Complete set of dimension-eight operators in the standard model effective field theory
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Abstract
We present a complete list of the dimension 8 operator basis in the standard\nmodel effective field theory using group theoretic techniques in a systematic\nand automated way. We adopt a new form of operators in terms of the irreducible\nrepresentations of the Lorentz group, and identify the Lorentz structures as\nstates in a $SU(N)$ group. In this way, redundancy from equations of motion is\nabsent and that from integration-by-part is treated using the fact that the\nindependent Lorentz basis forms an invariant subspace of the $SU(N)$ group. We\nalso decompose operators into the ones with definite permutation symmetries\namong flavor indices to deal with subtlety from repeated fields. For the first\ntime, we provide the explicit form of independent flavor-specified operators in\na systematic way. Our algorithm can be easily applied to higher dimensional\nstandard model effective field theory and other effective field theories,\nmaking these studies more approachable.\n