Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology

Abstract

We calculate the gauge terms of the one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory (SM EFT). Combining these results with our previous results for the $\lambda$ and Yukawa coupling terms completes the calculation of the one-loop anomalous dimension matrix for the dimension-six operators. There are 1350 $CP$-even and $1149$ $CP$-odd parameters in the dimension-six Lagrangian for 3 generations, and our results give the entire $2499\times 2499$ anomalous dimension matrix. We discuss how the renormalization of the dimension-six operators, and the additional renormalization of the dimension $d\le 4$ terms of the SM Lagrangian due to dimension-six operators, lays the groundwork for future precision studies of the SM EFT aimed at constraining the effects of new physics through precision measurements at the electroweak scale. As some sample applications, we discuss some aspects of the full RGE improved result for essential processes such as $gg\to h$, $h\to \gamma \gamma$ and $h\to Z\gamma$, for Higgs couplings to fermions, for the precision electroweak parameters $S$ and $T$, and for the operators that modify important processes in precision electroweak phenomenology, such as the three-body Higgs boson decay $h\to Z{\ell }^{+}{\ell }^{-}$ and triple gauge boson couplings. We discuss how the renormalization group improved results can be used to study the flavor problem in the SM EFT, and to test the minimal flavor violation (MFV) hypothesis. We briefly discuss the renormalization effects on the dipole coefficient $C_{e\gamma }$ which contributes to $\mu \to e\gamma$ and to the muon and electron magnetic and electric dipole moments.

28 pages + appendices v5: Minor corrections. The complete SMEFT RGE will be maintained at http://einstein.ucsd.edu/smeft/

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• Flavour alignment of New Physics in light of the $(g-2{)}_{\mu }$ anomaly
• Simple Rules for Evanescent Operators in One-Loop Basis Transformations
• EFT Diagrammatica II: Tracing the UV origin of bosonic D6 CPV and D8 SMEFT operators
• Renormalisation of SMEFT bosonic interactions up to dimension eight by LNV operators
• SMEFT top-quark effects on $\Delta F=2$ observables
• Combining chromomagnetic and four-fermion operators with leading SMEFT operators for $gg\to hh$ at NLO QCD
• Constraints on 2l2q operators from $\mu -e$ flavour-changing meson decays
• Higgs Pair Production as a Signal of Enhanced Yukawa Couplings
• Gearing up for the next generation of LFV experiments, via on-shell methods
• Benchmarks for Higgs Effective Theory: Extended Higgs Sectors
• Off-shell renormalization in Higgs effective field theories
• Dimension-8 SMEFT Matching Conditions for the Low-Energy Effective Field Theory
• Primary Observables for Indirect Searches at Colliders
• Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector
• Opportunistic CP Violation
• Bulk RS models, Electroweak Precision tests and the 125 GeV Higgs
• Charged lepton flavour change and Non-Standard neutrino Interactions
• Electroweak constraints on flavorful effective theories
• Renormalization group-induced phenomena of top pairs from four-quark effective operators
• 23, 381, 6242, 103268, 1743183, ...: Hilbert series for CP-violating operators in SMEFT
• Off-shell renormalization in the presence of dimension 6 derivative operators. I. General theory
• New physics and signal-background interference in associated $pp\to HZ$ production
• The shift-invariant orders of an ALP
• Effective Field Theory in the top sector: do multijets help?
• Portal Effective Theories: A framework for the model independent description of light hidden sector interactions
• Diboson production in the SMEFT from gluon fusion
• Higgs Potential from Derivative Interactions
• Two-loop running effects in Higgs physics in Standard Model Effective Field Theory
• Higgs decays to two leptons and a photon beyond leading order in the SMEFT
• The Geometric $\nu$SMEFT: Operators and Connections
• Renormalization group improved implications of semileptonic operators in SMEFT
• CP-violating Higgs-gauge boson couplings in $H\nu \bar{\nu }$ production at three energy stages of CLIC
• Limits on the anomalous $Wtq$ couplings
• Comparing EFT and Exact One-Loop Analyses of Non-Degenerate Stops
• Leptoquarks and Real Singlets: A Richer Scalar Sector Behind the Origin of Dark Matter
• A new evaluation of the $HZZ$ coupling: direct bounds on anomalous contributions and $CP$ violating effects via a new asymmetry
• One-loop matching of $CP$-odd four-quark operators to the gradient-flow scheme
• Renormalization-group running of dimension-8 four-fermion operators in the SMEFT
• Bounds on CP-violating Higgs-gluon interactions: the case of vanishing light-quark Yukawa couplings
• Anomalous Dimensions via on-shell Methods: Operator Mixing and Leading Mass Effects
• To Profile or To Marginalize -- A SMEFT Case Study
• Renormalization-group equations of the LEFT at two loops: dimension-six baryon-number-violating operators
• On the exotic Higgs decays in effective field theory
• Electroweak Constraints from the COHERENT Experiment
• Flavour Violating Effects of Yukawa Running in SMEFT
• New Covariant Feynman Rules for Effective Field Theories
• The Muon Magnetic Moment and Physics Beyond the Standard Model
• Lepton-flavour violating decays in theories with dimension 6 operators
• Four-lepton Z-boson decay constraints on the SMEFT
• One-loop Matching of Scotogenic Model onto Standard Model Effective Field Theory up to Dimension 7
• Snowmass 2021 White Paper: Charged lepton flavor violation in the tau sector
• High-energy frontier of the muon g-2 at a muon collider
• Dimension-six operators in Higgs pair production via vector-boson fusion at the LHC
• Effective Field Theory of Chirally-Enhanced Muon Mass and Dipole Operators
• Clustering of $\bar{B}\to D^{(\ast )}{\tau }^{-}{\bar{\nu }}_{\tau }$ kinematic distributions with ClusterKinG
• Dipole-induced anomalous top quark couplings at the LHC
• Electroweak bounds on Higgs pseudo-observables and $h\to 4\ell$ decays
• Relevance of one-loop SMEFT matching in the 2HDM
• Renormalizable Extension of the Abelian Higgs-Kibble Model with a dimension 6 operator
• Flavor physics in SU(5) GUT with scalar fields in the 45 representation
• Renormalization-group equations of the LEFT at two loops: dimension-five effects
• Constraining new physics effective interactions via a global fit of electroweak, Drell-Yan, Higgs, top, and flavour observables
• Testing for observability of Higgs effective couplings in triphoton production at FCC-hh
• Interplay of the charged Higgs effects in $R_{D^{(\ast )}}$, $b\to s{\ell }^{+}{\ell }^{-}$ and $W$-mass
• Complete One-loop Renormalization-group Equations in the Seesaw Effective Field Theories
• g-2 In the custodially protected RS model
• Prospects for the determination of the top-quark Yukawa coupling at future $e^{+}{e}^{-}$ colliders
• Renormalisation group effects in SMEFT for di-Higgs production
• Dimension-eight Operator Basis for Universal Standard Model Effective Field Theory
• Another SMEFT Story: $Z^{\prime }$ Facing New Results on ${\epsilon }^{\prime }/\epsilon$, $\Delta M_K$ and $K\to \pi \nu \bar{\nu }$
• Kaon Physics Without New Physics in ${\epsilon }_K$
• Quantifying Limits on CP Violating Phases from EDMs in Supersymmetry
• Dijets at Tevatron Cannot Constrain SMEFT Four-Quark Operators
• Semileptonic $\tau$ decays: powerful probes of non-standard charged current weak interactions
• Unification of Coupling Constants, Dimension six Operators and the Spectral Action
• Lepton-flavour violation in a Pati-Salam model with gauged flavour symmetry
• Extended Higgs sectors, effective field theory and Higgs phenomenology
• Renormalization Group Evolution of Dimension-seven Baryon- and Lepton-number-violating Operators
• $\bar{B}\to X_s\gamma$ with a warped bulk Higgs
• A theory vade mecum for PSI experiments
• Collider-Flavour Complementarity from the bottom to the top
• Polarized-boson pairs at NLO in the SMEFT
• SMEFT analysis of charged lepton flavor violating $B$-meson decays
• Does unitarity imply finiteness of electroweak oblique corrections at one-loop? - constraining extra neutral Higgs bosons -
• Renormalization-group equations of the LEFT at two loops: dimension-six operators
• Baryon Number Violation: From Nuclear Matrix Elements to BSM Physics
• The RG-improved Twin Higgs effective potential at NNLL
• Jet Substructure Measurements of Interference in Non-Interfering SMEFT Effects
• Effective approach to top-quark decay and FCNC processes at NLO accuracy
• Froggatt-Nielsen Meets the SMEFT
• Revisiting electroweak radiative corrections to $b\to s\ell \ell$ in SMEFT
• Anomalous gauge couplings vis-$\grave{a}$-vis $(g-2{)}_{\mu }$ and flavor observables
• Custodial Symmetry (Violation) in SMEFT
• The Electric Dipole Moment of the electron in the decoupling limit of the aligned Two-Higgs Doublet Model
• Two-Higgs Doublet Model Effective Field Theory
• Higgs, top and electro-weak precision measurements at future $e^{+}{e}^{-}$ colliders; a combined effective field theory analysis with renormalization mixing
• Perturbative Power Counting, Lowest-Index Operators and Their Renormalization in Standard Model Effective Field Theory
• On the EFT validity for Drell-Yan tails at the LHC
• Effective field theory in light of relative entropy
• Matching in $pp\to t\bar{t}W/Z/h+$ jet SMEFT studies
• Using Machine Learning techniques in phenomenological studies in flavour physics
• EFT, decoupling, Higgs boson mixing, and higher dimensional operators
• Veltman Criteria in Beyond Standard Model Effective Field Theory of Complex Scalar Triplet
• Renormalising the Field-Space Geometry
• Going beyond Top EFT
• Constraining the SMEFT Extended with Sterile Neutrinos at FCC-ee
• Implications of the muon anomalous magnetic moment for the LHC and MUonE
• RG evolution and effect of intermediate new physics on $\Delta B=2$ six-quark operators
• New Physics Through Drell Yan SMEFT Measurements at NLO
• Nucleon Energy Correlators as a Probe of Light-Quark Dipole Operators at the Electron-Ion Collider
• Lepton Flavor Violation: From Muon Decays to Muon Colliders
• Residual Symmetries and Scalar Multiplet Vacuum Alignment in Non-Abelian Flavour Models
• The Dual QCD @ Work
• Dirac and Majorana Feynman Rules with four-fermions
• Constraints on standard model effective field theory for a Higgs boson produced in association with W or Z bosons in the H $\to \mathrm{b}\bar{\mathrm{b}}$ decay channel in proton-proton collisions at $\sqrt{s}$ = 13 TeV
• Doubling down on down-type diquarks
• Mu to e gamma in the 2 Higgs Doublet Model: an exercise in EFT
• Multi-Component Dark Matter from Minimal Flavor Violation
• Top quark effective couplings from top-pair tagged photoproduction in $p{e}^{-}$ collisions
• Generalized Matter Parities from Finite Modular Symmetries
• Top quark physics in the Large Hadron Collider era
• RGE solver for the complete dim-7 SMEFT interactions and its application to $0\nu \beta \beta$ decay
• The HiggsTools Handbook: Concepts and observables for deciphering the Nature of the Higgs Sector
• Spontaneous CP Violation and Horizontal Symmetry in the MSSM: Toward Lepton Flavor Naturalness
• Factorizing Hidden Particle Production Rates
• Towards global fits in EFT's and New Physics implications
• Z lepton flavour violation as a probe for new physics at future $e^{+}{e}^{-}$ colliders
• Equivariant neural networks for robust $\text{CP}$ observables
• Nuclear EDM from SMEFT flavor-changing operator
• Oblique corrections when $m_W\ne m_Z\cos {\theta }_W$ at tree level
• The Standard Model from the LHC to future colliders: a contribution to the Workshop "What Next" of INFN
• Using dipole processes to constrain the flavour of four-fermion effective interactions
• A forgotten fermion: the hypercharge -3/2 doublet, its phenomenology and connections to dark matter
• General form of effective operators from hidden sectors
• Potential Blind Directions at TeraZ
• A Global Analysis of the Standard Model Effective Field Theory in the Production and Decay Channels of a Single Top Quark
• A Note on the Analytic Structure of Celestial Amplitudes
• Effective description of Nelson-Barr models and the theta parameter
• Effective field theories and pseudo-observables in the quest for physics beyond the Standard Model
• Complete two-loop Yukawa-induced running of the Higgs-gluon coupling in SMEFT
• Fermions in $(1+2)$-dimensions modified by nonminimal coupling and its applications to condensed matter physics
• Expectations for the Higgs boson identification at the ILC
• Lepton Flavor Violation at FCC-ee and CEPC
• Charting the new physics through one-loop effects in the muon magnetic dipole moment
• Exploring CP Violation beyond the Standard Model and the PQ Quality with Electric Dipole Moments
• Extending low energy effective field theory with a complete set of dimension-7 operators
• The Forward Physics Facility at the High-Luminosity LHC
• Probing CP Violation through Vector Boson Fusion at High-Energy Muon Colliders
• Hot news on the phase structure of the SMEFT
• Higgs probes of top quark contact interactions and their interplay with the Higgs self-coupling
• Dark Matter Effective Field Theory and an Application to Vector Dark Matter
• Constraints on the parameters of the neutrino extension of the Standard Model
• Synergies of top and $B$ anomalies in SMEFT
• Two-to-two processes at an electron-muon collider
• Prospects for bounds on electroweak and Higgs observables via scaling effects
• Covariant derivative expansion for the renormalization of gravity
• Renormalizable Extension of the Abelian Higgs-Kibble Model with a Dim.6 Derivative Operator
• Constraining lepton flavor violating SMEFT $2q2\ell$ operators from low-energy cLFV processes
• Riding the Seesaw: What Higgsstrahlung May Reveal about Massive Neutrinos
• Effective-field theories for charged lepton flavour violation
• Two loops, four tops and two ${\gamma }_5$ schemes: a renormalization story
• New Physics Hints from Flavour
• One-loop matching of the LEFT to the QCD gradient flow
• The Higgs Boson and its Physics -- an Overview
• One-loop matching for quark dipole operators in a gradient-flow scheme
• Constraining the Higgs potential using multi-Higgs production
• Running of neutrino mass parameters in the Zee model
• On magnitudes of some CKM matrix elements
• Searches for new interactions within the SMEFT framework at present and future colliders