We determine the current status of the fundamental composite electroweak dynamics paradigm after the discovery of the Higgs boson at the Large Hadron Collider experiments. Our analysis serves as universal and minimal template for a wide class of models with the two limits in parameter space being composite Goldstone Higgs models and Technicolor. This is possible because of the existence of a unified description, both at the effective and fundamental Lagrangian levels, of models of composite Higgs dynamics where the Higgs boson itself can emerge, depending on the way the electroweak symmetry is embedded, either as a pseudo-Goldstone boson or as a massive excitation of the condensate. We constrain the available parameter space at the effective Lagrangian level. We show that a wide class of models of fundamental composite electroweak dynamics, including Technicolor, are compatible with experiments. The results are relevant for future searches of a fundamental composite nature of the Higgs mechanism at the Large Hadron Collider.
I review the status of theoretical calculations relevant for electroweak physics at the Tevatron and LHC and discuss future directions. I also give a brief overview of current electroweak data and discuss future expectations.
A talk presented at "String Gravity and Physics at the Planck Energy Scale", Erice, September 1995, summarizing the current understanding of the electroweak phase transition.
I review recent progress on the electroweak phase transition and baryogenesis, focusing on the minimal supersymmetric standard model as the source of new physics.
We review the status of electroweak radiative corrections to top-pair production at a Linear Collider well above the production threshold. We describe the Fortran package topfit and present numerical results at sqrt(s) = 500 GeV, 1 TeV, and 3 TeV.
We match the electroweak chiral Lagrangian with two singlet scalars to the next-to-minimal composite Higgs model with $ SO(6)/SO(5) $ coset structure and extract the scalar divergences to one loop. Assuming the additional scalar to be heavy, we integrate it out and perform a matching to the well-established electroweak chiral Lagrangian with one light Higgs.
We update our analysis of technicolour theories with techniquarks in higher dimensional representations of the technicolour gauge group in the light of the new electroweak precision data on the Z resonance.
The lightest electroweak baryon as a topological object is investigated by using a general effective Lagrangian of composite electroweak symmetry breaking and the spin-independent electroweak baryon-nucleon scattering cross section is calculated. We explicitly show the masses of the electroweak baryons and the cross section as functions of the Peskin-Takeuchi $S$ parameter and the ratio of the masses of axial-vector and vector composite bosons. We find that it is acceptable to regard the electroweak baryon as a dark matter candidate and the even number of technicolor is favored.
We work out simple tree level relations in a top condensate model with dynamical electroweak symmetry breaking. We find that in this picture the mass of the composite Higgs boson at tree level is given by $m_H^2=\frac{m_t^2}{2}$ where $m_t$ is the mass of the top quark.
We study analytically and numerically the bounds imposed by the electroweak precision tests on a minimal composite Higgs model. The model is based on spontaneous SO(5)/SO(4) breaking, so that an approximate custodial symmetry is preserved. The Higgs arises as a pseudo-Goldstone boson at a scale below the electroweak symmetry breaking scale. We show that one can satisfy the electroweak precision constraints without much fine-tuning. This is the case if the left-handed top quark is fully composite, which gives a mass spectrum within the reach of the LHC. However a composite top quark is strongly…
If the electroweak symmetry is broken by some unspecified strong dynamics, composite fermions may exist with definite transformation properties under SU(2)_L x SU(2)_R/SU(2)_{L+R} and may play a role in giving masses by mixing to all the standard quarks and leptons. Assuming this to be the case, we analyze the role of Singlets, Doublets and Triplets in the ElectroWeak Precision Tests and in Flavour Physics. Doublets and Triplets are generically disfavoured. In the Singlet case, we specify the breaking patterns of the flavour group that allow to keep the CKM picture of flavour physics and we di…
In a strong-coupling picture of ElectroWeak Symmetry Breaking, a composite electroweak-neutral state in the TeV mass range, carrying a global (quasi-)conserved charge, makes a plausible Dark Matter (DM) candidate, with the ongoing direct DM searches being precisely sensitive to the expected signals. To exploit the crucial interplay between direct DM searches and the LHC, we consider a composite iso-singlet vector $V$, mixed with the hypercharge gauge field, as the essential mediator of the interaction between the DM particle and the nucleus. Based on a suitable effective chiral Lagrangian, we …
We present a model of electroweak symmetry breaking in a warped extra dimension where electroweak symmetry is broken at the UV (or Planck) scale. An underlying conformal symmetry is broken at the IR (or TeV) scale generating masses for the electroweak gauge bosons without invoking a Higgs mechanism. By the AdS/CFT correspondence the W,Z bosons are identified as composite states of a strongly-coupled gauge theory, suggesting that electroweak symmetry breaking is an emergent phenomenon at the IR scale. The model satisfies electroweak precision tests with reasonable fits to the S and T parameter.…
There are many reasons to believe that there might be new sources of CP-violation beyond the phases of the KM matrix. One of these is the possibility of electroweak baryogenesis. We describe some recent developments in this subject and make some comments on the possibility that the minimal standard model might itself be the origin of the baryon asymmetry. To appear in the Proceedings of the Third KEK Topical Conference on CP Violation, its Implications to Particle Physics and Cosmology, 16--18 November, 1993.
The Electroweak interactions of a strongly coupled gauge theory are discussed with outlook beyond the Standard Model (BSM) under global and gauge anomaly constraints. The theory is built on a minimal massless fermion doublet of the SU(2) BSM flavor group (bsm-flavor) with a confining gauge force at the TeV scale in the two-index symmetric (sextet) representation of the BSM SU(3) color gauge group (bsm-color). The intriguing possibility of near-conformal sextet gauge dynamics could lead to the minimal realization of the composite Higgs mechanism with a light $0^{++}$ scalar, far separated from …
Multi-boson splashes at future colliders from electroweak compositeness
Sorbonne Université & CNRS（索邦大学与法国国家科学研究中心）；Southern Denmark Univ.（南丹麦大学）；Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I（里昂第一大学、法国国家科学研究中心/法国国家粒子物理研究所、IP2I）；University of Johannesburg（约翰内斯堡大学）；Indian Institute of Technology Delhi（德里印度理工学院）；University of Graz（格拉茨大学）
The status of the Standard Model (SM) is reviewed. We emphazize the fact that in spite of the success of the SM for the descrition of the fermionic sector, the status of the bosonic sector (gauge and scalar) suffers from many theoretical deficiencies and from the lack of empirical support. This situation, which leaves room for several types of extensions or alternatives to SM, strongly motivates the pursue of intense efforts for finding hints of New Physics (NP) effects. We present a phenomenological description valid for energies lying below the NP scale. We discuss the indirect constraints e…
In this presentation Gfitter results from the global Standard Model (SM) fit to electroweak precision data are discussed. We have used the latest measurements of m_top and M_W and the most recent results for direct Higgs searches at LEP and Tevatron. We obtain M_H=121^{+17}_{-6} GeV and a 95% CL upper limit of 155 GeV for the SM Higgs mass. The forth-order result for the strong coupling constant is given by alpha_S(M_Z^2)=0.1193 +- 0.0028(exp) +- 0.0001(theo). In addition the electroweak fit has been performed with the top mass determined from the ttbar cross-section as measured at Tevatron.
A composite Higgs boson of 125 GeV mass, only mildly fine-tuned, requires top partners with a semi-perturbative coupling and a mass not greater than about a TeV. We analyze the strong constraints on such picture arising from flavour and electroweak precision tests in models of partial compositeness. We consider different representations for the composite fermions and compare the case of an anarchic flavour structure to models with a U(3)^3 and U(2)^3 flavour symmetry. Although non trivially, some models emerge that look capable of accommodating a 125 GeV Higgs boson with top partners in an int…
The scalar composite representations of the electroweak symmetry group of the Standard Model are exhibited in the case of two generations of quarks. The link between `strong' and `electroweak' eigenstates is investigated, showing that the quark content commonly attributed to pseudoscalar mesons needs to be modified. After doing so, the mechanism suppressing the decays K{+} into Pi{+} Pi{0} with respect to K{short} into Pi{+} Pi{-} is unraveled, without reference to any model of quark spectator or `factorization' hypothesis. The same mechanism is shown to suppress the decays K{long} into two pi…
We present results from the global electroweak fit to precision measurements in the Standard Model (SM). The fit uses the latest theoretical calculations for observables on the $Z$ pole and the $W$ boson mass, yielding precise SM predictions for the effective weak mixing angle and the masses of the $W$ and Higgs bosons, as well as the top quark. We study the impact of the latest measurements on the fit and provide comparisons of the resulting predictions for individual observables with recent measurements.
This talk summarizes the status of the standard model predictions for electroweak precision observables including g-2 for muons, and discusses the status of the standard model and the MSSM in view of the new data.
The current status of the theoretical predictions for the electroweak precision observables M_W, sin^2_theta_eff and m_h within the MSSM is briefly reviewed. The impact of recent electroweak two-loop results to the quantity Delta_rho is analysed and the sensitivity of the electroweak precision observables to the top-quark Yukawa coupling is investigated. Furthermore the level of precision necessary to match the experimental accuracy at the next generation of colliders is discussed.
We address electroweak baryogenesis in the context of composite Higgs models, pointing out that modifications to the Higgs and top quark sectors can play an important role in generating the baryon asymmetry. Our main observation is that composite Higgs models that include a light, gauge singlet scalar in the spectrum [as in the model based on the symmetry breaking pattern SO(6)/SO(5)], provide all necessary ingredients for viable baryogenesis. In particular, the singlet leads to a strongly first-order electroweak phase transition and introduces new sources of CP violation in dimension-five ope…
We study electroweak baryogenesis in the $SO(6)/SO(5)$ composite Higgs model with the third generation quarks being embedded in the $\textbf{20}'$ representation of $SO(6)$. The scalar sector contains one Higgs doublet and one real singlet, and their potential is given by the Coleman-Weinberg potential evaluated from the form factors of the lightest vector and fermion resonances. We show that the resonance masses at $\mathcal{O}(1\sim 10{\rm ~TeV})$ can generate a potential that triggers the strong first-order electroweak phase transition (SFOEWPT). The $CP$ violating phase arising from the di…
Talk given at the XVIII International Symposium on Lepton-Photon Interactions, Hamburg, 1997. 1. Introduction 2. Status of the Data 3. Precision Electroweak Data and the Standard Model 4. A More General Analysis of Electroweak Data 5. The Case for Physics beyond the Standard Model 6. The Search for the Higgs 7. New Physics at HERA? 8. Conclusion
In this paper, we construct an effective model that describes the electroweak symmetry breaking sector by means of composite Higgs-like scalars, following the ideas of Minimal Walking Technicolor (MWT). We argue that, because of the general failure of Extended Technicolor (ETC) to explain the mass of the top quark, it is necessary to introduce two composite Higgs bosons: one of them originated by a MWT-ETC sector and the other one produced by a Topcolor sector. We focus on the phenomenological differences between the light composite Higgs present in our model and the fundamental Higgs boson pr…
We present a comprehensive study of the electroweak phase transition in composite Higgs models, where the Higgs arises from a new, strongly-coupled sector which confines near the TeV scale. This work extends our study in Ref. [1]. We describe the confinement phase transition in terms of the dilaton, the pseudo-Nambu-Goldstone boson of broken conformal invariance of the composite Higgs sector. From the analysis of the joint Higgs-dilaton potential we conclude that in this scenario the electroweak phase transition can naturally be first-order, allowing for electroweak baryogenesis. We then exten…
This talk summarizes topical theoretical work for tests of the electroweak theory and reviews the status of the electroweak Standard Model in view of the recent precision data reported at the 1997 summer conferences.
We provide a unified description, both at the effective and fundamental Lagrangian level, of models of composite Higgs dynamics where the Higgs itself can emerge, depending on the way the electroweak symmetry is embedded, either as a pseudo-Goldstone boson or as a massive excitation of the condensate. We show that, in general, these states mix with repercussions on the electroweak physics and phenomenology. Our results will help clarify the main differences, similarities, benefits and shortcomings of the different ways one can naturally realize a composite nature of the electroweak sector of t…
The mechanism of resonance enhancement of neutrino oscillations in matter and some critical remarks to this mechanism are considered. Using of this resonance mechanism is very important to examine the model of electroweak interactions since the processes induced by this mechanism grow multiply. In contrast to the electromagnetic and strong interactions in weak interactions, $P$-parity is violated therefore a problem of mass generations in the weak interactions is considered (the interaction must be left-right symmetric for mass generations). It is concluded that a possibility of mass generatio…
In electroweak theory without elementary Higgs scalars existence of a solution, which breaks initial symmetry is shown. A composite scalar doublet serves as a substitute for usual Higgs. The mass of the surviving Higgs scalar is predicted to be $M_H = 117 \pm 7 GeV$. The resulting theory contains realistic $W, Z, t$ masses and composite massive Higgs. Parameters used are $g$, $θ_W$, cut-off $Λ\simeq 3500 GeV$ and triple gauge constant $λ_V \simeq -0.034$. Stable nontrivial solution for extra interactions of the Higgs particle gives contribution to muon $g-2$: $Δa = 49.4\cdot 10^{-10}$ that agr…
We derive dispersion relations for the electroweak oblique observables measured at LEP in the context of $SO(5)/SO(4)$ composite Higgs models. It is shown how these relations can be used and must be modified when modeling the spectral functions through a low-energy effective description of the strong dynamics. The dispersion relation for the parameter $ε_3$ is then used to estimate the contribution from spin-1 resonances at the 1-loop level. Finally, it is shown that the sign of the contribution to the $\hat S$ parameter from the lowest-lying spin-1 states is not necessarily positive definite,…
I describe, from the bottom up, a sequence of natural effective field theories. Below a TeV we have the minimal standard model with a light Higgs, and an extra neutral scalar. In the 1-10 TeV region these scalars are part of a multiplet of pseudo Nambu-Goldstone Bosons. Interactions with additional TeV mass scalars, gauge bosons, and vector-like charge 2/3 quarks stabilize the Higgs mass squared parameter without finetuning. Electroweak superconductivity may be determined in this effective theory as a UV insensitive vacuum alignment problem. Above the 10 TeV scale we have strongly coupled new …
We conduct a detailed numerical analysis of the composite pseudo-Nambu-Goldstone Higgs model based on the next-to-minimal coset $\text{SO}(6)/\text{SO}(5)\cong\text{SU}(4)/\text{Sp}(4)$, featuring an additional SM singlet scalar in the spectrum, which we allow to mix with the Higgs boson. We identify regions in parameter space compatible with all current experimental constraints, including radiative electroweak symmetry breaking, flavour physics, and direct searches at colliders. We find the additional scalar, with a mass predicted to be below a TeV, to be virtually unconstrained by current LH…
We investigate theories in which the technifermions in higher dimensional representations of the technicolor gauge group dynamically break the electroweak symmetry of the standard model. For the two-index symmetric representation of the gauge group the lowest number of techniflavors needed to render the underlying gauge theory quasi conformal is two. We confront the models with the recent electroweak precision measurements and demonstrate that the two technicolor theory is a valid candidate for a dynamical breaking of the electroweak symmetry. The electroweak precision measurements provide use…
Recently, a new class of models describing the quark mass hierarchy has been introduced. In this class, while the t quark plays a minor role in electroweak symmetry breaking (EWSB), it is crucial in providing the quark mass hierarchy. In this paper, we analyze the dynamics of a particular model in this class, in which the b' and t' quarks of the fourth family are mostly responsible for dynamical EWSB. The low energy effective theory in this model is derived. It has a clear signature, a 2 + 1 structure of composite Higgs doublets: two nearly degenerate Φ_{b'} and Φ_{t'}, and a heavier top-Higgs…
We study the strong first order electroweak phase transition (SFOEWPT) with the $SO(6)/SO(5)$ composite Higgs model, whose scalar sector contains one Higgs doublet and one real singlet. Six benchmark models are built with fermion embeddings in $\textbf{1}$, $\textbf{6}$, and $\textbf{15}$ of $SO(6)$. We show that SFOEWPT cannot be triggered under the minimal Higgs potential hypothesis, which assumes the scalar potential is dominated by the form factors from the lightest composite resonances. To get a SFOEWPT, the contributions from local operators induced by physics above the cutoff scale are …
We perform a global fit of the parameters of the Standard Model with a sequential fourth generation (SM4) to LHC and Tevatron Higgs data and electroweak precision data. Using several likelihood ratio tests we compare the performance of the SM4 and SM3 at describing the measured data. Since the SM3 and SM4 are not nested (i.e. the SM3 can not be considered as a special case of the SM4 with some parameters fixed) the usual analytical formulae for p-values in likelihood ratio tests do not hold. We thus apply a new method to compute these p-values. For a Higgs mass of 126.5 GeV and fourth-generati…
We construct effective Lagrangians, and corresponding counting schemes, valid to describe the dynamics of the lowest lying large N stable massive composite state emerging in strongly coupled theories. The large N counting rules can now be employed when computing quantum corrections via an effective Lagrangian description. The framework allows for systematic investigations of composite dynamics of non-Goldstone nature. Relevant examples are the lightest glueball states emerging in any Yang-Mills theory. We further apply the effective approach and associated counting scheme to composite models a…
In the context of a strongly coupled Electroweak Symmetry Breaking, composite triplet of heavy vectors belonging to the $SU(2)_{L+R}$ adjoint representation and a composite scalar singlet under $SU(2)_{L+R}$ may arise from a new strong interaction invariant under the global $SU(2)_L\times SU(2)_R$ symmetry, which is spontaneously broken down to $SU(2)_{L+R}$. This thesis consists of two parts. The first part is devoted to the study of the heavy composite vector pair production at the LHC via Vector Boson Fusion and Drell-Yan annihilation under the assumption that the interactions among these h…
We propose a model to describe the low energy physics of partially composite Standard Model, in which the electroweak sector in the Standard Model is weakly coupled to some strong dynamics. The vector resonances in the strong sector are introduced as the effective degrees of freedom, W' and Z', which mixes with the W and Z bosons through the electroweak symmetry breaking. Through the coupling to the strong sector, the Standard Model Higgs boson becomes partially composite, and its properties are modified. We study the constraints from the electroweak precision data and direct searches of W' an…
If the Higgs boson has a composite nature, it might be the 4-dimensional hologram of a gauge field living in a warped extra dimension. In this talk I discuss a minimal, calculable model that passes all electroweak precision tests, included that from Z->bb, and gives a natural account of the electroweak symmetry breaking.
A complete analysis of the electroweak precision observables is performed within a recently proposed minimal composite Higgs model, realized as a 5-dimensional warped compactification. In particular, we compute Z->bb and the one-loop correction to the rho parameter. We find that oblique data can be easily reproduced without a significant amount of tuning in the parameters of the model, while Z->bb imposes a stronger constraint. As a consequence of the latter, some of the new fermionic resonances must have mass around 4 TeV, which corresponds to an electroweak fine tuning of a few percent. Othe…
We consider the scenario where the composite Higgs arising as a pNGB in a two-site model with a non-local term included. Constraints from pion scattering and electroweak precision test are considered. We discuss the effects of composite resonances, in particular the one from composite vector-like fermions, on the oblique parameters. It is noticed that the gluon fusion production of Higgs boson is suppressed with respect to the Standard Model for about $6\%$ after imposing the unitarity and electroweak bounds.
If electroweak symmetry breaking arises via strong dynamics, electroweak precision tests and flavour physics experiments suggest that the minimal model should closely resemble the Standard Model at the LHC. I describe two directions going beyond the minimal model that result in radically different physics at the LHC. One direction extends the Higgs sector and the other involves composite leptoquark states.
I discuss two aspects of the electroweak interactions: the status of the precision measurement of the electroweak parameters and their impact on the Higgs search at future colliders.
We assess current experimental constraints on the bi-doublet + singlet model of top compositeness previously proposed in the literature. This model extends the standard model's spectrum by adding a custodially-embedded vector-like electroweak bi-doublet of quarks and a vector-like electroweak singlet quark. While either of those states alone would produce a model in tension with constraints from precision electroweak data, in combination they can produce a viable model. We show that current precision electroweak data, in the wake of the Higgs discovery, accommodate the model and we explore the…
We present an update of the Standard Model fit to electroweak precision data. We include newest experimental results on the top quark mass, the W mass and width, and the Higgs boson mass bounds from LEP, Tevatron and the LHC. We also include a new determination of the electromagnetic coupling strength at the Z pole. We find for the Higgs boson mass (91 +30 -23) GeV and (120 +12 -5) GeV when not including and including the direct Higgs searches, respectively. From the latter fit we indirectly determine the W mass to be (80.360 +0.014 -0.013) GeV. We exploit the data to determine experimental co…
We provide a simple mechanism for reconciling the direct dark matter experimental results. We consider light asymmetric composite dark matter which scatters off nuclei via Higgs and photon exchange. We demonstrate that the interference between these two channels naturally accommodates the experimental results. We discover that this happens for a compositeness scale of the order of the electroweak. We also provide a model realization based on strong dynamics at the electroweak scale.
Results from the global Standard Model fit to electroweak precision data, including newest Tevatron measurements, are reviewed and discussed. The complete fit using also the constraints from the direct Higgs boson searches yields an upper limit on the Higgs mass of 153 GeV at 95% CL. The top mass is indirectly determined to be (177.2 +10.5 -7.8) GeV and (179.5 +8.8 -5.2) GeV for fits including or not the constraints from the direct Higgs searches, respectively. Using the 3NLO perturbative prediction of the massless QCD Adler function, the strong coupling constant at the Z-mass scale is determi…
We propose a dynamical model with a (2 + 1)-structure of composite Higgs doublets: two nearly degenerate composites of the fourth family quarks t' and b', $Φ_{t^{\prime}} \sim \bar{t^{\prime}}_{R}(t^{\prime},b^{\prime})_L$ and $Φ_{b^{\prime}} \sim \bar{b^{\prime}}_{R}(t^{\prime},b^{\prime})_L$, and a heavier top-Higgs resonance $Φ_t \sim \bar{t}_{R}(t,b)_L$. This model naturally describes both the top quark mass and the electroweak symmetry breaking. Also, a dynamical mechanism providing the quark mass hierarchy can be reflected in the model. The properties of these composites are analyzed in …
