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We examine the vacuum stability of gauge symmetry breaking in five dimensions, compactified on the $S_1/(\mathbb{Z}_2 \times \mathbb{Z}'_2)$ orbifold. We consider $SU(N)$, $Sp(N)$, $SO(2N)$ and $SO(2N+1)$ theories in the bulk, and provide an exhaustive classification of possible parity assignments that lead to stable orbifolds and of the corresponding symmetry breaking patterns. We use these results in the search for viable asymptotic grand unification theories (aGUT), testing the stability criteria on models based on $SU(6)$ and $SU(8)$. As a result, we identify two viable aGUTs: a unique $SU(6)$ pathway down to the Standard Model, and one $SU(8)$ model leading to an intermediate Pati-Salam partial unification.

We investigate high and low energy implications of a gauge dual description of the Standard Model. The high energy electric theory features gauge dynamics involving only fermionic matter fields, while the low energy magnetic description features a quasi-supersymmetric spectrum testable at colliders. The flavour theory is constructed via operators generated at the Planck scale. We further show that duality opens novel avenues for theories of grand unification.

Strong dynamics for composite Higgs models predict spin-1 resonances which are expected to be in the same mass range as the usually considered top-partners. We study here QCD-coloured vector and axial-vector states stemming from composite Higgs dynamics in several relevant models based on an underlying gauge-fermion description. These states can come as triplet, sextet and octet representation. All models considered have a colour octet vector state in common which can be singly produced at hadron colliders as it mixes with the gluon. We explore the rich and testable phenomenology of these coloured spin-1 states at the LHC and future colliders.

The Swampland program, which looks for low energy theories consistent with quantum gravity, has led to the introduction of a dark dimension stemming from the cosmological constant. We show that the same argument leads to the emergence of the electroweak scale, once the dark dimension is realised in a warped background. A second warped extra dimension at the TeV scale is, therefore, postulated, where the long-standing problem of the hierarchy between the electroweak and the Planck scales can be addressed. Furthermore, standard model contributions to the cosmological constant are tamed, together with the gravitational ones. In the emergent holistic picture of gravity and gauge interactions, both Planck and the electroweak scales are emergent from a theory with two fundamental scales: $10^{-2}$ eV and $10^{10}$ GeV, which are of geometric origin and, following the Distance Conjecture, natural. Hence, a bridge is established between the two standard models of particle physics and cosmology.

Asymptotic Grand Unification theories (aGUTs) in five dimensions provide a valid alternative to standard quantitative unification. We define the pathway towards viable models starting from a general unified bulk gauge symmetry. Imposing the presence of ultra-violet fixed points for both gauge and Yukawa couplings strongly limits the possibilities. Within the SU(N) kinship, we identify and characterise only two realistic minimal models, both based on a bulk SU(6) symmetry. Both models feature the generation of either up or down-type Yukawas via gauge scalars, two Higgs doublets with build-in minimal flavour violation at low energies, and conservation of baryon number. We also propose interesting avenues beyond the minimality criterion.

We investigate the possibility that inflation originates from a composite field theory, in terms of an effective chiral Lagrangian involving a dilaton and pions. The walking dynamics of the theory constrain the potential in a specific way, where the anomalous dimensions of operators involving pions play a crucial role. For realistic values of the anomalous dimensions, we find a successful hybrid inflation occurring via the dilaton-inflaton, with the pions acting as waterfall fields. Compositeness consistency strongly constrain the model, predicting a dilaton scale $f_\chi \sim \mathcal{O} (1)$ in unit of the Planck scale, an inflation scale $H_\text{inf} \sim 10^{10}$ GeV, and the pion scale around $10^{14}$ GeV. We further discuss possible phenomenological consequences of this theory.

The attractive feature of supersymmetry is predictive power, due to the large number of calculable properties and to coupling non-renormalisation. This power can be fully expressed in hidden sectors where supersymmetry may be exact, as these sectors are secluded from the visible one where instead supersymmetry must be broken. This suggests a new paradigm for supersymmetric dark sectors, where supersymmetry is exact at the dark matter scale, implying that many properties of hidden supersymmetric dark sectors can be fully computed. As a proof of concept we discuss a concrete example based on $\mathcal{N}=1$ super Yang-Mills.

Composite Higgs models with extended symmetries can feature mesonic dark matter candidates. In fundamental CHMs, the origin of dark parity can be explained in the UV theory. Combined with top partial compositeness, this leads to non-chiral Yukawa interaction connecting mesonic DM with one dark top partner and one SM top. We examine the DM phenomenology in SU(6)/SO(6) and SU(6)/Sp(6) CHMs with the presence of dark top partners. Phenomenological constraints require the mass of top partner in even parity to be of the multi-TeV order.

We propose a new family structure for the Standard Model fermions, where the muon is assigned to the third family, taking the placeholder from the tau lepton. This reassignment, which is a mere choice of convention in the Standard Model, becomes physically meaningful in the presence of new physics assuming a direct link between quarks and leptons. In fact, when quark and leptons are coupled by new interactions, the choice of which lepton is assigned to a particular quark generation brings physical consequences, revealing potentially meaningful patterns in the masses and mixings, while pointing to precise and testable predictions for experiments.

We present a new grand unification paradigm, where gauge couplings do not need to be equal at any given scale, instead they run towards the same fixed point in the deep ultraviolet. We provide a concrete example based on SU(5) with a compactified extra space dimension. By construction, fermions are embedded in different SU(5) bulk fields, hence baryon number is conserved and proton decay is forbidden. The lightest Kaluza-Klein tier consists of stable states, providing an asymmetric Dark Matter candidate via their baryonic charges, with a mass of 2.4 TeV. The model features an interesting and predictive flavour structure.

New Physics models with either an elementary or composite origin are often associated with a similar imprint in a direct search at colliders, case in point being the production of a light pseudoscalar in association with a monochromatic photon from the decay of a Z boson at future $e+e-$ colliders. We exploit the correlation between the discovery of a signal in the Z decays and electroweak precision measurements as a tool to distinguish a composite model from an elementary scalar one. Our results offer an appealing and rich physics case for future colliders and demonstrate how a lepton collider at the Z mass can be a discovery machine for new physics in the Higgs sector.

The Standard Model of Particle Physics and its description of Nature have been recently challenged by a series of precision measurements performed via different accelerator machines. Statistically significant anomalies emerged in the heavy meson physics sector, when measuring the muon magnetic momentum, and very recently when deducing the mass of the W boson. Here we consider a radiative extension of the Standard Model devised to be sufficiently versatile to reconcile the various experimental results while further predicting the existence of new bosons and fermions with a mass spectrum in the TeV energy scale. The resulting spectrum is, therefore, within the energy reach of the proton-proton collisions at the LHC experiments at CERN. The model investigated here allows to interpolate between composite and elementary extensions of the Standard Model with emphasis on a new modified Yukawa sector that is needed to accommodate the anomalies. Focusing on the radiative regime of the model, we introduce interesting search channels of immediate impact for the ATLAS and CMS experimental programs such as the associate production of Standard Model particles with either invisible or long-lived particles. We further show how to adapt earlier SUSY-motivated searchers of new physics to constrain the spectrum and couplings of the new scalars and fermions. Overall, the new physics template simultaneously accounts for the bulk of the observed experimental anomalies while suggesting a wide spectrum of experimental signatures relevant for the current LHC experiments.

We explicitly test the asymptotic grand unification of a minimal 5-dimensional model with SO(10) gauge theory compactified on an $S^{1}/Z_{2}\times Z^{\prime}_{2}$ orbifold. We consider all matter fields as propagating in the bulk and show that the gauge couplings asymptotically run to a fixed point in the UV. However, the Yukawa couplings will typically hit a Landau pole right above the compactification scale in this class of SO(10) models.

We summarize the state of Beyond the Standard Model (BSM) model building in particle physics for Snowmass 2021, focusing mainly on several whitepaper contributions to BSM model building (TF08) and closely related areas.

Higgs sectors extended by electroweakly charged scalars can be explored by scalar pair production at the LHC. We consider a fermiophobic scenario, with decays into a pair of gauge bosons, and a fermiophilic one, with decays into top and bottom quarks. After establishing the current bounds on simplified models, we focus on an SU(5)/SO(5) composite Higgs model. This first exploration demonstrates the need for dedicated searches at current and future colliders.

This is the Snowmass2021 Energy Frontier (EF) Beyond the Standard Model (BSM) report. It combines the EF topical group reports of EF08 (Model-specific explorations), EF09 (More general explorations), and EF10 (Dark Matter at Colliders). The report includes a general introduction to BSM motivations and the comparative prospects for proposed future experiments for a broad range of potential BSM models and signatures, including compositeness, SUSY, leptoquarks, more general new bosons and fermions, long-lived particles, dark matter, charged-lepton flavor violation, and anomaly detection.

We revisit the impact of top partial compositeness on electroweak precision observables in the misaligned vacuum basis. We identify a new source for $S$ in the singlet mixing case, and for $S$-$T$ in the bi-doublet mixing, stemming from misalignment in the gauge couplings of the top partners. Hence, a positive shift in $T$ can be obtained in both cases, as preferred by the recent CDF measurement of the $W$ mass. These results, obtained for the minimal fundamental coset SU(4)/Sp(4), apply to any composite Higgs model with top partial compositeness.

We consider the implications of the CDF collaboration high-precision measurement of the W boson mass on models with a non-standard Higgs. We show that this requires an enhancement of 3-10% in the non-standard Higgs coupling to the gauge bosons. This is naturally accommodated in dynamical models such as the dilaton Higgs, the Technicolor and glueball Higgs. The needed composite scale between 2 and 3 TeV can also explain the muon g-2 anomaly, as well as possible violations of lepton flavour universality.

Composite Higgs models usually contain additional pseudo Nambu Goldstone bosons and vector-like quarks. We discuss various aspects related to their LHC phenomenology and provide summary plots of exclusion limits using currently available information. We also describe a general parametrisation implemented in a software for Monte Carlo simulations and study the SU(5)/SO(5) scenario as a concrete example.

The search for a Dark Matter particle is the new grail and hard-sought nirvana of the particle physics community. From the theoretical side, it is the main challenge to provide a consistent and model-independent tool for comparing the bounds and reach of the diverse experiments. We propose a first complete classification of minimal consistent Dark Matter models, which provides the missing link between experiments and top-down models. Consistency is achieved by imposing renormalisability and invariance under the full Standard Model symmetries. We apply this paradigm to fermionic Dark multiplets with up to one mediator. We also reconsider the one-loop contributions to direct detection, including the relevant effect of (small) mass splits in the Dark multiplet. Our work highlights the presence of unexplored viable models, and paves the way for the ultimate systematic hunt for the Dark Matter particle.

Dark Matter searches in collider and non-collider experiments requires systematic and consistent approach. We suggest and perform classification of Minimal Consistent Dark Matter models which are aimed to create a solid framework for Dark Matter exploration.

We consider a particular composite Higgs model which contains SU(3) color octet top partners besides the usually considered triplet representations. Moreover, color singlet top partners are present as well which can in principle serve as dark matter candidates. We investigate the LHC phenomenology of these unusual top partners. Some of these states could be confused with gluinos predicted in supersymmetric models at first glance.

We propose a novel class of composite models that feature both a technicolor and a composite Higgs vacuum limit, resulting in an asymmetric dark matter candidate. These Techni-Composite Higgs models are based on an extended left-right electroweak symmetry with a pseudo-Nambu Goldstone boson Higgs and stable dark matter candidates charged under a global $\mathrm{U}(1)_X$ symmetry, connected to the baryon asymmetry at high temperatures via the $SU(2)_{\rm R}$ sphaleron. We consider, as explicit examples, four-dimensional gauge theories with fermions charged under a new confining gauge group $G_{\rm HC} $.

We explore the collider relevance of a charge-radius coupling among light mesons in composite Higgs models. In particular, we focus of a coupling of the photon to the composite Higgs and a composite singlet, arising from isospin violation in the underlying theory. This coupling offers a deep probe of the composite nature of the Higgs mechanism, being sensitive to the electromagnetic and weak isospin structure of its constituents. The main collider effect consists in the production of the Higgs boson in association with a light composite pseudo-scalar. We present an exploratory cut-and-count analysis at hadron colliders, like the LHC, showing that an efficient background suppression can be achieved. More sophisticated techniques, however, are necessary to select a sufficient number of signal events, due to the small production rates. This justifies further investigation of this channel, which is highly complementary to other searches for compositeness in the Higgs sector.

We detailed our discovery of a chiral enhancement in the production cross sections of massive spin-2 gravitons, below the electroweak symmetry breaking scale, that makes them ideal dark matter candidates for the freeze-in mechanism. The result is independent of the physics at high scales, and points toward masses in the keV- MeV range. The graviton is, therefore, a sub-MeV dark matter particle, as favored by the small scale galaxy structures. We apply the novel calculation to a Randall-Sundrum model with multiple branes, showing a significant parameter space where the first two massive gravitons saturate the dark matter relic density.

We study the possibility of observing a light pseudo-scalar $a$ at LHCb. We target the mass region $1 \lesssim m_a \lesssim 60$ GeV and various decay channels, some of which have never been considered before: muon pairs, tau pairs, $D$ meson pairs, and di-photon. We interpret the results in the context of models of 4D Composite Higgs and Partial Compositeness in particular.

In this paper, we describe the potential of the LHCb experiment to detect Stealth physics. This refers to dynamics beyond the Standard Model that would elude searches that focus on energetic objects or precision measurements of known processes. Stealth signatures include long-lived particles and light resonances that are produced very rarely or together with overwhelming backgrounds. We will discuss why LHCb is equipped to discover this kind of physics at the Large Hadron Collider and provide examples of well-motivated theoretical models that can be probed with great detail at the experiment.

In Standard Model (SM) Higgs Boson pair production initiated by photons ($\gamma \gamma \to h h$) is loop-generated process and thereby very sensitive to any new couplings and particles that may come in loops. The Composite Higgs Models provide an alternate mechanism to address the hierarchy problem of SM where Higgs instead of being an elementary field could be a bound state of a strongly interacting sector. These set of models apart from modifying the SM Higgs couplings could also introduce new effective couplings that can have substantial impact on the loop processes. In this work we have studied the impact of such modifications by Composite Higgs models in $\gamma\gamma \to h h$ production process.

The Tera-Z phase of future $e^+ e^-$ colliders, FCC-ee and CepC, is a goldmine for exploring $Z$ portal physics. We focus on axion-like particles (ALPs) that can be produced via $Z$ decays with a monochromatic photon. As a template model, we consider composite Higgs models with a light pseudo-scalar that couples through the Wess-Zumino-Witten term to the electroweak gauge bosons. For both photophilic and photophobic cases, we show that the Tera-Z can probe composite scales up to $100$s of TeV, well beyond the capability of the LHC and current precision physics. Our results also apply to generic ALPs and, in particular, severely constrain models that explain the muon $g-2$ anomaly.

We show that the observed anomalies in the lepton sector can be explained in extensions of the Standard Model that are natural and, therefore, resolve the Higgs sector hierarchy problem. The scale of new physics is around the TeV and Technicolor-like theories are ideal candidate models.

We present a minimal model of asymptotic grand unification based on an $SU(5)$ gauge theory in a compact $S^1/(\mathbb{Z}_2 \times \mathbb{Z}'_2)$ orbifold. The gauge couplings run to a unified fixed point in the UV, without supersymmetry. By construction, fermions are embedded in different $SU(5)$ bulk fields. As a consequence, baryon number is conserved, thus preventing proton decay, and the lightest Kaluza-Klein tier consists of new states that cannot decay into standard model ones. We show that the Yukawa couplings can be either in the bulk or localized, and run to an asymptotically free fixed point in the UV. The lightest massive state can play the role of Dark Matter, produced via baryogenesis, for a Kaluza-Klein mass of about $2.4$ TeV.

The next generation electron-positron colliders are designed for precision studies of the Standard Model and its extensions, in particular in the Higgs sector. We consider the potential for discovery of composite Higgs models in Higgs pair production through photon collisions. This process is loop-generated, thus it provides access to all Higgs couplings and can show new physics effects in polarized and unpolarized cross-sections starting at relatively low collider energies. It is, therefore, relevant for all electron-positron colliders planned or in preparation. Sizeable deviations from the Standard Model predictions are present in a general class of composite Higgs models, as couplings of one or more Higgs bosons to fermions, or fermionic and scalar resonances, modify the destructive interference present in the Standard Model. In particular, large effects are due to the new quartic coupling of the Higgs to tops and to the presence of a light scalar resonance.

We present a composite scotogenic model for neutrino masses, which are generated via loops of $\mathbb{Z}_2$-odd composite scalars. We consider three different approaches to the couplings of the neutrinos (including three right-handed singlets) and the composite sector: ETC-like four-fermion interactions, fundamental partial compositeness and fermion partial compositeness. In all cases, the model can feature sizeable couplings and remain viable with respect to various experimental constraints if the three $ \mathbb{Z}_2 $-odd right-handed neutrinos have masses between the TeV and the Planck scales. Additionally, the lightest $\mathbb{Z}_2$-odd composite scalar may play the role of Dark Matter, either via thermal freeze-out or as an asymmetric relic. This mechanism can be featured in a variety of models based on vacuum misalignment. For concreteness, we demonstrate it in a composite two-Higgs scheme based on the coset SU(6)/Sp(6).

Singlet scalar Dark Matter can naturally arise in composite Higgs models as an additional stable pseudo-Nambu-Goldstone boson. We study the properties of such a candidate in a model based on $SU(6)/SO(6)$, with the light quark masses generated by 4-fermion interactions. The presence of non-linearities in the couplings allows to saturate the relic density for masses $400 < m_{\rm DM} < 1000$ GeV, and survive the bound from Direct Detection and Indirect Detection. The viable parameter regions are in reach of the sensitivities of future upgrades, like XENONnT and LZ.

In a recent letter we proposed a new non-thermal mechanism of Dark Matter production based on vacuum misalignment, where both the Higgs boson and a very light pseudo-scalar $\eta$ emerge from the Dark sector. In this letter, we identify the parameter space in a composite scenario where the light pseudo-scalar can be produced in the sun and explain the XENON1T excess in electron recoil data. The model's Dark Matter candidate has a mass around $50$ TeV and out of range for Direct Detection. Testable predictions include Gravitational waves at frequencies in the Hz range from a cosmological phase transition, an exotic decay $Z \to \gamma + \mbox{inv.}$ with rates $4 \div 16 \cdot 10^{-12}$ testable at a future Tera-Z collider, and an enhancement by $17\div 40$ % of the branching ratio $K_L \to \pi^0 + \mbox{inv.}$, not enough to explain the KOTO anomaly. All these predictions may be confirmed by future experiments.

Composite Higgs models can be extended to the Planck scale by means of the partially unified partial compositeness (PUPC) framework. We present in detail the Techni-Pati-Salam model, based on a renormalizable gauge theory $SU(8)_{PS}\times SU(2)_L\times SU(2)_R$. We demonstrate that masses and mixings for all generations of standard model fermions can be obtained via partial compositeness at low energy, with four-fermion operators mediated by either heavy gauge bosons or scalars. The strong dynamics is predicted to be that of a confining $Sp(4)_{\rm HC}$ gauge group, with hyper-fermions in the fundamental and two-index anti-symmetric representations, with fixed multiplicities. This motivates for Lattice studies of the Infra-Red near-conformal walking phase, with results that may validate or rule out the model. This is the first complete and realistic attempt at providing an Ultra-Violet completion for composite Higgs models with top partial compositeness. In the baryon-number conserving vacuum, the theory also predicts a Dark Matter candidate, with mass in the few TeV range, protected by semi-integer baryon number.

The high-energy scattering of massive electroweak bosons, known as vector boson scattering (VBS), is a sensitive probe of new physics. VBS signatures will be thoroughly and systematically investigated at the LHC with the large data samples available and those that will be collected in the near future. Searches for deviations from Standard Model (SM) expectations in VBS facilitate tests of the Electroweak Symmetry Breaking (EWSB) mechanism. Current state-of-the-art tools and theory developments, together with the latest experimental results, and the studies foreseen for the near future are summarized. A review of the existing Beyond the SM (BSM) models that could be tested with such studies as well as data analysis strategies to understand the interplay between models and the effective field theory paradigm for interpreting experimental results are discussed. This document is a summary of the EU COST network "VBScan" workshop on the sensitivity of VBS processes for BSM frameworks that took place December 4-5, 2019 at the LIP facilities in Lisbon, Portugal. In this manuscript we outline the scope of the workshop, summarize the different contributions from theory and experiment, and discuss the relevant findings.

We present an extension of the large $N_f$ formalism that allows to study cases with multiple fermion representations. The pole structure in the beta function is traced back to the intrinsic non-abelian nature of the gauge group, independently on the fermion representation. This result validates the conjectured existence of an interactive UV fixed point for non-abelian gauge theories with large fermion multiplicity. Finally, we apply our results to chiral gauge theories and to extended Grand Unified Theories.

This report presents the activities of the `New Physics' working group for the `Physics at TeV Colliders' workshop (Les Houches, France, 10--28 June, 2019). These activities include studies of direct searches for new physics, approaches to exploit published data to constrain new physics, as well as the development of tools to further facilitate these investigations. Benefits of machine learning for both the search for new physics and the interpretation of these searches are also presented.

We introduce fundamental gauge theories that can be employed to construct informed composite bright and dark extensions of the Standard Model, within and beyond the standard paradigms. The gap between theory and experiments is bridged by providing predictions and ways to test them, for example, at the Fermi scale and via precision flavor experiments. We will review time-honoured paradigms from (walking) technicolor to composite Goldstone Higgs and discuss their features and differences. Standard model fermion mass generation in composite models will also be discussed along with the challenges and opportunities that it offers. To be concrete and pedagogical we will concentrate on minimal constructions featuring strongly coupled gauge theories supporting the global symmetry breaking pattern SU(4)/Sp(4). The most minimal underlying fundamental description consists of an SU(2) gauge theory with two Dirac fermions transforming according to the fundamental representation of the gauge group. This minimal choice enables us to use first principle lattice results to predict the massive spectrum for models of composite (Goldstone) Higgs dynamics and strongly interacting dark matter, of immediate impact for current and future experimental searches. Because composite dynamics embraces a rich spectrum of theories with dynamics ranging from QCD-like behaviour to (near) conformal one, we also report here the state-of-the-art of numerical and analytic properties of several strongly coupled theories including their spectrum, phase diagrams and, when applicable, their (near) conformal data.

We consider a color octet scalar particle and its exotic decay in the channel gluon-$\gamma$ using an effective Lagrangian description for its strong and electromagnetic interactions. Such a state is present in many extensions of the Standard Model, and in particular in composite Higgs models with top partial compositeness, where couplings to photons arise via the Wess-Zumino-Witten term. We find that final states with one or two photons allow for a better reach at the LHC, even for small branching ratios. Masses up to $1.2$ TeV can be probed at the HL-LHC by use of all final states. Finally, we estimate the sensitivity of the hadronic FCC.

We propose a new non-thermal mechanism of dark matter production based on vacuum misalignment. A global $X$-charge asymmetry is generated at high temperatures, under which both the will-be Higgs and the dark matter are charged. At lower energies, the vacuum changes alignment and breaks the $U(1)_X$, leading to the emergence of the Higgs and of a fraction of charge asymmetry stored in the stable dark matter relic. This mechanism can be present in a wide variety of models based on vacuum misalignment, and we demonstrate it in a composite Higgs template model, where all the necessary ingredients are naturally present. A light pseudo-scalar $\eta$ is always predicted, with interesting implications for cosmology, future supernova observations and exotic $Z \to \gamma \eta$ decays.

Providing an Ultra-Violet completion valid up to the Planck scale is of paramount importance to validate the composite Higgs paradigm, at par with supersymmetry. We propose the first complete and feasible framework, based on partial unification of a confining hypercolor gauge group, where couplings of the standard model fermions are mediated by both gauge and scalar bosons. We demonstrate our approach by providing an explicit model based on a Techni-Pati-Salam unification, $SU(8)_{\rm PS}\times SU(2)_L\times SU(2)_R$, able to generate masses for all fermion generations, including neutrinos, via partial compositeness. We predict an $Sp(4)$ hypercolor group, and lattice studies will be crucial to validate the model.

Many standard model extensions, including composite Goldstone Higgs models, predict vector-like fermionic top-partners at the TeV scale. The intensive search programmes by ATLAS and CMS focus on decays into a 3$^{\rm rd}$ generation quark and an electroweak boson ($W,Z,h$). However, underlying models of partial compositeness contain additional states that give rise to exotic top partner decays. We consider a well-motivated scenario in which a charge-$2/3$ top-partner decays into a pseudo-scalar, $T\rightarrow t\ a$, with $a\rightarrow gg \mbox{ or } b\bar{b}$ dominating below the $t\bar{t}$ threshold. We show that the constraints on the top partner mass from QCD pair production are substantially weakened, still allowing a top partner mass as light as $400$ GeV.

Exotic decays of top partners in new bosons are the norm in realistic models of a composite Higgs. We focus on the custodial charge-$5/3$ partner, which normally decays exclusively into $tW^+$. The new channels include a colour-sextet, $X_{5/3} \to \bar{b} \pi_6$, as well as singly and doubly charged scalars, $X_{5/3} \to t \phi^+$, $b \phi^{++}$. We use existing same-sign lepton searches to show that the new final states are constrained at the same level as the standard one. At the same time, exotic final states also offer opportunities for improvement: examples include a hard photon in $X_{5/3}\rightarrow t\phi^+\rightarrow tW^+\gamma$ decays, and top-rich channels which arise in several exotic $X_{5/3}$ decays.

We consider a realisation of composite Higgs models in the context of $SU(6)/ SO(6)$ symmetry, which features a custodial bi-triplet, two Higgs doublets and dark matter candidates. This model can arise from an underlying gauge-fermion theory. The general vacuum structure is explored using the top partial compositeness to generate a special vacuum characterised by a single angle aligned with the first Higgs doublet. We present the CP and Dark Matter $\mathbb{Z}_2$ parity in two different pNGB bases and analyse the spectra in the absence of tadpoles and tachyons. For the phenomenology, we discuss the constraints from electroweak precision tests and from a potentially light CP-odd singlet (other than the Dark Matter) in the model.

A composite Higgs boson is likely to be accompanied by additional light states generated by the same dynamics. This expectation is substantiated when realising the composite Higgs mechanism by an underlying gauge theory. We review the dynamics of such objects, which may well be the first sign of compositeness at colliders. We also update our previous analysis of the bounds from LHC searches to the latest results, and discuss the projected reach of the High-Luminosity run.

This is the third out of five chapters of the final report [1] of the Workshop on Physics at HL-LHC, and perspectives on HE-LHC [2]. It is devoted to the study of the potential, in the search for Beyond the Standard Model (BSM) physics, of the High Luminosity (HL) phase of the LHC, defined as $3~\mathrm{ab}^{-1}$ of data taken at a centre-of-mass energy of $14~\mathrm{TeV}$, and of a possible future upgrade, the High Energy (HE) LHC, defined as $15~\mathrm{ab}^{-1}$ of data at a centre-of-mass energy of $27~\mathrm{TeV}$. We consider a large variety of new physics models, both in a simplified model fashion and in a more model-dependent one. A long list of contributions from the theory and experimental (ATLAS, CMS, LHCb) communities have been collected and merged together to give a complete, wide, and consistent view of future prospects for BSM physics at the considered colliders. On top of the usual standard candles, such as supersymmetric simplified models and resonances, considered for the evaluation of future collider potentials, this report contains results on dark matter and dark sectors, long lived particles, leptoquarks, sterile neutrinos, axion-like particles, heavy scalars, vector-like quarks, and more. Particular attention is placed, especially in the study of the HL-LHC prospects, to the detector upgrades, the assessment of the future systematic uncertainties, and new experimental techniques. The general conclusion is that the HL-LHC, on top of allowing to extend the present LHC mass and coupling reach by $20-50\%$ on most new physics scenarios, will also be able to constrain, and potentially discover, new physics that is presently unconstrained. Moreover, compared to the HL-LHC, the reach in most observables will generally more than double at the HE-LHC, which may represent a good candidate future facility for a final test of TeV-scale new physics.

We present a novel paradigm that allows to define a composite theory at the electroweak scale that is well defined all the way up to any energy by means of safety in the UV. The theory flows from a complete UV fixed point to an IR fixed point for the strong dynamics (which gives the desired walking) before generating a mass gap at the TeV scale. We discuss two models featuring a composite Higgs, Dark Matter and partial compositeness for all SM fermions. The UV theories can also be embedded in a Pati-Salam partial unification, thus removing the instability generated by the $\mbox{U}(1)$ running. Finally, we find a Dark Matter candidate still allowed at masses of $260$ GeV, or $1.5 \sim 2$ TeV, where the latter mass range will be covered by next generation direct detection experiments.

We propose simulation strategies for single production of third generation vector-like quarks at the LHC, implementing next-to-leading-order corrections in QCD and studying in detail their effect on cross sections and differential distributions. We also investigate the differences and the relative incertitudes induced by the use of the Four-Flavour Number Scheme ${\it versus}$ the Five-Flavour Number Scheme. As a phenomenological illustration, we concentrate on the production of vector-like quarks coupling to the third generation of the Standard Model in association with a jet and assuming standard couplings to gauge and Higgs bosons.

We discuss the phenomenology associated with a resonant monotop collider signal, i.e. a signal in which a single top quark is resonantly produced in association with missing energy through an s-channel scalar exchange. We study both the bounds originating from dedicated monotop searches performed by the ATLAS and CMS experiments, and the constraints associated with other processes that could be induced by a new physics context favouring monotop production at colliders. The latter class of constraints includes, in particular, the recasting of analyses from the LHC and the TeVatron. All theoretical calculations are performed at the next-to-leading order accuracy in QCD, and we finally combine all results to establish the present limits on the parameter space and test the relevance of the monotop signal at the LHC Run 2.

We show that the presence of a lightish scalar resonance, $\sigma$, that mixes with the composite Goldstone-Higgs boson can relax the typical bounds found in this class of models. This mechanism, inbred in models with a walking dynamics above the condensation scale, allows for a low compositeness scale $f \gtrsim 400$ GeV, corresponding to a misalignment angle $\sin\theta \lesssim 0.6$, contrary to the common lore of a smaller angle. According to recent lattice results, the light $\sigma$ emerges thanks to a near-conformal phase above the condensation scale, consistent to the requirements from flavour physics. We study this effect in a general way, showing that it appears in all cosets emerging from an underlying gauge-fermion dynamics, in the presence of top partial compositeness. The scenario is testable both on the Lattice and experimentally, as it requires the presence of a second broad Higgs-like resonance, below 1 TeV, that can be revealed at the LHC in the $ZZ$ and $t\bar{t}$ channels.

In this work we present a simple extension of the Standard Model that contains, as the only new physics component, a massive spin-one matter field in the adjoint representation of $SU(2)_{L}$. In order to be consistent with perturbative unitarity, the vector field must be odd under a $Z_{2}$ symmetry. Radiative corrections make the neutral component of the triplet ($V^{0}$) slightly lighter than the charged ones. We show that $V^{0}$ can be the dark matter particle while satisfying all current bounds if it has a mass between $2.8$ and $3.8$ TeV. We present the current limit on the model parameter space from highly complementary experimental constraints including dark matter relic density measurement, dark matter direct and indirect detection searches, LHC data on Higgs couplings to photons and LHC data on disappearing track searches. We show that the two-dimensional parameter space can be substantially covered by disappearing track searches at a future 100 TeV hadron collider, which will probe DM mass upto about 1.2 TeV.

Composite Higgs models based on SU(5)/SO(5) are characterised by the presence of custodial triplets, like the Georgi-Machacek model. We classify all the operators giving rise to the top mass and Higgs potential in presence of fermion partial compositeness, with top partners in two-index representations of SU(5). A detailed study of each operator allows us to find correlations in the couplings of Higgs and non-Higgs pseudo-Nambu-Goldstone bosons, which depend only on one, two or three independent parameters. We also analyse the Higgs potential, finding that a misalignment along the custodial invariant triplet direction is forbidden by CP conservation. Avoiding custodial breaking allows us to select a handful of feasible models, which feature universal patterns in the scalar masses related to their transformation properties under the custodial symmetry. Finally, we briefly study the LHC phenomenology of the scalars, which are always below 1 TeV even for multi-TeV condensation scales, and find promising same-sign lepton final states enriched by hard photons.

The existence of new vector-like quarks is often predicted by models of new physics beyond the Standard Model, and the development of discovery strategies at colliders is the object of an intense effort from the high-energy community. Our analysis aims at identifying the constraints on and peculiar signatures of simplified scenarios containing \textittwo vector-like quark doublets mixing with \textitany of the SM quark generations. This scenario is a necessary ingredient of a broad class of theoretically motivated constructions. We focus on the two charge $2/3$ states $t_{1,2}^\prime$ that, due to their peculiar mixing patterns, feature new production and decay modes that are not searched for at the LHC: single production of the heavier state can dominate over the light one, while pair production via electroweak interactions overcomes the QCD one for masses at the TeV scale.

We present the activities of the `New Physics' working group for the `Physics at TeV Colliders' workshop (Les Houches, France, 5--23 June, 2017). Our report includes new physics studies connected with the Higgs boson and its properties, direct search strategies, reinterpretation of the LHC results in the building of viable models and new computational tool developments.

Many standard model extensions that address the hierarchy problem contain Dirac-fermion partners of the top quark, which are typically expected around the TeV scale. Searches for these vector-like quarks mostly focus on their decay into electroweak gauge bosons and Higgs plus a standard model quark. In this article, backed by models of composite Higgs, we propose a set of simplified scenarios, with effective Lagrangians and benchmarks, that include more exotic decay channels, which modify the search strategies and affect the bounds. Analysing several classes of underlying models, we show that exotic decays are the norm and commonly appear with significant rates. All these models contain light new scalars that couple to top partners with charge $5/3$, $2/3$, and $-1/3$.

We provide a general classification of template operators, up to next-to-leading order, that appear in chiral perturbation theories based on the two flavour patterns of spontaneous symmetry breaking SU($N_F$)/Sp($N_F$) and SU($N_F$)/SO($N_F$). All possible explicit-breaking sources parametrised by spurions transforming in the fundamental and in the two-index representations of the flavour symmetry are included. While our general framework can be applied to any model of strong dynamics, we specialise to composite-Higgs models, where the main explicit breaking sources are a current mass, the gauging of flavour symmetries, and the Yukawa couplings (for the top). For the top, we consider both bilinear couplings and linear ones a la partial compositeness. Our templates provide a basis for lattice calculations in specific models. As a special example, we consider the SU(4)/Sp(4)$\cong$ SO(6)/SO(5) pattern which corresponds to the minimal fundamental composite-Higgs model. We further revisit issues related to the misalignment of the vacuum. In particular, we shed light on the physical properties of the singlet $\eta$, showing that it cannot develop a vacuum expectation value without explicit CP violation in the underlying theory.

A light pseudo-scalar that is copiously produced at the LHC may still be allowed by present searches. While masses above 65 GeV are effectively covered by di-photon searches, the lower mass window can be tested by a new search for boosted di-tau resonances. We test this strategy on a set of composite Higgs models with top partial compositeness, where most models can be probed with an integrated luminosity below 300 fb$^{-1}$.

The unification of gauge and top Yukawa couplings is an attractive feature of gauge-Higgs unification models in extra-dimensions. This feature is usually considered difficult to obtain based on simple group theory analyses. We reconsider a minimal toy model including the renormalisation group running at one loop. Our results show that the gauge couplings unify asymptotically at high energies, and that this may result from the presence of an UV fixed point. The Yukawa coupling in our toy model is enhanced at low energies, showing that a genuine unification of gauge and Yukawa couplings may be achieved.

Building upon the fundamental partial compositeness framework we provide consistent and complete composite extensions of the standard model. These are used to determine the effective operators emerging at the electroweak scale in terms of the standard model fields upon consistently integrating out the heavy composite dynamics. We exhibit the first effective field theories matching these complete composite theories of flavour and analyse their physical consequences for the third generation quarks. Relations with other approaches, ranging from effective analyses for partial compositeness to extra dimensions as well as purely fermionic extensions, are briefly discussed. Our methodology is applicable to any composite theory of dynamical electroweak symmetry breaking featuring a complete theory of flavour.

We investigate Higgs-boson pair production at the LHC when the final state system arises from decays of vector-like quarks coupling to the Higgs boson and the Standard Model quarks. Our phenomenological study includes next-to-leading-order QCD corrections, which are important to guarantee accurate predictions, and focuses on a detailed analysis of a di-Higgs signal in the four $b$-jet channel. Whereas existing Run II CMS and ATLAS analyses are not specifically designed for probing non-resonant, vector-like-quark induced, di-Higgs production, we show that they nevertheless offer some potential for these modes. We then investigate the possibility of distinguishing between the various di-Higgs production mechanisms by exploiting the kinematic properties of the signal.

We investigate the possibility that Dark Matter arises as a composite state of a fundamental confining dynamics, together with the Higgs boson. We focus on the minimal SU(4)$\times$SU(4)/SU(4) model which has both a Dark Matter and a Higgs candidates arising as pseudo-Nambu-Goldstone bosons. At the same time, a simple underlying gauge-fermion theory can be defined providing an existence proof of, and useful constraints on, the effective field theory description. We focus on the parameter space where the Dark Matter candidate is mostly a gauge singlet. We present a complete calculation of its relic abundance and find preferred masses between 500 GeV to a few TeV. Direct Dark Matter detection already probes part of the parameter space, ruling out masses above 1 TeV, while Indirect Detection is relevant only if non-thermal production is assumed. The prospects for detection of the odd composite scalars at the LHC are also established.

The inert Two Higgs Doublet Model (i2HDM) is a theoretically well-motivated example of a minimal consistent Dark Matter(DM) model which provides mono-jet, mono-Z, mono-Higgs and Vector-Boson-Fusion+Missing Transverse Momentum signatures at the LHC, complemented by signals in direct and indirect DM search experiments. In this paper we have performed a detailed analysis of the constraints in the full 5D parameter space of the i2HDM, coming from perturbativity, unitarity, electroweak precision data, Higgs data from LHC, DM relic density, direct/indirect DM detection and LHC mono-jet analysis, as well as implications of experimental LHC studies on disappearing charged tracks relevant to high DM mass region. We demonstrate the complementarity of the above constraints and present projections for future LHC data and direct DM detection experiments to probe further i2HDM parameter space. The model is implemented into the CalcHEP and micrOMEGAs packages, which are publicly available at the HEPMDB database, and is ready for a further exploration in the context of the LHC, relic density and DM direct detection.

Composite Higgs Models are often constructed including fermionic top partners with a mass around the TeV scale, with the top partners playing the role of stabilizing the Higgs potential and enforcing partial compositeness for the top quark. A class of models of this kind can be formulated in terms of fermionic strongly coupled gauge theories. A common feature they all share is the presence of specific additional scalar resonances, namely two neutral singlets and a colored octet, described by a simple effective Lagrangian. We study the phenomenology of these scalars, both in a model independent and model dependent way, including the bounds from all the available searches in the relevant channels with di-boson and di-top final states. We develop a generic framework which can be used to constrain any model containing pseudo-scalar singlets or octets. Using it, we find that such signatures provide strong bounds on the compositeness scale complementary to the traditional EWPT and Higgs couplings deviations. In many cases a relatively light scalar can be on the verge of discovery as a first sign of new physics.

We consider present constraints on Two Higgs Doublet Models, both from the LHC at Run 1 and from other sources in order to explore the possibility of constraining a neutral scalar or pseudo-scalar particle lighter than the 125 GeV Higgs boson. Such a lighter particle is not yet completely excluded by present data. We show with a simplified analysis that some new constraints could be obtained at the LHC if such a search is performed by the experimental collaborations, which we therefore encourage to continue carrying out light diphoton resonance searches at $\sqrt{s}=$ 13 TeV in the context of Two Higgs Doublet Models.

We present the activities of the 'New Physics' working group for the 'Physics at TeV Colliders' workshop (Les Houches, France, 1-19 June, 2015). Our report includes new physics studies connected with the Higgs boson and its properties, direct search strategies, reinterpretation of the LHC results in the building of viable models and new computational tool developments. Important signatures for searches for natural new physics at the LHC and new assessments of the interplay between direct dark matter searches and the LHC are also considered.