In a supersymmetric theory, large mass hierarchies can lead to large uncertainties in fixed-order calculations of the Standard Model (SM)-like Higgs mass. A reliable prediction is then obtained by performing the calculation in an effective field theory (EFT) framework, involving a matching to the full supersymmetric theory at the high scale to include contributions from the heavy particles, and a subsequent renormalisation-group running down to the low scale. We report on the prediction of the SM-like Higgs mass within the CP-violating next-to-minimal supersymmetric extension of the SM (NMSSM) in a scenario where all non-SM particles feature TeV-scale masses. The matching conditions are calculated at full one-loop order using two approaches. These are the matching of the quartic Higgs couplings as well as of the SM-like Higgs pole masses of the low- and high-scale theory. A comparison between the two methods allows us to estimate the size of terms suppressed by the heavy mass scale that are neglected in a pure EFT calculation as given by the quartic-coupling matching. Furthermore, we study the different sources of uncertainty which enter our calculation as well as the effect of CP-violating phases on the Higgs mass prediction. The matching calculation is implemented in a new version of the public program package $$\texttt {NMSSMCALC}$$ .

Germany

Christoph Borschensky

Vietnam

Thi Dao

Martin Gabelmann

Margarete Mühlleitner

Heidi Rzehak

Higgs mass predictions in the CP-violating high-scale NMSSM

The search for Dark Matter (DM) at colliders is primarily pursued via the detection of missing energy in particular final states. These searches are based on the production and decay processes where final states include DM particles and at least one Standard Model (SM) particle. DM will then reveal itself as missing energy. An alternative form to get a hint of a dark sector is via loop contribution to SM processes. In this case, it is not even relevant if the new particles have their origin in the dark sector of the model. In this work we discuss the impact of an arbitrary number of coloured scalars with $$Z_2$$ -odd parity in single Higgs and double Higgs production at the Large Hadron Collider (LHC), and we show their complementarity. We determine the range of variation of the corrections relative to the SM for an arbitrary number of coloured scalars . We discuss the cases $$n=1$$ and $$n=2$$ for a specific model in more detail, which includes direct searches at the LHC. We also find that the electroweak observable parameter imposes significant restrictions on the difference of the heavy coloured scalar masses.

Portugal

Pedro Gabriel

Daniel Neacsu

Rui Santos

Dark coloured scalars impact on single and di-Higgs production at the LHC

We here report on the progress of the HHH Workshop, that took place in Dubrovnik in July 2023. After the discovery of a particle that complies with the properties of the Higgs boson of the Standard Model, all Standard Model (SM) parameters are in principle determined. However, in order to verify or falsify the model, the full form of the potential has to be determined. This includes the measurement of the triple and quartic scalar couplings.

Morocco

Hamza Abouabid

Abdesslam Arhrib

United States

Hannah Arnold

Duarte Azevedo

Croatia

Vuko Brigljevic

United Kingdom

Maggie Chen

Daniel Diaz

Javier Duarte

Netherlands

Tristan Pree

Jaouad Falaki

Dinko Ferencek

Pedro. Ferreira

France

Benjamin Fuks

India

Japan

Sanmay Ganguly

Osama Karkout

Marina Kolosova

Jacobo Konigsberg

Greg Landsberg

Canada

China

Bingxuan Liu

CERN

Switzerland

Brian Moser

Andreas Papaefstathiou

Sweden

Roman Pasechnik

Tania Robens

Brian Sheldon

Gregory Soyez

Marko Stamenkovic

Panagiotis Stylianou

Tatjana Susa

Gilberto Tetlalmatzi-Xolocotzi

Georg Weiglein

Giulia Zanderighi

Rui Zhang

HHH whitepaper

The production of three Higgs bosons could be a stretch goal for the LHC and a strategic case for future colliders. In this work, we analyse the phenomenological prospects of (neutral) triple Higgs compared to di-Higgs boson production, for a range of Higgs-sector extensions from a strong first-order electroweak phase transition perspective. In parallel, we include constraints from existing exotics and Higgs boson measurements that further limit the parameter space of such models. Resonance contributions offer large modifications in particular for triple Higgs production, albeit starting from a small SM expectation. With enhancements of order 40 over the SM, however, experimental efforts to obtain limits at the HL-LHC are well motivated and well placed. This is further highlighted by the potential of these processes to inform the investigation of the thermal history of our Universe.

Lisa Biermann

Christoph Englert

Wrishik Naskar

Double and triple Higgs boson production to probe the electroweak phase transition

There are many extensions of the Standard Model with a dark matter (DM) candidate obtained via the freeze-out mechanism. It can happen that after all experimental and theoretical constraints are taken into account, all parameter points have a relic density below the experimentally measured value. This means that the models solve only partially the DM problem, and at least one more candidate is needed. In this work we show that it is possible to further extend the model with a DM candidate obtained via the freeze-in mechanism to be in agreement with the relic density experimental measurement. Once the relic density problem is solved with this addition, new questions are raised. This new model with at least two DM candidates could have a freeze-out undetectable DM particle both in direct and indirect detection. This could happen if the freeze-out DM particle would have a very low density. Hence, a collider DM hint via excess in the missing energy with no correspondence in direct and indirect detection experiments, could signal the existence of a Feebly Interacting Massive Particle (FIMP). Conversely, if a DM particle is found and a particular model can explain all observables except the correct relic density, an extension with an extra FIMP would solve the problem. The freeze-in DM candidate, due to the small portal couplings, will not change the remaining phenomenology.

Rodrigo Capucha

Karim Elyaouti

Johann Plotnikov

Freeze-in as a complementary process to freeze-out

We show how effects of compositeness emerging in a Composite 2-Higgs Doublet Model can enter Standard Model (SM)-like Higgs boson pair production at the Large Hadron Collider in both resonant and non-resonant mode. Such effects can arise from modified trilinear Higgs self-couplings and top-Yukawa couplings, as well as from loops of new heavy quarks and additional quartic Higgs-fermion interactions. In the resonant case, significant distortions of the Breit-Wigner shape of a new scalar state decaying into the two SM-like Higgs states may occur due to interference effects amongst not only the SM-like diagrams but also those involving the new heavy quarks. In the non-resonant case, a modification of the underlying line-shape and a local maximum at twice a new heavy quark mass appear simultaneously. We quantify these effects by taking into account the relevant theoretical and latest experimental bounds.

Italy

Stefania Curtis

Luigi Rose

Felix Egle

Stefano Moretti

Poland

Kodai Sakurai

Composite 2-Higgs doublet model: strong effects on Higgs pair production

The complex two-Higgs doublet model (C2HDM) is one of the simplest extensions of the Standard Model with a source of CP-violation in the scalar sector. It has a  $${\mathbb{Z}}_{2}$$  symmetry, softly broken by a complex coefficient. There are four ways to implement this symmetry in the fermion sector, leading to models known as Type-I, Type-II, Lepton-Specific and Flipped. In the latter three models, there is a priori the surprising possibility that the 125 GeV Higgs boson couples mostly as a scalar to top quarks, while it couples mostly as a pseudoscalar to bottom quarks. This “maximal” scenario was still possible with the data available in 2017. Since then, there have been more data on the 125 GeV Higgs boson, direct searches for CP-violation in angular correlations of τ-leptons produced in Higgs boson decays, new results on the electron electric dipole moment, new constraints from LHC searches for additional Higgs bosons and new results on b → sγ transitions. Highlighting the crucial importance of the physics results of LHC’s Run 2, we combine all these experiments and show that the “maximal” scenario is now excluded in all models. Still, one can have a pseudoscalar component in  $$h\tau \overline{\tau }$$  couplings in the Lepton-Specific case as large as 87% of the scalar component for all mass orderings of the neutral scalar bosons.

Thomas Biekötter

Duarte Fontes

Jorge Romão

João Silva

Impact of new experimental data on the C2HDM: the strong interdependence between LHC Higgs data and the electron EDM

The Higgs potentials of extended Higgs sectors exhibit a complex and interesting vacuum structure. When travelling back in time, i.e. going to higher temperatures, the structure may change and exhibit interesting phase patterns and sequences of phases related to the respective minima of the potential. The investigation of the vacuum structure can give us indirect insights in beyond-Standard-Model physics and the evolution of the Universe. In this paper, we investigate the possibility of an intermediate charge-breaking (CB) phase in the 2-Higgs-Doublet Model (2HDM) type I. The existence has been reported previously by using a simple potential setup. We here confirm that the intermediate CB phase can still exist when using the one-loop corrected effective potential including thermal masses. We discuss its features and the relation with SU(2) symmetry (non-)restoration as well as its consistency with the current experimental data. Lastly, we show for some selected benchmark points the rich and interesting phase patterns and sequences that the 2HDM can undergo during its evolution from the early Universe to today’s electroweak vacuum.

Mayumi Aoki

Igor Ivanov

Hiroto Shibuya

Intermediate charge-breaking phases and symmetry non-restoration in the 2-Higgs-Doublet Model

The top quark as the heaviest particle in the Standard Model (SM) defines an important mass scale for Higgs physics and the electroweak scale itself. It is therefore a well-motivated degree of freedom which could reveal the presence of new interactions beyond the SM. Correlating modifications of the top-Higgs interactions in the 2-Higgs-Doublet Model (2HDM), we analyse effective field theory deformations of these interactions from the point of view of a strong first-order electroweak phase transition (SFOEWPT). We show that such modifications are compatible with current Higgs data and that an SFOEWPT can be tantamount to a current overestimate of exotic Higgs searches’ sensitivity at the LHC in   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> </math>  $$ t\overline{t} $$  and four top quark final states. We argue that these searches remain robust from the point of accidental signal-background interference so that the current experimental strategy might well lead to 2HDM-like discoveries in the near future.

 Anisha

Effective 2HDM Yukawa interactions and a strong first-order electroweak phase transition

We present the prediction of the electroweak  $$\rho $$  <math> <mi>ρ</mi> </math>   parameter and the W boson mass in the CP-violating Next-to-Minimal Supersymmetric extension of the Standard Model (NMSSM) at the two-loop order. The  $$\rho $$  <math> <mi>ρ</mi> </math>   parameter is calculated at the full one-loop and leading and sub-leading two-loop order  $${\mathcal {O}}(\alpha + \alpha _t\alpha _s + \left( \alpha _t+\alpha _\lambda +\alpha _\kappa \right) ^2)$$  <math> <mrow> <mi>O</mi> <mo>(</mo> <mi>α</mi> <mo>+</mo> <msub> <mi>α</mi> <mi>t</mi> </msub> <msub> <mi>α</mi> <mi>s</mi> </msub> <mo>+</mo> <msup> <mfenced> <msub> <mi>α</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>α</mi> <mi>λ</mi> </msub> <mo>+</mo> <msub> <mi>α</mi> <mi>κ</mi> </msub> </mfenced> <mn>2</mn> </msup> <mo>)</mo> </mrow> </math>  . The new  $$\Delta \rho $$  <math> <mrow> <mi>Δ</mi> <mi>ρ</mi> </mrow> </math>   prediction is incorporated into a prediction of  $$M_W$$  <math> <msub> <mi>M</mi> <mi>W</mi> </msub> </math>   via a full supersymmetric (SUSY) one-loop calculation of  $$\Delta r$$  <math> <mrow> <mi>Δ</mi> <mi>r</mi> </mrow> </math>  . Furthermore, we include all known state-of-the-art SM higher-order corrections to  $$\Delta r$$  <math> <mrow> <mi>Δ</mi> <mi>r</mi> </mrow> </math>  . By comparing results for  $$\Delta \rho $$  <math> <mrow> <mi>Δ</mi> <mi>ρ</mi> </mrow> </math>   obtained using on-shell (OS) and  $$\overline{\text {DR}}$$  <math> <mover> <mtext>DR</mtext> <mo>¯</mo> </mover> </math>   renormalization conditions in the top/stop sector, we find that the scheme uncertainty is reduced at one-loop order by 55%, at two-loop  $${\mathcal {O}}(\alpha _s\alpha _t)$$  <math> <mrow> <mi>O</mi> <mo>(</mo> <msub> <mi>α</mi> <mi>s</mi> </msub> <msub> <mi>α</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> </math>   by 22%, and at two-loop  $${\mathcal {O}}(\alpha _t+\alpha _\kappa +\alpha _\lambda )^2$$  <math> <mrow> <mi>O</mi> <msup> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>α</mi> <mi>κ</mi> </msub> <mo>+</mo> <msub> <mi>α</mi> <mi>λ</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </math>   by 16%, respectively. The influence of the two-loop results on the  $$M_W$$  <math> <msub> <mi>M</mi> <mi>W</mi> </msub> </math>   mass prediction is found to be sub-leading. The new calculation is made public in the computer program NMSSMCALC. We perform an extensive comparison in the W-mass, Higgs boson mass and the muon anomalous magnetic moment prediction between our calculation and three other publicly available tools and find very good agreement provided that the input parameters and renormalization scales are treated in the same way. Finally, we study the impact of the CP-violating phases on the W-mass prediction which is found to be smaller than the overall size of the SUSY corrections.

The  $$\mathcal{O}(\alpha _t+\alpha _\lambda +\alpha _\kappa )^2$$  <math> <mrow> <mi>O</mi> <msup> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mi>t</mi> </msub> <mo>+</mo> <msub> <mi>α</mi> <mi>λ</mi> </msub> <mo>+</mo> <msub> <mi>α</mi> <mi>κ</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </math>   correction to the  $$\rho $$  <math> <mi>ρ</mi> </math>   parameter and its effect on the W boson mass calculation in the complex NMSSM