Phenomenology of the Higgs Effective Lagrangian via FeynRules

TL;DR

The authors develop a Higgs-focused dimension-six EFT and implement it in FeynRules with Universal Feynman Output, enabling MG5 simulations of complete Higgs interactions across production and decay channels. They derive both gauge-basis and mass-basis formulations, including kinetic-term normalization and explicit mappings between operator coefficients. Through a suite of phenomenological studies—ranging from hVV couplings and custodial-symmetry tests to VH and di-Higgs production and fermionic contact interactions—they demonstrate how differential distributions and high-energy observables can reveal non-SM Higgs physics. The work provides a practical framework for global EFT fits and data-driven recasts, leveraging the UFO/MG5 pipeline for versatile collider analyses at the LHC and future machines.

Abstract

The Higgs discovery and the lack of any other hint for new physics favor a description of non-standard Higgs physics in terms of an effective field theory. We present an implementation of a general Higgs effective Lagrangian containing operators up to dimension six in the framework of FeynRules and provide details on the translation between the mass and interaction bases, in particular for three- and four-point interaction vertices involving Higgs and gauge bosons. We illustrate the strengths of this implementation by using the UFO interface of FeynRules capable to generate model files that can be understood by the MadGraph 5 event generator and that have the specificity to contain all interaction vertices, without any restriction on the number of external legs or on the complexity of the Lorentz structures. We then investigate several new physics effects in total rates and differential distributions for different Higgs production modes, including gluon fusion, associated production with a gauge boson and di-Higgs production. We finally study contact interactions of gauge and Higgs bosons to fermions.

Figures (6)

• Figure 1: Distribution of the angular separation of the decay planes associated with each of the (possibly virtual) $Z$-bosons resulting from the decay of a Higgs boson produced in the gluon fusion mode. We show the Standard model distribution (green-solid histogram) to which we superimpose predictions associated with a non-zero $\bar{c}_{ W}$= 0.3 (black-dotted line) and -1.5 (blue-solid line) Wilson coefficient.
• Figure 2: Distribution of the angular distance $\Delta R(\ell_1,\ell_2)$ between the two charged leptons originating from a pair of $W$-bosons issued from the decay of a Higgs boson produced via gluon fusion. The left panel of the figure illustrates that for $\bar{c}_W = 0.05$ (red-dashed line) and $\bar{c}_{HW} = 0.05$ (blue-solid line), no sizable effect beyond the SM predictions (green-solid histogram) can be expected. In contrast, the right panel of the figure shows that for larger values of the Wilson coefficients set to $-1$, sensitive effects can be observed.
• Figure 3: Correlations of several Higgs boson partial widths when different Wilson coefficients are chosen non-vanishing. In the upper-left (upper-right) panel of the figure, we investigate simultaneous new physics effects on the $h\to \gamma \, \gamma$ and $h\to Z\, \gamma$ ($h\to Z\, Z$) partial widths, in its central-left (central-right) panel on the $h\to Z\, \gamma$ and $h\to W \, W$ ($h\to Z \, Z$) partial widths and in its lower panel on the $h\to Z \, Z$ and $h\to W\, W$ partial widths. We indicate the Standard Model expectation by an orange dot.
• Figure 4: Double ratio ${\cal R}$ of total cross sections at $\sqrt{S} = 8$ TeV and 14 TeV, as defined in Eq. \ref{['eq:doubleR']}, given as a function of the value of the $\bar{c}_{ HW}$ parameter for the process $p p \to W^\pm h\to \ell\nu b \bar{b}$ at the LHC. No selection on the final state lepton and missing energy has been accounted for.
• Figure 5: Invariant-mass $m_{Vh}$ distribution of a two-body system comprised of a Higgs boson and a gauge boson for LHC collisions at a center-of-mass energy of 14 TeV. We show results for the Standard Model (red-solid histogram) to which we superimpose predictions computed when $\bar{c}_{HW}=0.1$ (blue-dotted line) and $\bar{c}_{W}=0.1$ (black-solid line) couplings are allowed.