Operator (biology)

Pure mathematics

Algebra over a field

Mathematics

Gauge (firearms)

Standard Model (mathematical formulation)

Gene

Repressor

Transcription factor

Standard basis

Biochemistry

Monomial

Field (mathematics)

Archaeology

Dimension (graph theory)

Geometry

Basis (linear algebra)

Chemistry

Discrete mathematics

History

Physical review. D/Physical review. D.

We present a complete and independent list of the dimension-nine operator basis in the Standard Model effective field theory by an automatic algorithm based on the amplitude-operator correspondence. A complete basis ($Y$-basis) is first constructed by enumerating the Young tableau of an auxiliary $SU(N)$ group and the gauge groups, with the equation-of-motion and integration-by-part redundancies all removed. In the presence of repeated fields, another basis ($P$-basis) with explicit flavor symmetries among them is derived from the $Y$-basis, which further induces a basis of independent monomial operators through a systematic process called desymmetrization. Our form of operators has advantages over the traditional way of presenting operators constrained by flavor relations, in the simplicity of both eliminating flavor redundancies and identifying independent flavor-specified operators. We list the 90456 (560) operators for three (one) generations of fermions, all of which violate baryon number or lepton numbe...

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