Higgs Effective Theory Research Articles

Production of two, three, and four Higgs bosons: where SMEFT and HEFT depart

In this article we study the phenomenological implications of multiple Higgs boson production from longitudinal vector boson scattering in the context of effective field theories. We find compact representations for effective tree-level amplitudes with up to four final state Higgs bosons. Total cross sections are then computed for scenarios relevant at the LHC in which we find the general Higgs Effective Theory (HEFT) prediction avoids the heavy suppression observed in Standard Model Effective Field Theory (SMEFT).

Software tools for computing EW chiral amplitudes

We present an implementation of the Electroweak Chiral Lagrangian (also denoted as Higgs Effective Theory) in several high energy physics Mathematica packages. In particular, we implement the bosonic part of the electoweak Lagrangian up to next-to-leading order for FeynRules, FeynArts and FeynCalc. These tools are publicly available and can be used to readily calculate the Feynman rules and amplitudes in the theory.

Deciphering the maximal transcendentality principle via bootstrap

We prove the principle of maximal transcendentality for a class of form factors, including the general two-loop minimal form factors, the two-loop three-point form factor of tr(F2), and the two-loop four-point form factor of tr(F3). Our proof is based on a recently developed bootstrap method using the representation of master integral expansions, together with some unitarity cuts that are universal in general gauge theories. The maximally transcendental parts of the two-loop four-gluon form factor of tr(F3) are obtained for the first time in both planar mathcal{N} = 4 SYM and pure YM theories. This form factor can be understood as the Higgs-plus-four-gluon amplitudes involving a dimension-seven operator in the Higgs effective theory. In this case, we find that the maximally transcendental part of the mathcal{N} = 4 SYM result is different from that of pure YM, and the discrepancy is due to the gluino-loop contributions in mathcal{N} = 4 SYM. In contrast, the scalar-loop contributions have no maximally transcendental parts. Thus, the maximal transcendentality principle still holds for the form factor results in mathcal{N} = 4 SYM and QCD, after a proper identification of the fundamental quarks and adjoint gluinos as nf→ 4Nc. This seems to be the first example of the maximally transcendental principle that involves fermion-loop contributions. As another intriguing observation, we find that the four-point form factor of the half-BPS tr(ϕ3) operator is precisely a building block in the form factor of tr(F3).

Electroweak phase transition in the nearly aligned Higgs effective field theory

We investigate the strongly first-order electroweak phase transition using an effective field theoretical approach. The standard effective field theory with finite number truncation of higher dimensional operators fails in the typical parameter space where the strongly first-order phase transition is realized because it cannot describe the non-decoupling quantum effect of new physics beyond the standard model. To parameterize the non-decoupling quantum effect, we employ the nearly aligned Higgs effective theory in which the Higgs potential is parameterized by a Coleman-Weinberg like form. Extending this framework with finite temperature corrections, we study the parameter space for realizing the strongly first-order phase transition, and estimate the gravitational wave produced at the phase transition.

Introducing tools to test Higgs boson interactions via WW scattering: One-loop calculations and renormalization in the Higgs effective field theory

Effective field theories are useful tools to search for physics beyond the Standard Model (SM). However, effective theories can lead to non-unitary behavior with fastly growing amplitudes. This unphysical behavior may lead to large sensitivity to SM deviations, making necessary a unitarization of the amplitudes prior to a comparison with experiment. In the present work, we focus on all the processes entering the two-Higgs production by longitudinal $WW$ scattering: we perform a full one-loop calculation of all relevant processes, we determine the necessary counterterms in the on-shell scheme, and we study how the full inclusion of the gauge degrees of freedom modifies the previously computed masses and widths of the dynamical resonances arising from the unitarization process in the vector-isovector channel. Altogether, we are able to provide the technical tools that are needed to study the low-energy couplings in the Higgs effective theory under the requirements of unitarity and causality.

Two-loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes

We consider two-loop renormalization of high-dimensional Lorentz scalar operators in the gluonic sector of QCD. These operators appear also in the Higgs effective theory obtained by integrating out the top quark loop in the gluon fusion process. We first discuss the classification of operators and how to construct a good set of basis using both off-shell field theory method and on-shell form factor formalism. To study loop corrections, we apply efficient unitarity-IBP strategy and compute the two-loop minimal form factors of length-3 operators up to dimension sixteen. From the UV divergences of form factor results, we extract the renormalization matrices and analyze the operator mixing behavior in detail. The form factors we compute are also equivalent to Higgs plus three-gluon amplitudes that capture high-order top mass corrections in Higgs EFT. We obtain the analytic finite remainder functions which exhibit several universal transcendentality structures.

Hidden analytic relations for two-loop Higgs amplitudes in QCD

We compute the Higgs plus two-quark and one-gluon amplitudes () and Higgs plus three-gluon amplitudes () in the Higgs effective theory with a general class of operators. By changing the quadratic Casimir C F to C A , the maximally transcendental parts of the amplitudes turn out to be equivalent to that of the amplitudes, which also coincide with the counterparts in SYM. This generalizes the so-called maximal transcendentality principle to the Higgs amplitudes with external quark states, thus the full QCD theory. We further verify that the correspondence applies also to two-loop form factors of more general operators, in both QCD and scalar-YM theory. Another interesting relation is also observed between the planar amplitudes and the minimal density form factors in SYM.

Resonant production of Wh and Zh at the LHC

We examine the production of Wh and Zh pairs at the LHC in the context of a Strongly Interacting Symmetry Breaking Sector of the Standard Model. Our description is based on a non-linear Higgs Effective Theory, including only the Standard Model particles. We focus on its scalar sector (Higgs boson h and electroweak Goldstones associated to WL± and ZL), which is expected to give the strongest beyond Standard Model rescattering effects. The range of the effective theory is extended with dispersion-relation based unitarization, and compared to the alternative extension with explicit axial-vector resonances. We estimate the Wh and Zh production cross-section, where an intermediate axial-vector resonance is generated for certain values of the chiral couplings. We exemplify our analysis with a benchmark axial-vector with MA = 3 TeV. Interestingly enough, these different approaches provide essentially the same prediction. Finally we discuss the sensitivity of ATLAS and CMS to such resonances.

When matching matters: Loop effects in Higgs effective theory

Effective Lagrangians are a useful tool for a data-driven approach to physics beyond the Standard Model at the LHC. However, for the new physics scales accessible at the LHC, the effective operator expansion is only relatively slowly converging at best. For tree-level processes, it has been found that the agreement between the effective Lagrangian and a range of UV-complete models depends sensitively on the appropriate definition of the matching. We extend this analysis to the one-loop level, which is relevant for electroweak precision data and Higgs decay to photons. We show that near the scale of electroweak symmetry breaking the validity of the effective theory description can be systematically improved through an appropriate matching procedure. In particular, we find a significant increase in accuracy when including suitable terms suppressed by the Higgs vacuum expectation value in the matching.

Extending the limits of Higgs effective theory

Based on a vector triplet model we study a possible failure of dimension-6 operators in describing LHC Higgs kinematics. First, we illustrate that including dimension-6 contributions squared can significantly improve the agreement between the full model and the dimension-6 approximation, both in associated Higgs production and in weak-boson-fusion Higgs production. Second, we test how a simplified model with an additional heavy scalar could improve the agreement in critical LHC observables. In weak boson fusion we find an improvement for virtuality-related observables at large energies, but at the cost of sizeable deviations in interference patterns and angular correlations.

Pushing Higgs effective theory to its limits

At the LHC, an effective theory of the Higgs sector allows us to analyze kinematic distributions in addition to inclusive rates, although there is no clear hierarchy of scales. We systematically analyze how well dimension-6 operators describe LHC observables in comparison to the full theory, and in a range where the LHC will be sensitive. The key question is how the breakdown of the dimension-6 description affects Higgs measurements during the upcoming LHC run for weakly interacting models. We cover modified Higgs sectors with a singlet and doublet extension, new top partners, and a vector triplet. First, weakly interacting models only generate small relevant subsets of dimension-6 operators. Second, the dimension-6 description tends to be justified at the LHC. Scanning over model parameters, significant discrepancies can nevertheless arise; their main source is the matching procedure in the absence of a well-defined hierarchy of scales. This purely theoretical problem should not affect future LHC analyses.

Higgs pair production: Improved description by matrix element matching

Higgs pair production is crucial for measuring the Higgs boson self-coupling. The dominant channel at hadron colliders is gluon fusion via heavy-quark loops. We present the results of a fully exclusive simulation of gluon fusion Higgs pair production based on the matrix elements for $hh+0$, 1 partons including full heavy-quark loop dependence, matched to a parton shower. We examine and validate this new description by comparing it with (a) Higgs effective theory predictions, (b) exact $hh+0$-parton sample showered by Pythia, and (c) exact $hh+1$-parton distributions, by looking at the most relevant kinematic distributions, such as ${p}_{T}^{h}$, ${p}_{T}^{hh}$, ${M}_{hh}$ spectra, and the jet rate as well. We find that matched samples provide a state-of-the-art accurate exclusive description of the final state.