Complete set of dimension-eight operators in the standard model effective field theory

We present a complete list of the dimension 8 operator basis in standard model effective field theory using group theoretic techniques systematic and automated way. adopt new form operators terms irreducible representations Lorentz group, identify structures as states $SU(N)$ group. In this way, redundancy from equations motion is absent that integration-by-part treated fact independent forms an invariant subspace also decompose into ones with definite permutation symmetries among flavor indices to deal subtlety repeated fields. For first time, we provide explicit flavor-specified Our algorithm can be easily applied higher dimensional other theories, making these studies more approachable.