Low Energy Effective Field Theory Operator Basis at $d\le 9$

Abstract

We obtain the complete operator bases at mass dimensions 5, 6, 7, 8, 9 for the low energy effective field theory (LEFT), which parametrize various physics effects between the QCD scale and the electroweak scale. The independence of the operator basis regarding the equation of motion, integration by parts and flavor relations, is guaranteed by our algorithm, whose validity for the LEFT with massive fermions involved is proved by a generalization of the amplitude-operator correspondence. At dimension 8 and 9, we list the 35058 (756) and 704584 (3686) operators for three (one) generations of fermions categorized by their baryon and lepton number violations $(\Delta B,\Delta L)$, as these operators are of most phenomenological relevance.

arXiv comment131 pages, 8 tables, corrected minor arithmetic error in counting, no revision on form of operators

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• One-loop Matching of the Type-II Seesaw Model onto the Standard Model Effective Field Theory
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• Constraining the SMEFT Extended with Sterile Neutrinos at FCC-ee
• Hidden U(N) Symmetry behind N=1 Superamplitudes
• Basis for Non-Factorizable Superamplitudes in N = 1 Supersymmetry
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