Low-Energy Effective Field Theory below the Electroweak Scale: Dimension-8 Operators

Abstract

We construct a complete basis of dimension-8 operators in the Low-Energy Effective Field Theory below the Electroweak Scale (LEFT). We find there are 35058 dimension-8 operators in the LEFT for two generations of up-type quarks and three generations of down-type quarks, charged leptons, and left-handed neutrinos. The existence of this operator basis is a necessary prerequisite for matching to the Standard Model Effective Field Theory at the dimension-8 level.

29 pages, 20 tables; v3: minor typos corrected

References in corpus (5)

• Renormalization group evolution of dimension-six baryon number violating operators
• Operator bases, $S$-matrices, and their partition functions
• Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox
• Hilbert Series for Flavor Invariants of the Standard Model
• Renormalization Group Evolution of Dimension-seven Operators in Standard Model Effective Field Theory and Relevant Phenomenology

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• Computing Tools for Effective Field Theories
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• Optimal determination of New Physics couplings: A comparative study
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• Renormalization-group equations of the LEFT at two loops: dimension-six operators
• Constraining the SMEFT Extended with Sterile Neutrinos at FCC-ee
• New chiral structures for baryon number violating nucleon decays
• Uncovering the Root of LEFT in SMEFT
• Sensitivities on the anomalous quartic $\gamma \gamma \gamma \gamma$ and $\gamma \gamma \gamma Z$ couplings at the CLIC
• The future muon collider for the research of the anomalous neutral quartic $Z\gamma \gamma \gamma$, $ZZ\gamma \gamma$, and $ZZZ\gamma$ couplings
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