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

Germany

Felix Egle

Sweden

United Kingdom

Stefano Moretti

Margarete Mühlleitner

Japan

Poland

Kodai Sakurai

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

A precise modelling of the dynamics of bubbles nucleated during first-order phase transitions in the early Universe is pivotal for a quantitative determination of various cosmic relics, including the stochastic background of gravitational waves. The equation of motion of the bubble front is affected by the out-of-equilibrium distributions of particle species in the plasma which, in turn, are described by the corresponding Boltzmann equations. In this work we provide a solution to these equations by thoroughly incorporating the non-linearities arising from the population factors. Moreover, our methodology relies on a spectral decomposition that leverages the rotational properties of the collision integral within the Boltzmann equations. This novel approach allows for an efficient and robust computation of both the bubble speed and profile. We also refine our analysis by including the contributions from the electroweak gauge bosons. We find that their impact is dominated by the infrared modes and proves to be non-negligible, contrary to the naive expectations.

Andrea Guiggiani

Spain

Ángel Muyor

Giuliano Panico

Non-linearities in cosmological bubble wall dynamics

CERN

Carlotta Accettura

Dean Adams

United States

Rohit Agarwal

Claudia Ahdida

Chiara Aimè

Nicola Amapane

David Amorim

Paolo Andreetto

Fabio Anulli

Robert Appleby

Artur Apresyan

Aram Apyan

France

Sergey Arsenyev

Pouya Asadi

Egypt

Mohammed Mahmoud

Aleksandr Azatov

John Back

Lorenzo Balconi

Laura Bandiera

Roger Barlow

Nazar Bartosik

Emanuela Barzi

Fabian Batsch

Matteo Bauce

J. Berg

Andrea Bersani

Alessandro Bertarelli

Alessandro Bertolin

Kevin Black

Fulvio Boattini

Alex Bogacz

Maurizio Bonesini

Bernardo Bordini

Salvatore Bottaro

Luca Bottura

Alessandro Braghieri

Marco Breschi

Natalie Bruhwiler

Xavier Buffat

Laura Buonincontri

Philip Burrows

Graeme Burt

Dario Buttazzo

Barbara Caiffi

Marco Calviani

Simone Calzaferri

Daniele Calzolari

Rodolfo Capdevilla

Christian Carli

Fausto Casaburo

Massimo Casarsa

Luca Castelli

Maria Catanesi

Lorenzo Cavallucci

Gianluca Cavoto

Francesco Celiberto

Luigi Celona

Alessandro Cerri

Gianmario Cesarini

Cari Cesarotti

Portugal

Grigorios Chachamis

Antoine Chance

Switzerland

Siyu Chen

Yang-Ting Chien

Mauro Chiesa

Anna Colaleo

Francesco Collamati

Gianmaria Collazuol

Marco Costa

Nathaniel Craig

Camilla Curatolo

Canada

David Curtin

Giacomo Molin

Magnus Dam

Heiko Damerau

Sridhara Dasu

Jorge Blas

Ernesto Matteis

Stefania Rosa

Jean-Pierre Delahaye

Dmitri Denisov

Türkiye

Haluk Denizli

Christopher Densham

Radovan Dermisek

Luca Luzio

Elisa Meco

Biagio Micco

Keith Dienes

Eleonora Diociaiuti

Tommaso Dorigo

Alexey Dudarev

Robert Edgecock

Filippo Errico

Marco Fabbrichesi

Stefania Farinon

Anna Ferrari

Jose Somoza

Netherlands

Frank Filthaut

Davide Fiorina

Erratum: Towards a muon collider

A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

Towards a muon collider

The dynamics of the true-vacuum bubbles nucleated during a first-order phase transition is affected by the distribution functions of the particle species in the plasma, driven out-of-equilibrium by the travelling domain wall. An accurate modelling of this phenomenon is relevant for a quantitative description of phase transitions in the early universe and for the determination of the corresponding cosmic relics, such as, among the others, the stochastic background of gravitational waves. We address this problem by developing a new spectral method devised for a fast and reliable computation of the collision integral in the Boltzmann equations. In a scalar singlet extension of the Standard Model chosen as a benchmark scenario, we test our algorithm, determining the bubble speed and profile, and we assess the impact of the out-of-equilibrium dynamics.

Luigi Delle Rose

Collision integrals for cosmological phase transitions

First order phase transitions could play a major role in the early universe, providing important phenomenological consequences, such as the production of gravitational waves and the generation of baryon asymmetry. An important aspect that determines the properties of the phase transition is the dynamics of the true-vacuum bubbles, which is controlled by the density perturbations in the hot plasma. We study this aspect presenting, for the first time, the full solution of the linearized Boltzmann equation for the top quark species coupled to the Higgs field during a first-order electroweak phase transition. Our approach, differently from the traditional one based on the fluid approximation, does not rely on any ansatz and can fully capture the density perturbations in the plasma. We find that our results significantly differ from the ones obtained in the fluid approximation (including its extensions and modifications), both at the qualitative and quantitative level. In particular sizable differences are found for the friction acting on the bubble wall.

Bubble wall dynamics at the electroweak phase transition

We study CP-Violation (CPV) in a Composite 2-Higgs Doublet Model (C2HDM) based on the global symmetry breaking SO(6)/[SO(4) × SO(2)], wherein the strong sector is modeled by a two-site moose structure. Non-trivial complex phases in the interactions involving fermions in both the elementary and strong sectors can induce CPV in the Higgs potential as well as the Yukawa coupling parameters. We compute both of the latter and analyse their dependence upon the aforementioned complex phases. Finally, we discuss physics observables which are distinctive of this model. Even in the simplest case with only one complex phase in the strong sector we can get significant CPV effects.

Ryo Nagai

Kei Yagyu

CP-Violation in a composite 2-Higgs doublet model

The future 100 TeV FCC-hh hadron collider will give access to rare but clean final states which are out of reach of the HL-LHC. One such process is the Zh production channel in the   <math> <mfenced> <mrow> <mi>v</mi> <mover> <mi>v</mi> <mo>¯</mo> </mover> <mo>/</mo> <msup> <mi>ℓ</mi> <mo>+</mo> </msup> <msup> <mi>ℓ</mi> <mo>−</mo> </msup> </mrow> </mfenced> <mi>γγ</mi> </math>  $$ \left(v\overline{v}/{\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-}\right)\gamma \gamma $$  final states. We study the sensitivity of this channel to the   <math> <msubsup> <mi>O</mi> <mi>φq</mi> <mfenced> <mn>1</mn> </mfenced> </msubsup> <mo>,</mo> <mspace width="0.5em"></mspace> <msubsup> <mi>O</mi> <mi>φq</mi> <mfenced> <mn>3</mn> </mfenced> </msubsup> <mo>,</mo> <mspace width="0.5em"></mspace> <msub> <mi>O</mi> <mi>φu</mi> </msub> </math>  $$ {\mathcal{O}}_{\varphi q}^{(1)},\kern0.5em {\mathcal{O}}_{\varphi q}^{(3)},\kern0.5em {\mathcal{O}}_{\varphi u} $$ , and   <math> <msub> <mi>O</mi> <mi>φd</mi> </msub> </math>  $$ {\mathcal{O}}_{\varphi d} $$  SMEFT operators, which parametrize deviations of the W and Z couplings to quarks, or, equivalently, anomalous trilinear gauge couplings (aTGC). While our analysis shows that good sensitivity is only achievable for   <math> <msubsup> <mi>O</mi> <mi>φq</mi> <mfenced> <mn>3</mn> </mfenced> </msubsup> </math>  $$ {\mathcal{O}}_{\varphi q}^{(3)} $$ , we demonstrate that binning in the Zh rapidity has the potential to improve the reach on   <math> <msubsup> <mi>O</mi> <mi>φq</mi> <mfenced> <mn>1</mn> </mfenced> </msubsup> </math>  $$ {\mathcal{O}}_{\varphi q}^{(1)} $$ . Our estimated bounds are one order of magnitude better than projections at HL-LHC and is better than global fits at future lepton colliders. The sensitivity to   <math> <msubsup> <mi>O</mi> <mi>φq</mi> <mfenced> <mn>3</mn> </mfenced> </msubsup> </math>  $$ {\mathcal{O}}_{\varphi q}^{(3)} $$  is competitive with other channels that could probe the same operator at FCC-hh. Therefore, combining the different diboson channels sizeably improves the bound on   <math> <msubsup> <mi>O</mi> <mi>φq</mi> <mfenced> <mn>3</mn> </mfenced> </msubsup> </math>  $$ {\mathcal{O}}_{\varphi q}^{(3)} $$ , reaching a precision of |δg 1z | ≲ × 10 −4 on the deviations in the ZWW interactions.

Fady Bishara

Philipp Englert

Christophe Grojean

Marc Montull

Alejo Rossia

Precision from the diphoton Zh channel at FCC-hh

We study the occurrence of a strong first-order electroweak phase transition in composite Higgs models. Minimal constructions realising this scenario are based on the coset SO(6)/SO(5) which delivers an extended Higgs sector with an additional scalar. In such models, a two-step phase transition can be obtained with the scalar singlet acquiring a vacuum expectation value at intermediate temperatures. A bonus of the Nambu-Goldstone boson nature of the scalar-sector dynamics is the presence of non-renormalisable Higgs in- teractions that can trigger additional sources of CP violation needed to realise baryogenesis at the electroweak scale. Another interesting aspect of this scenario is the generation of gravitational wave signatures that can be observed at future space-based interferometers.

Composite dynamics in the early Universe

We consider a Composite Higgs Model (CHM) with two isospin doublet Higgs fields arising as pseudo Nambu-Goldstone bosons from a SO(6) → SO(4) × SO(2) breaking. The main focus of this work is to explicitly compute the properties of these Higgses in terms of the fundamental parameters of the composite sector such as masses, Yukawa and gauge couplings of the new spin-1 and spin-1/2 resonances. Concretely, we calculate the Higgs potential at one-loop level through the Coleman-Weinberg mechanism from the explicit breaking of the SO(6) global symmetry by the partial compositeness of fermions and gauge bosons. We derive then the phenomenological properties of the Higgs states and highlight the main signatures of this Composite 2-Higgs Doublet Model at the Large Hadron Collider, including modifications to the SM-like Higgs couplings as well as production and decay channels of heavier Higgs bosons. We also consider flavour bounds that are typical of CHMs with more than one Higgs doublet.

A concrete composite 2-Higgs doublet model