The Feynman rules for the SMEFT in the background field gauge

Abstract

We present a package for FeynRules which derives the Feynman rules for the Standard Model Effective Field Theory up to dimension-six using the background field method for gauge fixing. The package includes operators which shift the kinetic and mass terms of the Lagrangian up to dimension-eight and including dimension-six squared effects consistently. To the best of the author's knowledge this is the first publicly available package to include dimension-six squared effects consistently. The package is validated in a partner publication by analyzing the Ward Identities at dimension-six and one-loop order. We also extend the partner work in this article by including the dimension-six squared effects further demonstrating the consistency of their implementation. In doing so we find that failure to consistently include field shifts to dimension-six squared causes a breakdown in the Ward identities implying concerns about many calculations in the literature which do not properly incorporate these effects. The FeynRules files, as well as Mathematica notebooks performing the relevant calculations, can be downloaded from the FeynRules website and are included as ancillary files to this publication.

arXiv comment16 pages excluding appendix. 2 tables

References in corpus (56)

• The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations
• FeynRules 2.0 - A complete toolbox for tree-level phenomenology
• Dimension-Six Terms in the Standard Model Lagrangian
• Automatized One-Loop Calculations in 4 and D dimensions
• Generating Feynman Diagrams and Amplitudes with FeynArts 3
• Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology
• Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integrals
• Application of the Background-Field Method to the electroweak Standard Model
• Updated Global SMEFT Fit to Higgs, Diboson and Electroweak Data
• Reduced Effective Lagrangians
• The SMEFTsim package, theory and tools
• The Higgs boson from an extended symmetry
• The Chiral Approach to the Electroweak Interactions
• A Higgs-Higgs bound state due to New Physics at a TeV
• A Monte Carlo global analysis of the Standard Model Effective Field Theory: the top quark sector
• Robust Determination of the Higgs Couplings: Power to the Data
• O new physics, where art thou? A global search in the top sector
• Constraining anomalous Higgs interactions
• Renormalization Group Scaling of Higgs Operators and Γ(h -> γγ)
• Disentangling a dynamical Higgs
• Low-energy effective field theory below the electroweak scale: matching at one loop
• Non-resonant New Physics in Top Pair Production at Hadron Colliders
• The Gauge-Higgs Legacy of the LHC Run I
• The Gauge-Higgs Legacy of the LHC Run II
• Feynman Rules for the Standard Model Effective Field Theory in $R_{\xi }$-gauges
• Putting SMEFT Fits to Work
• Effective Theory of a Dynamically Broken Electroweak Standard Model at NLO
• Gauge Invariance of Green Functions: Background-Field Method versus Pinch Technique
• On one-loop corrections in the standard model effective field theory; the $\Gamma (h\to \gamma \gamma )$ case
• Electroweak Sector Under Scrutiny: A Combined Analysis of LHC and Electroweak Precision Data
• Determining Triple Gauge Boson Couplings from Higgs Data
• Higgs decay to two photons at one-loop in the SMEFT
• The complete HEFT Lagrangian after the LHC Run I
• A Higgs or Not a Higgs? What to Do if You Discover a New Scalar Particle
• The Geometric Standard Model Effective Field Theory
• Flavour symmetries in the SMEFT
• Electroweak and QCD Corrections to $Z$ and $W$ pole observables in the SMEFT
• The CKM parameters in the SMEFT
• Effective field theory approach to top-quark decay at next-to-leading order in QCD
• Equations of Motion for Effective Lagrangians and Penguins in Rare B-Decays
• Validity of SMEFT studies of VH and VV Production at NLO
• The $Z$ decay width in the SMEFT: $y_t$ and $\lambda$ corrections at one loop
• Top-quark electroweak interactions at high energy
• NLO Effects in EFT Fits to $W^{+}{W}^{-}$ Production at the LHC
• Gauge fixing the Standard Model Effective Field Theory
• One-loop corrections to $h\to b\bar{b}$ and $h\to \tau \bar{\tau }$ decays in the Standard Model Dimension-6 EFT: four-fermion operators and the large-$m_t$ limit
• Exact SMEFT formulation and expansion to $\mathcal{O}(v^4/{\Lambda }^4)$
• QCD Corrections in SMEFT Fits to $WZ$ and $WW$ Production
• NLO corrections to $h\to b\bar{b}$ decay in SMEFT
• Dyson summation without violating Ward identities and the Goldstone-boson equivalence theorem
• QCD radiative corrections for $h\to b\bar{b}$ in the Standard Model Dimension-6 EFT
• Effective Field Theory for Nonstandard Top Quark Couplings
• Giving top quark effective operators a boost
• Ward Identities for the Standard Model Effective Field Theory
• Effect of Fermionic Operators on the Gauge Legacy of the LHC Run I
• Higgs decay to fermion pairs at NLO in SMEFT

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• Higgs decays to two leptons and a photon beyond leading order in the SMEFT
• The Geometric $\nu$SMEFT: Operators and Connections
• An EWPD SMEFT likelihood for the LHC -- and how to improve it with measurements of W and Z boson properties