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Effective Field Theory Beyond the Standard Model

Scott Willenbrock, Cen Zhang

TL;DR

The paper argues that effective field theory with dimension-six operators provides a principled, gauge-invariant framework to parameterize physics beyond the Standard Model at energies below a new physics scale $\Lambda$. It discusses operator bases (BW, HISZ, GGPR), how operators affect weak boson production and precision electroweak observables, and how one- and two-loop effects constrain these coefficients. The work highlights the interplay between Higgs data and electroweak measurements, the role of operator mixing under renormalization, and the necessity of global analyses to avoid misleading bounds. The framework offers a path to infer properties of any underlying new physics from measured $c_i/\Lambda^2$ coefficients, while emphasizing careful treatment of correlations and scale evolution.

Abstract

We review the effective field theory approach to physics beyond the Standard Model using dimension-six operators. Topics include the choice of operator basis, electroweak boson pair production, precision electroweak physics (including one-loop contributions), and Higgs physics. By measuring the coefficients of dimension-six operators with good accuracy, we can hope to infer some or all of the features of the theory that lies beyond the Standard Model.

Effective Field Theory Beyond the Standard Model

TL;DR

The paper argues that effective field theory with dimension-six operators provides a principled, gauge-invariant framework to parameterize physics beyond the Standard Model at energies below a new physics scale . It discusses operator bases (BW, HISZ, GGPR), how operators affect weak boson production and precision electroweak observables, and how one- and two-loop effects constrain these coefficients. The work highlights the interplay between Higgs data and electroweak measurements, the role of operator mixing under renormalization, and the necessity of global analyses to avoid misleading bounds. The framework offers a path to infer properties of any underlying new physics from measured coefficients, while emphasizing careful treatment of correlations and scale evolution.

Abstract

We review the effective field theory approach to physics beyond the Standard Model using dimension-six operators. Topics include the choice of operator basis, electroweak boson pair production, precision electroweak physics (including one-loop contributions), and Higgs physics. By measuring the coefficients of dimension-six operators with good accuracy, we can hope to infer some or all of the features of the theory that lies beyond the Standard Model.

Paper Structure

This paper contains 9 sections, 21 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Operator basis
  3. Weak boson pair production
  4. Flavor
  5. Beyond $S$ and $T$
  6. Precision Electroweak Measurements
  7. Constraints at One Loop
  8. Higgs boson
  9. Final Thoughts

Figures (4)

  • Figure 1: Feynman diagram for $f\bar{f}\rightarrow W^+W^-$. The dot represents an interaction arising from a dimension-six operator.
  • Figure 2: The invariant mass distribution for $W^+W^-$ production at the LHC. The lowest (blue) curve is the Standard Model prediction; the middle (purple) curve includes the effect of the dimension-six operator ${\cal O}_{WWW}$; and the upper (red) curve is the unitarity bound. The data are hypothetical.
  • Figure 3: Bound on $c_{BW}/\Lambda^2$ and $c_{\Phi,1}/\Lambda^2$, assuming all other operator coefficients vanish. The curves (from outer to inner) are 99%, 95% and 68% confidence level.
  • Figure 4: Feynman diagrams involving operators ${\cal O}_{WW}$ and ${\cal O}_{BB}$ that contribute to precision electroweak measurements. The dots represent interactions arising from these operators ${\cal O}_{WW}$ and ${\cal O}_{BB}$.