Complete Set of Dimension-9 Operators in the Standard Model Effective Field Theory

Abstract

We present a complete and independent list of the dimension 9 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 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 de-symmetrization. Our form of operators have 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 number conservation; among them we find new violation patterns as $\Delta B=2$ and $\Delta L=3$, which only appear at the dimensions $d\ge 9$.

arXiv comment58 pages, 1 figure, 10 tables

References in corpus (32)

• Dimension-Six Terms in the Standard Model Lagrangian
• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology
• Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence
• Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence
• Dimension-8 Operators in the Standard Model Effective Field Theory
• Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators
• Complete Set of Dimension-8 Operators in the Standard Model Effective Field Theory
• Classification of Effective Neutrino Mass Operators
• Renormalization group evolution of dimension-six baryon number violating operators
• Operators up to Dimension Seven in Standard Model Effective Field Theory Extended with Sterile Neutrinos
• A Survey of Lepton Number Violation Via Effective Operators
• A neutrinoless double beta decay master formula from effective field theory
• On the impact of dimension-eight SMEFT operators on Higgs measurements
• Baryon Number, Lepton Number, and Operator Dimension in the Standard Model
• On-shell constructibility of tree amplitudes in general field theories
• Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons
• The electroweak effective field theory from on-shell amplitudes
• An explicit construction of the dimension-9 operator basis in the standard model effective field theory
• Renormalization group coefficients and the S-matrix
• Inclusive Nucleon Decay Searches as a Frontier of Baryon Number Violation
• Standard Model Effective Field Theory from On-shell Amplitudes
• Enumerating the operators of an effective field theory
• Constructing effective field theories via their harmonics
• The Rise of SMEFT On-shell Amplitudes
• DEFT: A program for operators in EFT
• An electroweak basis for neutrinoless double $\beta$ decay
• Renormalization Group Evolution of Dimension-seven Operators in Standard Model Effective Field Theory and Relevant Phenomenology
• Implications of an Improved Neutron-Antineutron Oscillation Search for Baryogenesis: A Minimal Effective Theory Analysis
• High-dimensional neutrino masses
• Baryon Number, Lepton Number, and Operator Dimension in the SMEFT with Flavor Symmetries
• $\Delta L=3$ processes: Proton decay and LHC

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