<p>While gluon fusion dominates Higgs pair production at the LHC, vector boson fusion (VBF) offers a unique window into beyond the Standard Model (BSM) physics through its distinctive kinematic features and direct sensitivity to Higgs-vector boson interactions. We perform a comprehensive analysis of double Higgs production via VBF in the Standard Model effective field theory (SMEFT), systematically investigating how dimension-6 and dimension-8 bosonic operators—particularly those involving field derivatives—can enhance the production rate. We identify the most relevant Wilson coefficients (WCs) affecting the trilinear Higgs coupling (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mi>h</mi><mi>h</mi></math>) and Higgs-vector boson interactions (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mi>V</mi><mi>V</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>h</mi><mi>h</mi><mi>V</mi><mi>V</mi></math>). Using constraints from global fits and interpolating fit results for unconstrained WCs with naive dimensional analysis, we assess their effects on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mi>V</mi><mo stretchy="false">→</mo><mi>h</mi><mi>h</mi></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mi>V</mi><mo>=</mo><mi>W</mi></mrow><mo>,</mo><mrow><mi>Z</mi></mrow></mrow></math>) scattering amplitudes and cross sections. Our analysis includes a study of EFT convergence and validity in models with scalar extensions of the SM. Numerical simulations for the planned High-Luminosity LHC experiment (HL-LHC) in general reveal only a modest and challenging to detect enhancement of the VBF di-Higgs production rate over the SM prediction. However, we show that in optimistic scenarios, such a process could be observed at the HL-LHC. In certain cases, when the enhancement is dominated by the dimension-6 or dimension-8 operators containing field derivatives (and thus leading to stronger energy-dependent effects), this channel becomes competitive with di-Higgs production via gluon fusion. This work highlights the role of VBF di-Higgs production as a complementary channel for probing anomalous Higgs couplings and their impact on BSM physics.</p>

Greece

Athanasios Dedes

Poland

Janusz Rosiek

Italy

Michał Ryczkowski

Double Higgs boson production via vector boson fusion in SMEFT

<p>We demonstrate the cancellation of chiral anomalies in the Standard Model (SM) effective field theory (EFT), achieved through a consistent choice of loop momentum routing in triangle diagrams with dimension-6 operator insertions. By enforcing gauge invariance and Bose symmetry, we show that Goldstone-boson contributions cancel anomalies arising from massive gauge-boson vertices, thereby preserving the consistency of the SM EFT. We compute neutral triple gauge-boson vertices at one loop, revealing dominant contributions from dimension-6 operators at all energies below the EFT cutoff. A UV-complete anomaly-free model with a heavy vectorlike electron validates our approach, illustrating how heavy fermion decoupling generates SM EFT operators while maintaining anomaly cancellation. Our results highlight the phenomenological relevance of these vertices for probing new physics at colliders, particularly through dimension-6 effects that scale as the inverse of the center of mass energy squared, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><mi>s</mi></math>, offering a viable pathway for experimental detection.</p>

Dimitrios Beis

Chiral anomaly cancellation and neutral triple gauge boson vertices in the SM EFT

In recent years, theoretical and phenomenological studies with effective field theories have become a trending and prolific line of research in the field of high-energy physics. In order to discuss present and future prospects concerning automated tools in this field, the SMEFT-Tools 2022 workshop was held at the University of Zurich from 14th–16th September 2022. The current document collects and summarizes the content of this workshop.

Switzerland

Jason Aebischer

CERN

Matteo Fael

Spain

Javier Fuentes-Martìn

Anders Thomsen

Javier Virto

Lukas Allwicher

Supratim Bakshi

Croatia

Hermès Bélusca-Maïto

Jorge Blas

Mikael Chala

Juan Criado

Renato Fonseca

United States

Angelica Goncalves

Amon Ilakovac

Germany

Matthias König

India

Sunando Patra

Paul Kühler

Marija Mador-Božinović

Mikołaj Misiak

Víctor Miralles

Ignacy Nałȩcz

United Kingdom

Méril Reboud

Laura Reina

Michal Ryczkowski

José Santiago

Luca Silvestrini

Peter Stangl

Dominik Stöckinger

Peter Stoffer

Avelino Vicente

Matthias Weißwange

Computing tools for effective field theories

In this study we present a universal effective action for one-loop matching of all scalar leptoquarks. We use both the Universal One-Loop Effective Action (UOLEA) and covariant diagrams to evaluate the Wilson coefficients directly in the Green basis for up to dimension-6 operators. On the technical side, we use the newly developed method of evaluating supertraces, to further validate the results stemming from the use of covariant diagrams. As an application, we perform a fully functional matching onto Standard Model Effective Field Theory (SMEFT) of a model with two scalar leptoquark fields: a weak isospin singlet and a doublet. We demonstrate its use by calculating several observables, such as lepton magnetic and electric dipole moments, neutrino masses, proton decay rate, while we comment upon fine tuning issues in this model. Apart from its phenomenological interest, this model generates the majority of dimension-6 operators and provides an EFT benchmark towards future matching automation.

Kostas Mantzaropoulos

Universal scalar leptoquark action for matching

We calculate the S-matrix element for the Higgs boson decay to a Z-boson and a photon, h → Zγ, at one-loop in the Standard-Model Effective Field Theory (SMEFT) framework and in linear R  ξ  -gauges. Our SMEFT expansion includes all relevant operators up to dimension-6 considered in Warsaw basis without resorting to any flavour or CP- conservation assumptions. Within this approximation there are 23 dimension-6 operators affecting the amplitude, not including flavour and hermitian conjugation. The result for the on-shell h → Zγ amplitude is gauge invariant, renormalisation-scale invariant and gauge-fixing parameter independent. The calculated ratio of the SMEFT versus the SM expectation for the h → Zγ decay width is then written in a semi-numerical form which is useful for further comparisons with related processes. For example, the h → Zγ amplitude contains 16 operators in common with the h → γγ amplitude and one can draw useful results about its feasibility at current and future LHC data.

Kristaq Suxho

Lampros Trifyllis

The decay h → Zγ in the Standard-Model Effective Field Theory