundancy from equations of motion is absent and that from integration-by-part is treated using the fact that the independent Lorentz basis forms an invariant subspace of the $SU(N)$ group.
• We also decompose operators into the ones with definite permutation symmetries among flavor indices to deal with subtlety from repeated fields.