Multi-Higgs Amplitudes Bootstrapped: Dissecting SMEFT and HEFT

Abstract

The precise measurement of the Higgs boson properties requires a robust framework to parametrize possible deviations from Standard Model (SM) predictions in the most model-independent way possible. The Effective Field Theory (EFT) framework has become the most widely used since it offers a broad scope and a consistent path to increase the precision of the computations. Two prominent EFTs are the Standard Model Effective Field Theory (SMEFT) and the Higgs Effective Field Theory (HEFT). While similar in many aspects, their phenomenological differences are nowhere more pronounced than in multi-Higgs production. To precisely chart the separation between both EFTs, we study gluon-fusion double and triple Higgs production using bootstrapped on-shell amplitudes. This allows us to get the kinematic dependence of the gauge-invariant amplitude without field-redefinition ambiguities. As part of our study, we develop a technique that allows to build tree-level five-point on-shell amplitudes from lower-point on-shell amplitudes and bootstrapped contact terms. We then match the bootstrapped on-shell scattering amplitudes to the amplitudes computed in SMEFT (up to order $1/{\Lambda }^4$) and HEFT (at NNLO) and analyze the EFT order at which each kinematic structure appears. We also show how certain structures in $gg\to hhh$ appear only at dimension-12 in SMEFT or N${}^3$LO in HEFT.

25+23 pages, 5 appendices. v2: Expanded discussions, minor typos corrected, added references. Matches version published in JHEP

References in corpus (49)

• FeynRules 2.0 - A complete toolbox for tree-level phenomenology
• Dimension-Six Terms in the Standard Model Lagrangian
• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• FeynCalc 9.3: New features and improvements
• The Standard Model as an Effective Field Theory
• On Tree Amplitudes in Gauge Theory and Gravity
• The Effective Chiral Lagrangian for a Light Dynamical "Higgs Particle"
• Dimension-8 Operators in the Standard Model Effective Field Theory
• Effective Field Theories from Soft Limits
• A direct proof of the CSW rules
• A Higgs-Higgs bound state due to New Physics at a TeV
• On-Shell Recursion Relations for Effective Field Theories
• Disentangling a dynamical Higgs
• A Geometric Formulation of Higgs Effective Field Theory: Measuring the Curvature of Scalar Field Space
• Geometry of the Scalar Sector
• On the Power Counting in Effective Field Theories
• Effective Theory of a Dynamically Broken Electroweak Standard Model at NLO
• The Standard Model effective field theory at work
• Analysis of General Power Counting Rules in Effective Field Theory
• Is SMEFT Enough?
• The complete HEFT Lagrangian after the LHC Run I
• Which EFT
• On-shell constructibility of tree amplitudes in general field theories
• Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons
• The electroweak effective field theory from on-shell amplitudes
• On the two-loop virtual QCD corrections to Higgs boson pair production in the Standard Model
• Simple Recursion Relations for General Field Theories
• Renormalization group coefficients and the S-matrix
• Enumerating higher-dimensional operators with on-shell amplitudes
• The Rise of SMEFT On-shell Amplitudes
• Constructing massive on-shell contact terms
• Recursion Relations for Tree-level Amplitudes in the SU(N) Non-linear Sigma Model
• Standard Model Effective Field Theory up to Mass Dimension 12
• Complete NLO Operators in the Higgs Effective Field Theory
• The flair of Higgsflare: Distinguishing electroweak EFTs with $W_L{W}_L\to n\times h$
• An EFT hunter's guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes
• On-shell Higgsing for EFTs
• SMEFT is falsifiable through multi-Higgs measurements (even in the absence of new light particles)
• Complete NNLO Operator Bases in Higgs Effective Field Theory
• SmeftFR v3 -- Feynman rules generator for the Standard Model Effective Field Theory
• EFT matching from analyticity and unitarity
• Jet Bundle Geometry of Scalar Field Theories
• Primary Observables for Indirect Searches at Colliders
• Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector
• The New Formulation of Higgs Effective Field Theory
• Anomalous Dimensions via on-shell Methods: Operator Mixing and Leading Mass Effects
• Renormalization of effective field theories via on-shell methods: the case of axion-like particles
• Dimension-8 SMEFT contact-terms for vector-pair production via on-shell Higgsing

Cited by in corpus (3)

• The Art of Counting: a reappraisal of the HEFT expansion
• Assessing (H)EFT theory errors by pitting EoM against Field Redefinitions
• Higgs pair production in gluon fusion to higher orders in Higgs Effective Field Theory