On the Power Counting in Effective Field Theories

Abstract

We discuss the systematics of power counting in general effective field theories, focussing on those that are nonrenormalizable at leading order. As an illuminating example we consider chiral perturbation theory gauged under the electromagnetic $U(1)$ symmetry. This theory describes the low-energy interactions of the octet of pseudo-Goldstone bosons in QCD with photons and has been discussed extensively in the literature. Peculiarities of the standard approach are pointed out and it is shown how these are resolved within our scheme. The presentation follows closely our recent discussion of power counting for the electroweak chiral Lagrangian. The systematics of the latter is reviewed and shown to be consistent with the concept of chiral dimensions. The results imply that naive dimensional analysis (NDA) is incomplete in general effective field theories, while still reproducing the correct counting in special cases.

14 pages, no figures

References in corpus (1)

• A Higgs-Higgs bound state due to New Physics at a TeV

Cited by in corpus (87)

• The Standard Model as an Effective Field Theory
• Effective description of general extensions of the Standard Model: the complete tree-level dictionary
• Precision Measurements of Higgs Couplings: Implications for New Physics Scales
• Disentangling a dynamical Higgs
• Towards consistent Electroweak Precision Data constraints in the SMEFT
• Signals of the electroweak phase transition at colliders and gravitational wave observatories
• Analysis of General Power Counting Rules in Effective Field Theory
• Current and future constraints on Higgs couplings in the nonlinear Effective Theory
• On one-loop corrections in the standard model effective field theory; the $\Gamma (h\to \gamma \gamma )$ case
• A Systematic Approach to the SILH Lagrangian
• Higgs boson pair production in non-linear Effective Field Theory with full $m_t$-dependence at NLO QCD
• Complete One-Loop Renormalization of the Higgs-Electroweak Chiral Lagrangian
• Flavor Physics and Flavor Anomalies in Minimal Fundamental Partial Compositeness
• Anomalies in Bottom from new physics in Top
• Signatures of a nonstandard Higgs from flavor physics
• Scheming in the SMEFT... and a reparameterization invariance!
• Direct and indirect constraints on CP-violating Higgs-quark and Higgs-gluon interactions
• Renormalization group evolution of Higgs effective field theory
• Pseudo-observables in Higgs decays
• One-loop $\gamma \gamma \to W_L^{+}{W}_L^{-}$ and $\gamma \gamma \to Z_L{Z}_L$ from the Electroweak Chiral Lagrangian with a light Higgs-like scalar
• Fitting Higgs Data with Nonlinear Effective Theory
• Higgs Physics: It ain't over till it's over
• Benchmarking Di-Higgs Production in Various Extended Higgs Sector Models
• On the Predictiveness of Single-Field Inflationary Models
• Determining the Shape of Higgs Potential at Future Colliders
• Standard Model Extended by a Heavy Singlet: Linear vs. Nonlinear EFT
• Note on Anomalous Higgs-Boson Couplings in Effective Field Theory
• On the renormalization of the electroweak chiral Lagrangian with a Higgs
• Crawling technicolor
• Search for nonresonant pair production of Higgs bosons in the $b\bar{b}b\bar{b}$ final state in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
• Vacuum misalignment and pattern of scalar masses in the SU(5)/SO(5) composite Higgs model
• A non-linear EFT description of $gg\to HH$ at NLO interfaced to POWHEG
• Chiral effective theories with a light scalar at one loop
• Inflation in Motion: Unitarity Constraints in Effective Field Theories with Broken Lorentz Symmetry
• One-loop renormalization of the electroweak chiral Lagrangian with a light Higgs
• Complete NLO Operators in the Higgs Effective Field Theory
• Classification of NLO operators for composite Higgs models
• Symmetry and geometry in generalized Higgs effective field theory -- Finiteness of oblique corrections v.s. perturbative unitarity
• SMEFT predictions for $gg\to hh$ at full NLO QCD and truncation uncertainties
• Fingerprints of heavy scales in electroweak effective Lagrangians
• Consistent Searches for SMEFT Effects in Non-Resonant Dijet Events
• Effective field theory approach to trans-TeV supersymmetry: covariant matching, Yukawa unification and Higgs couplings
• Complete NNLO Operator Bases in Higgs Effective Field Theory
• Renormalization group evolution of the universal theories EFT
• Anatomy of Higgs decays into $\gamma \gamma$ and $\gamma Z$ within the EChL in the $R_{\xi }$ gauges
• Minimal Fundamental Partial Compositeness
• Loop counting matters in SMEFT
• First Constraints on WIMP-Nucleon Effective Field Theory Couplings in an Extended Energy Region From LUX-ZEPLIN
• Computing Tools for Effective Field Theories
• Testing anomalous $H-W$ couplings and Higgs self-couplings via double and triple Higgs production at $e^{+}{e}^{-}$ colliders
• Colorful Imprints of Heavy States in the Electroweak Effective Theory
• Higgs-Electroweak Chiral Lagrangian: One-Loop Renormalization Group Equations
• Multi-Higgs Boson Production with Anomalous Interactions at Current and Future Proton Colliders
• Status and prospects of precision analyses with $e^{+}{e}^{-}\to W^{+}{W}^{-}$
• Anomalous couplings in Higgs-boson pair production at approximate NNLO QCD
• EFTs meet Higgs Nonlinearity, Compositeness and (Neutral) Naturalness
• Higgs boson couplings: measurements and theoretical interpretation
• Effective Field Theory in the top sector: do multijets help?
• Comment on "Analysis of General Power Counting Rules in Effective Field Theory"
• The Global Higgs Picture at 27 TeV
• A bottom-up approach within the electroweak effective theory: constraining heavy resonances
• Higgs Factories: Higgs-Strahlung versus W-Fusion
• Resonant production of Wh and Zh at the LHC
• Renormalization-group equations of the LEFT at two loops: dimension-five effects
• Double Higgs Production in Vector Boson Fusion at NLO QCD in HEFT
• Effective Field Theory Perspective on Next-to-Minimal Composite Higgs
• Renormalisation group effects in SMEFT for di-Higgs production
• Exploring correlations between HEFT Higgs couplings ${\kappa }_V$ and ${\kappa }_{2V}$ via HH production at $e^{+}{e}^{-}$ colliders
• Left-right non-linear dynamical Higgs
• The Art of Counting: a reappraisal of the HEFT expansion
• Perturbative Power Counting, Lowest-Index Operators and Their Renormalization in Standard Model Effective Field Theory
• Top-pair production via gluon fusion in the Standard Model Effective Field Theory
• Extracting Higgs Self-Coupling Constraints through Triple Higgs Boson Production at Future Hadron Colliders
• $h\to gg$ and $h\to \gamma \gamma$ with Anomalous Couplings at Next-to-Leading Order in QCD
• Diboson excess and $Z^{\prime }$-predictions via left-right non-linear Higgs
• Scalar and fermion on-shell amplitudes in generalized Higgs effective field theory
• Master formula for one-loop renormalization of bosonic SMEFT operators
• Multi-Higgs Amplitudes Bootstrapped: Dissecting SMEFT and HEFT
• SMEFT truncation effects in Higgs boson pair production at NLO QCD
• CP violation from spin-1 resonances in a left-right dynamical Higgs context
• Is there new particle running in the loop-induced $H\gamma \gamma$ and $Hgg$ vertex?
• Assessing (H)EFT theory errors by pitting EoM against Field Redefinitions
• The HiggsTools Handbook: Concepts and observables for deciphering the Nature of the Higgs Sector
• Higgs pair production in gluon fusion to higher orders in Higgs Effective Field Theory
• Comment on 'Primary Dimensions'
• Operator Dimension Parity Fractionalization
• Projected Sensitivity of Paleo-Detectors to Dark Matter Effective Interactions with Nuclei