<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

We provide a set of theoretical constraints on models in which the Standard Model field content is extended by vectorlike fermions and in some cases also by a real scalar singlet. Our approach is based on the study of electroweak vacuum stability, perturbativity of model couplings, and gauge couplings unification with the use of renormalization group equations. We show that careful analysis of these issues leads to strong constraints on the parameter space of the considered models. This, in turn, has important implications for phenomenology, as we show using examples of the double Higgs boson production, electroweak precision observables, and the electroweak phase transition.

France

Amit Adhikary

Marek Olechowski

Theoretical constraints on models with vectorlike fermions

We propose a method of measuring the CP-odd part of the Yukawa interaction of Higgs boson and  $$\tau $$  <math> <mi>τ</mi> </math>   leptons by observing the forward–backward asymmetry in the decay  $$H \rightarrow \tau ^+ \, \tau ^- \, \gamma $$  <math> <mrow> <mi>H</mi> <mo>→</mo> <msup> <mi>τ</mi> <mo>+</mo> </msup> <mspace width="0.166667em"></mspace> <msup> <mi>τ</mi> <mo>-</mo> </msup> <mspace width="0.166667em"></mspace> <mi>γ</mi> </mrow> </math>  . The source of such asymmetry is the interference of the CP-even loop-level contribution coming from  $$H \rightarrow Z \, \gamma \rightarrow \tau ^+ \, \tau ^- \, \gamma $$  <math> <mrow> <mi>H</mi> <mo>→</mo> <mi>Z</mi> <mspace width="0.166667em"></mspace> <mi>γ</mi> <mo>→</mo> <msup> <mi>τ</mi> <mo>+</mo> </msup> <mspace width="0.166667em"></mspace> <msup> <mi>τ</mi> <mo>-</mo> </msup> <mspace width="0.166667em"></mspace> <mi>γ</mi> </mrow> </math>   decay channel with the contribution from tree-level CP-odd Yukawa interaction. We find that the CP violating effect is maximum when the invariant mass of the  $$\tau ^+\,\tau ^-$$  <math> <mrow> <msup> <mi>τ</mi> <mo>+</mo> </msup> <mspace width="0.166667em"></mspace> <msup> <mi>τ</mi> <mo>-</mo> </msup> </mrow> </math>   pair is equal to the mass of the Z boson. We propose and utilise various Dalitz plot asymmetries to quantify the maximal size of the asymmetry and perform Monte Carlo simulations to study the feasibility of measuring it in the high luminosity phase of the Large Hadron Collider (HL-LHC).

Norway

Erlend Aakvaag

Nikolai Fomin

Anna Lipniacka

Stefan Pokorski

Dibyakrupa Sahoo

Exploring CP violation in  $$\varvec{H \rightarrow \tau ^+\,\tau ^-\,\gamma }$$  <math> <mrow> <mi>H</mi> <mo>→</mo> <msup> <mi>τ</mi> <mo>+</mo> </msup> <mspace width="0.166667em"></mspace> <msup> <mi>τ</mi> <mo>-</mo> </msup> <mspace width="0.166667em"></mspace> <mi>γ</mi> </mrow> </math>

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

Using the well established principles of Lorentz invariance, CP and CPT symmetry, and quantum statistics we do a model-independent study of effects of possible non-standard couplings of (Dirac and Majorana) neutrinos. The study is sensitive to the different quantum statistical properties of the Dirac and Majorana neutrinos which, contrary to neutrino-mediated processes of lepton number violation, could lead to observable effects not suppressed by the small ratios of neutrino and heavier particle masses. For processes with a neutrino-antineutrino pair of the same flavor in the final state, we formulate the “Dirac Majorana confusion theorem (DMCT)” showing why it is normally very difficult to observe the different behaviour of both kinds of neutrinos in experiments if they have only the standard model (SM)-like left-handed vector couplings to gauge bosons. We discuss deviations from the confusion theorem in the presence of non-standard neutrino interactions, allowing to discover or constrain such novel couplings. We illustrate the general results with two chosen examples of neutral current processes,  $$Z \rightarrow \nu \, {\overline{\nu }}$$  <math> <mrow> <mi>Z</mi> <mo>→</mo> <mi>ν</mi> <mspace width="0.166667em"></mspace> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </mrow> </math>   and  $${\mathcal {P}}_i \rightarrow {\mathcal {P}}_f \, \nu \, {\overline{\nu }}$$  <math> <mrow> <msub> <mi>P</mi> <mi>i</mi> </msub> <mo>→</mo> <msub> <mi>P</mi> <mi>f</mi> </msub> <mspace width="0.166667em"></mspace> <mi>ν</mi> <mspace width="0.166667em"></mspace> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </mrow> </math>   (with  $${\mathcal {P}}_{i,f}$$  <math> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>f</mi> </mrow> </msub> </math>   denoting pseudoscalar mesons, such as  $$B,K,\pi $$  <math> <mrow> <mi>B</mi> <mo>,</mo> <mi>K</mi> <mo>,</mo> <mi>π</mi> </mrow> </math>  ). Our analysis shows that using 3-body decays the presence of non-standard interactions can not only be constrained but one can also distinguish between Dirac and Majorana neutrino possibilities.

South Korea

C. Kim

Probing the non-standard neutrino interactions using quantum statistics

Flavour oscillations of sub-GeV atmospheric neutrinos and antineutrinos, traversing different distances inside the Earth, are a promising source of information on the leptonic CP phase δ. In that energy range, the oscillations are very fast, far beyond the resolution of modern neutrino detectors. However, the necessary averaging over the experimentally typical energy and azimuthal angle bins does not wash out the CP violation effects. In this paper we derive very accurate analytic compact expressions for the averaged oscillations probabilities. Assuming spherically symmetric Earth, the averaged oscillation probabilities are described in terms of two analytically calculable effective parameters. Based on those expressions, we estimate maximal magnitude of CP-violation effects in such measurements and propose optimal observables best suited to determine the value of the CP phase in the PMNS mixing matrix.

Armenia

Ara Ioannisian

Analytical description of CP violation in oscillations of atmospheric neutrinos traversing the Earth

The forthcoming precision data on lepton flavour violating (LFV) decays require precise and efficient calculations in New Physics models. In this article lepton flavour violating processes within the Minimal Supersymmetric Standard Model (MSSM) are calculated using the method based on the Flavour Expansion Theorem, a recently developed technique performing a purely algebraic mass-insertion expansion of the amplitudes. The expansion in both flavour-violating and flavour-conserving off-diagonal terms of sfermion and supersymmetric fermion mass matrices is considered. In this way the relevant processes are expressed directly in terms of the parameters of the MSSM Lagrangian. We also study the decoupling properties of the amplitudes. The results are compared to the corresponding calculations in the mass eigenbasis (i.e. using the exact diagonalization of the mass matrices). Using these methods, we consider the following processes: ℓ → ℓ  ′  γ, ℓ→3ℓ  ′  , ℓ→2ℓ  ′  ℓ  ′′ , h→ℓℓ  ′  as well as μ→e conversion in nuclei. In the numerical analysis we update the bounds on the flavour changing parameters of the MSSM and examine the sensitivity to the forthcoming experimental results. We find that flavour violating muon decays provide the most stringent bounds on supersymmetric effects and will continue to do so in the future. Radiative ℓ → ℓ  ′  γ decays and leptonic three-body decays ℓ → 3ℓ  ′  show an interesting complementarity in eliminating “blind spots” in the parameter space. In our analysis we also include the effects of non-holomorphic A-terms which are important for the study of LFV Higgs decays.

Andreas Crivellin

Zofia Fabisiewicz

Weronika Materkowska

Ulrich Nierste

Lepton flavour violation in the MSSM: exact diagonalization vs mass expansion

It is possible that measurements of vector boson scattering (VBS) processes at the LHC will reveal disagreement with Standard Model predictions, but no new particles will be observed directly. The task is then to learn as much as possible about the new physics from a VBS analysis carried within the framework of the Effective Field Theory (EFT). In this paper we discuss issues related to the correct usage of the EFT when the WW invariant mass is not directly accessible experimentally, as in purely leptonic W decay channels. Strategies for future data analyses in case such scenario indeed occurs are proposed.

Jan Kalinowski

Paweł Kozów

Michał Szleper

Sławomir Tkaczyk

Same-sign WW scattering at the LHC: can we discover BSM effects before discovering new states?