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Effective Field Theory: A Modern Approach to Anomalous Couplings

Celine Degrande, Nicolas Greiner, Wolfgang Kilian, Olivier Mattelaer, Harrison Mebane, Tim Stelzer, Scott Willenbrock, Cen Zhang

TL;DR

The paper addresses model-independent ways to parameterize beyond-Standard-Model physics while preserving gauge symmetries, advocating effective field theory (EFT) over anomalous couplings. It outlines how dimension-six operators provide the leading low-energy effects and demonstrates mappings between EFT coefficients and traditional anomalous couplings, yielding a minimal, gauge-consistent parameter set. The authors show that EFT enables consistent tree- and loop-level analyses and clarifies unitarity within the theory’s domain of validity, with a concrete focus on electroweak vector-boson self-interactions and WW production. The work argues that adopting EFT offers a cleaner, more predictive framework for interpreting precision electroweak data and guiding new-physics searches.

Abstract

We advocate an effective field theory approach to anomalous couplings. The effective field theory approach is the natural way to extend the standard model such that the gauge symmetries are respected. It is general enough to capture any physics beyond the standard model, yet also provides guidance as to the most likely place to see the effects of new physics. The effective field theory approach also clarifies that one need not be concerned with the violation of unitarity in scattering processes at high energy. We apply these ideas to pair production of electroweak vector bosons.

Effective Field Theory: A Modern Approach to Anomalous Couplings

TL;DR

The paper addresses model-independent ways to parameterize beyond-Standard-Model physics while preserving gauge symmetries, advocating effective field theory (EFT) over anomalous couplings. It outlines how dimension-six operators provide the leading low-energy effects and demonstrates mappings between EFT coefficients and traditional anomalous couplings, yielding a minimal, gauge-consistent parameter set. The authors show that EFT enables consistent tree- and loop-level analyses and clarifies unitarity within the theory’s domain of validity, with a concrete focus on electroweak vector-boson self-interactions and WW production. The work argues that adopting EFT offers a cleaner, more predictive framework for interpreting precision electroweak data and guiding new-physics searches.

Abstract

We advocate an effective field theory approach to anomalous couplings. The effective field theory approach is the natural way to extend the standard model such that the gauge symmetries are respected. It is general enough to capture any physics beyond the standard model, yet also provides guidance as to the most likely place to see the effects of new physics. The effective field theory approach also clarifies that one need not be concerned with the violation of unitarity in scattering processes at high energy. We apply these ideas to pair production of electroweak vector bosons.

Paper Structure

This paper contains 12 sections, 19 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Effective Field Theory
  3. Dimension-Six Operators
  4. Anomalous Couplings
  5. Lagrangian approach
  6. Vertex function approach
  7. Anomalous Couplings from Effective Field Theory
  8. Unitarity bounds
  9. Conclusions
  10. Acknowledgements
  11. Odd-Dimensional Operators Violate Lepton and/or Baryon Number
  12. Derivation of Cross Section Unitarity Bound

Figures (1)

  • Figure 1: Differential cross section versus invariant mass for the process $pp \rightarrow W^+ W^-$ at the CERN Large Hadron Collider (14 TeV). Both the SM cross section and the cross section including the dimension six operator $O_{WWW}$ are shown. Also shown is the unitarity bound on the cross section. Results were generated with Whizard Kilian:2007gr and checked with MadGraph Alwall:2011uj.