Primary Observables for Indirect Searches at Colliders

Abstract

We consider the complete set of observables for collider searches for indirect effects of new heavy physics. They consist of $SU(3{)}_{\mathrm{C}}\times U(1{)}_{\mathrm{EM}}$ invariant interaction terms/operators that parameterize deviations from the Standard Model. We show that, under very general assumptions, the leading deviations from the Standard Model are given by a finite number of `primary' operators, with the remaining operators given by `Mandelstam descendants' whose effects are suppressed by powers of Mandelstam variables divided by the mass scale $M$ of the heavy physics. We explicitly determine all 3 and 4-point primary operators relevant for Higgs signals at colliders by using the correspondence between on-shell amplitudes and independent operators. We give a detailed discussion of the methods used to obtain this result, including a new analytical method for determining the independent operators. The results are checked using the Hilbert series that counts independent operators. We also give a rough sketch of the phenomenology, including unitarity bounds on the interaction strengths and rough estimates of their importance for Higgs decays at the HL-LHC. These results motivate further exploration of Higgs decays to $Z\bar{f}f$, $W\bar{f}{f}^{\prime }$, $\gamma \bar{f}f$, and $Z\gamma \gamma$.

arXiv comment46 pages, 2 figures, 13 tables. Final published version in JHEP

References in corpus (40)

• Dimension-Six Terms in the Standard Model Lagrangian
• The Strongly-Interacting Light Higgs
• Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology
• The Standard Model as an Effective Field Theory
• Effective Lagrangian for a light Higgs-like scalar
• Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO
• The Effective Chiral Lagrangian for a Light Dynamical "Higgs Particle"
• Reduced Effective Lagrangians
• The Chiral Approach to the Electroweak Interactions
• Higgs windows to new physics through d = 6 operators: Constraints and one-loop anomalous dimensions
• Operator bases, $S$-matrices, and their partition functions
• Low-derivative operators of the Standard Model effective field theory via Hilbert series methods
• Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox
• Hilbert series and operator bases with derivatives in effective field theories
• Is SMEFT Enough?
• The complete HEFT Lagrangian after the LHC Run I
• Which EFT
• A simple approach to counterterms in N=8 supergravity
• Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons
• Patterns of Strong Coupling for LHC Searches
• The electroweak effective field theory from on-shell amplitudes
• The Geometric Standard Model Effective Field Theory
• Standard Model Effective Field Theory from On-shell Amplitudes
• Pseudo-observables in Higgs decays
• The Higgs Trilinear Coupling and the Scale of New Physics
• Enumerating higher-dimensional operators with on-shell amplitudes
• Constructing massive on-shell contact terms
• 2, 12, 117, 1959, 45171, 1170086, ...: A Hilbert series for the QCD chiral Lagrangian
• Determining the Shape of Higgs Potential at Future Colliders
• Constraints on Fermion Magnetic and Electric Moments from LEP-I
• Hilbert Series, the Higgs Mechanism, and HEFT
• Induced Electroweak Symmetry Breaking and Supersymmetric Naturalness
• Non-Decoupling New Particles
• Complete NLO Operators in the Higgs Effective Field Theory
• Amplitude bases in generic EFTs
• Higgs Coupling Measurements and the Scale of New Physics
• Higgs decay into four charged leptons in the presence of dimension-six operators
• The Scale of New Physics from the Higgs Couplings to $\gamma \gamma$ and $\gamma Z$
• Custodial Symmetry (Violation) in SMEFT
• The Scale of New Physics from the Higgs Couplings to gg

Cited by in corpus (7)

• EFT matching from analyticity and unitarity
• Dimension-8 SMEFT contact-terms for vector-pair production via on-shell Higgsing
• Primary Observables for Electroweak Gauge Boson Collider Signals
• Multi-Higgs Amplitudes Bootstrapped: Dissecting SMEFT and HEFT
• General Signals for Charged Lepton Flavor Violating Decays
• Quantifying EFT Uncertainties in LHC Searches
• Scalar leptoquark contributions to the $gg\to Zh$ process