We show that QCD instantons can generate large effects at small length scales in the ultraviolet in standard composite Higgs models that utilise partial compositeness. This has important implications for possible solutions of the strong CP problem in these models. First we show that in the simplest known UV completions of composite Higgs models, if an axion is also present, it can have a mass much larger than the usual QCD axion. Even more remarkable is the case where there are no axions, but the strong CP problem can be solved by generating the up quark mass entirely from the contribution of instantons thus reviving the massless up-quark solution for these models. In both cases no additional field content is required apart from what is required to realise partial compositeness.
A self-consistent ansatz is presented for a four-dimensional euclidean solution (instanton) in the vacuum sector of constrained SU(2) Yang-Mills-Higgs theory.
Self-consistent Ansaetze are presented for the left- and right-handed isodoublet fermion zero-modes of the constrained instanton Istar in the vacuum sector of euclidean SU(2) Yang-Mills-Higgs theory. These left- and right-handed fermion wave functions do not coincide and, most likely, have maxima at different positions. This may be important for the fermion zero-mode contribution to the euclidean 4-point Green's function in chiral Yang-Mills-Higgs theory and the high-energy behaviour of fermion-fermion scattering processes.
We present an evaluation of the fluctuation determinant which appears as a prefactor in the instanton transition rate for the two-dimensional Abelian Higgs model. The corrections are found to change the rate at most by a factor of 2 for 0.4 < M_W/M_H < 2.0.
Two-dimensional Abelian Higgs model is considered. It is shown that Higgs mechanism of the gauge bosons masses generating is broken in presence of instantons. It is supposed that discussion can be generalized into the standard model of electroweak interactions.
The properties of periodic instanton solutions of the classical SU(2) gauge theory with a Higgs doublet field are described analytically at low energies, and found numerically for all energies up to and beyond the sphaleron energy. Interesting new classes of bifurcating complex periodic instanton solutions to the Yang-Mills-Higgs equations are described.
We solve numerically for periodic, spherically symmetric, classical solutions of SU(2)-Higgs theory in four-dimensional Euclidean space. In the limit of short periods the solutions approach tiny instanton-anti-instanton superpositions while, for longer periods, the solutions merge with the static sphaleron. A previously predicted bifurcation point, where two branches of periodic solutions meet, appears for Higgs boson masses larger than $3.091 M_W$.
We consider 't Hooft-Polyakov monopole (TPM) as a topological soliton in the 5-dimensional (5D) theory of gauge-Higgs unification. This scenario provides a very natural framework to incorporate the TPM, since the adjoint scalar is builtin as the extra-space component of higher dimensional gauge field. In the process of the analysis, we realize that the condition to be satisfied by the Bogomolny-Prasad-Sommerfield (BPS) state of TPM, the BPS monopole, is equivalent to an (anti-)self-dual condition for the higher dimensional gauge field. This observation, in turn, suggests the presence of instan…
We clarify relations among topological solitons in various dimensions: a domain wall, non-Abelian vortex, magnetic monopole and Yang-Mills instanton, together with a (non-Abelian) sine-Gordon soliton, baby Skyrmion (lump) and Skyrmion. We construct a composite configuration consisting of a domain wall, vortex, magnetic monopole and Yang-Mills instanton (wall-vortex-monopole-instanton) using the effective theory technique or moduli approximation. Removing some solitons from such a composite, we obtain all possible composite solitons in the form of solitons within a soliton, including all the pr…
The one-loop fermionic contribution to the probability of an instanton transition with fermion number violation is calculated in the chiral Abelian Higgs model in 1+1 dimensions, where the fermions have a Yukawa coupling to the scalar field. The dependence of the determinant on fermionic, scalar and vector mass is determined. We show in detail how to renormalize the fermionic determinant in partial wave analysis, which is convenient for computations.
The fundamental Higgs doublet may be replaced in the Standard Model by certain non-perturbative four-quark interactions, whose effect is to induce a composite Higgs sector responsible for electroweak symmetry breaking. A simple composite two-Higgs-doublet model is presented. The four-quark interactions arise naturally if there are either extra spatial dimensions or larger gauge symmetries at a multi-TeV scale. Some theoretical and phenomenological implications of these scenarios are discussed.
We study electroweak symmetry breaking in minimal composite Higgs models $SU(4)/Sp(4)$ with purely fermionic UV completions based on a confining Hypercolor gauge group and find that the extra Higgs potential from the underlying preon mass can destruct the correlation between the mass of Higgs and composite partners. Thus the composite partners can be very heavy for successful electroweak symmetry breaking without enhancing the separation between the new physical scale and Higgs VEV. So this kind of model can be easily realized by ordinary strong dynamics theories without artificial assumptions…
Yang-Mills instantons in a pure Yang-Mills theory in four Euclidean space can be promoted to particle-like topological solitons in d=4+1 dimensional space-time. When coupled to Higgs fields, they transform themselves in the Higgs phase into Skyrmions, lumps and sine-Gordon kinks, with trapped inside a non-Abelian domain wall, non-Abelian vortex and monopole string, respectively. Here, we point out that a closed monopole string, non-Abelian vortex sheet and non-Abelian domain wall in $S^1$, $S^2$ and $S^3$ shapes, respectively, are all Yang-Mills instantons if their $S^1$, $S^2$ and $S^3$ modul…
We study the consequences of combining SUSY with a pseudo Nambu-Goldstone boson Higgs coming from an SO(5)/SO(4) coset and partial compositeness. In particular, we focus on how electroweak symmetry breaking and the Higgs mass are reproduced in models where the symmetry SO(5) is linearly realized. The global symmetry forbids tree-level contributions to the Higgs potential coming from D-terms, differently from what happens in most of the SUSY little-Higgs constructions. While the stops are generally heavy, light fermion top partners below 1 TeV are predicted. In contrast to what happens in non-S…
In this talk I argue that a light techni-dilaton exists in models of walking technicolor near the conformal window. The light techni-dilaton then mixes with the composite Higgs, which is predicted to be narrow and light in walking technicolor models. It is an interesting possibility that the newly discovered boson at LHC might be a mixed state of techni-dilaton and the composite Higgs.
We examine the (softly broken) supersymmetric gauge-Higgs-Yukawa theories satisfying the compositeness conditions at a certain scale. In these theories the Higgs superfields can be regarded as the chiral composite fields. It is found that there are the fundamental theories, which contain the dimension 5 interactions and the hard SUSY breaking in perturbation, turn to be renormalizable and also softly broken theories in the nonperturbative framework. The soft SUSY breaking parameters as well as the Yukawa coupling in the corresponding gauge-Higgs-Yukawa theories are restricted by the renormaliz…
We present a novel realization of a composite Higgs, which can naturally produce top partners above the current LHC bounds without increasing the tuning above 10%. The essential ingredients are softened breaking of the Higgs shift symmetry as well as maximal symmetry, which turn out to perfectly complement each other. The 5D realization of this model is particularly simple: universal UV and IR boundary conditions for the bulk fermions containing the SM fields will cure the problems of existing holographic composite Higgs models and provide a complete viable model for a naturally light Higgs wi…
We consider four-dimensional UV descriptions of composite Higgs models without elementary scalars, in which four-fermion interactions are introduced to an underlying gauge theory like in the gauged NJL model. When the anomalous dimension of the fermion bilinear is large, these interactions drive the spontaneous global symmetry breaking in the model, with the Higgs identified as a Nambu-Goldstone boson. The UV descriptions support composite top partner operators, also with large anomalous dimensions, thereby providing an explicit realisation of the idea of partial compositeness. In particular, …
We find the exchange symmetry between left and right handed top quark in composite Higgs model with partial compositeness is efficient to soften the Higgs potential and reduce fine tuning. This symmetry can keep the Higgs potential in top sector invariant under trigonometric parity $\sin (h/f) \leftrightarrow \cos (h/f)$ and thus the Higgs quadratic divergences can be completely cancelled, resulting a UV insensitive Higgs potential. We explicitly construct the minimal left-right symmetric model based on coset space $SO(6)/SO(5)$ which is locally isomorphic to $SU(4)/Sp(4)$ and thus has well de…
The generation of gauge--dependent fermion vacuum condensates in Yang--Mills theory would dynamically break the gauge symmetry and thus provide an alternative to the Higgs mechanism in unified theories. We explore a simple example: instanton-induced quark pair (diquark) condensation in QCD with 2 flavors and $N_c$ colors. We do find diquark condensates in the vacuum, but only for $N_c = 2$, where they are equivalent to the standard quark-antiquark condensate. At $N_c \geq 3$ diquark condensates exist as meta--stable saddle points of the instanton-induced effective QCD action and may strongly a…
We study the idea of a composite Higgs in the framework of a five-dimensional AdS theory. We present the minimal model of the Higgs as a pseudo-Goldstone boson in which electroweak symmetry is broken dynamically via top loop effects, all flavour problems are solved, and contributions to electroweak precision observables are below experimental bounds. Since the 5D theory is weakly coupled, we are able to fully determine the Higgs potential and other physical quantities. The lightest resonances are expected to have a mass around 2 TeV and should be discovered at the LHC. The top sector is mostly…
We consider composite two-Higgs doublet models based on gauge-Yukawa theories with strongly interacting fermions generating the top-bottom mass hierarchy. The model features a single "universal" Higgs-Yukawa coupling, $ g $, which is identified with the top quark $ g\equiv g_t \sim \mathcal{O}(1) $. The top-bottom mass hierarchy arises by soft breaking of a $ \mathbb{Z}_2 $ symmetry by a condensate of strongly interacting fermions. A mass splitting between vector-like masses of the confined techni-fermions controls this top-bottom mass hierarchy. This mechanism can be present in a variety of m…
We describe a concrete, predictive incarnation of the general paradigm of a composite Higgs boson, which provides a valid alternative to the standard holographic models in five space-time dimensions. Differently from the latter, our model is four-dimensional and simple enough to be implemented in an event generator for collider studies. The model is inspired by dimensional deconstruction and hence it retains useful features of the five-dimensional scenario, in particular, the Higgs potential is finite and calculable. Therefore our setup, in spite of being simple, provides a complete descriptio…
We propose a four dimensional description of Composite Higgs Models which represents a complete framework for the physics of the Higgs as a pseudo-Nambu-Goldstone boson. Our setup captures all the relevant features of 5D models and more in general of composite Higgs models with partial compositeness. We focus on the minimal scenario where we include a single multiplet of resonances of the composite sector, as these will be the only degrees of freedom which might be accessible at the LHC. This turns out to be sufficient to compute the effective potential and derive phenomenological consequences…
We propose a novel mechanism in composite models that provides self-interacting dark matter along with the Higgs itself as composite particles, alleviating the Standard Model naturalness problem and explaining small-scale discrepancies such as the core-cusp and "too big to fail" problems. These dark matter candidates are stable due to global U(1) symmetries of the composite dynamics and their strong self-interactions are created by the novel mechanism based on top-quark partial compositeness. The relic density of the dark matter candidates is particle anti-particle symmetric and due to thermal…
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 sc…
We construct UV completions of bottom-up models with a pseudo Nambu-Goldstone Boson (NGB) composite Higgs and partial compositeness, admitting a weakly coupled description of the composite sector. This is identified as the low energy description of an SO(N) supersymmetric gauge theory with matter fields in the fundamental of the group. The Higgs is a NGB associated to an SO(5)/SO(4) coset of a global symmetry group and is identified with certain components of matter fields in a Seiberg dual description of the theory. The Standard Model (SM) gauge fields are obtained by gauging a subgroup of th…
We present a novel class of calculable four dimensional composite pseudo-Goldstone boson Higgs models based on symmetric G/H coset spaces which contain a Higgs-parity operator V as well as a linear representation $Σ'$ for the Goldstone bosons. For such cosets the low-energy effective Lagrangian for the Standard Model fields can have an enhanced global symmetry which we call the maximal symmetry. We show that such a maximally symmetric case leads to a finite and fully calculable Higgs potential, which also minimizes the tuning by eliminating double tuning and reducing the Higgs mass. We present…
Our goal is to discover possible new 4-dimensional euclidean solutions (instantons) in fundamental SU(2) Yang-Mills-Higgs theory, with a constraint added to prevent collapse of the scale. We show that, most likely, there exists one particular new constrained instanton (\Istar) with vanishing Pontryagin index. This is based on a topological argument that involves the construction of a non-contractible loop of 4-dimensional configurations with a certain upperbound on the action, which we establish numerically. We expect \Istar to be the lowest action non-trivial solution in the vacuum sector of …
We use semiclassical methods to calculate the probability of inducing a change of topology via a high-energy collision in the SU(2)-Higgs theory. This probability is determined by a complex solution to a classical boundary value problem on a contour in the complex time plane. In the case of small particle number it is the probability of instanton-like processes in particle collisions. We obtain numerically configurations with the correct topological features and expected properties in the complex time plane. Our work demonstrates the feasibility of the numerical approach to the calculation of …
We consider a possibility that electroweak symmetry breaking (EWSB) is triggered by a fundamental Higgs and a composite Higgs arising in a dynamical symmetry breaking mechanism induced by a new strong dynamics. The resulting Higgs sector is a partially composite two-Higgs doublet model with specific boundary conditions on the coupling and mass parameters originating at a compositeness scale. The phenomenology of this model is discussed including the collider phenomenology at LHC and ILC.
In this talk, we report unitarity constraints and phenomenological studies at the Large Hadron Collider for the extra Higgs bosons of a Composite 2-Higgs Doublet Model.
One of the solutions to the hierarchy problem of the Standard Model is the composite Higgs scenario, where the Higgs emerges as a composite pseudo-Nambu-Goldstone boson. In this work we present and study the basic characteristics of the composite Higgs scenario, based on the $SO(5)/SO(4)$ and $SO(6)/SO(5)$ cosets. We construct their effective Lagrangians through the Callan-Coleman-Wess-Zumino construction. The first coset does not differ much from the Standard Model and the second contains a singlet scalar in addition to the Higgs doublet. In these models we study the gauge sector, the fermion…
We show that instantons violate a supersymmetric identity in a classically supersymmetric Higgs model with no massless fermions. This anomalous breaking arises because the correct perturbative expansion in the instanton sector is not supersymmetric. The attempt to construct a manifestly supersymmetric expansion generates infra-red divergences.
Pairs of standard model fermions can annihilate to produce mini black holes with gauge quantum numbers of the Higgs boson at $M_{Planck}$. This leads to a Nambu-Jona-Lasinio model at the Planck scale with strong coupling which binds fermion pairs into Higgs fields. At critical coupling the renormalization group dresses these objects, which then descend in scale to emerge as OBSERVABLE boundstate Higgs bosons at low energies, and we obtain the multi-Higgs spectrum of a "scalar democracy." The observed Higgs boson is a gravitationally bound $\bar{t}t$ composite. Sequential states may be seen at …
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.
In composite Higgs models light fermionic top partners often play an important role in obtaining a 126 GeV Higgs mass. The presence of these top partners implies that coloured vector mesons, or massive gluon partners, most likely exist. Since the coupling between the top partners and gluon partners can be large there are then sizeable two-loop contributions to the composite Higgs mass. We compute the radiative correction to the Higgs mass from a gluon partner in the minimal composite Higgs model and show that the Higgs mass is in fact reduced. This allows the top partner masses to be increased…
The lattice data on the instanton size distribution suggest an additional O($ρ^2)$ action. The small-$ρ$ effect O($ρ^4)$ predicted by the Operator Product Expansion (OPE) is not observed. Similar deviations are also found for non-perturbative response to a small static color dipoles: it is O(r) not O(r$^2$). We suggest that small instanton radii in the QCD vacuum and small radii of the QCD strings (to which this observation relates) are consequences of the same phenomenon: a very robust dual superconductivity in the QCD vacuum, with relatively large Higgs VEV and surprisingly large Higgs mass.
If the Higgs boson is composite, signs of this compositeness should appear via a formfactor-like suppression of Higgs scattering cross sections at momentum transfers above the compositeness scale. We explore this by computing the cross section for e+e- ---> ZH (Higgsstrahlung) in a warped five-dimensional gauge-Higgs unification model known as the Minimal Composite Higgs Model (MCHM). We observe that the Higgsstrahlung cross section in the MCHM is strongly suppressed compared to that in the Standard Model at center-of-mass energies above the scale of the first Kaluza-Klein excitations, due to …
Composite Higgs models provide an attractive solution to the hierarchy problem. However, many realistic models suffer from tuning problems in the Higgs potential. There are often large contributions from the UV dynamics of the composite resonances to the Higgs potential, and tuning between the quadratic term and the quartic term is required to separate the electroweak breaking scale and the compositeness scale. We consider a composite Higgs model based on the $SU(6)/Sp(6)$ coset, where an enhanced symmetry on the fermion resonances can minimize the Higgs quadratic term. Moreover, a Higgs quart…
We explore the Higgs couplings to gauge bosons in the minimal $SO(5)/SO(4)$ 4D composite Higgs model. The pions scatterings put unitary constraints on the couplings and therefore determine the branch ratios of various Higgs decays. Through fine tuning the parameters, enhancement of Higgs to diphoton rate is possible to be achieved with the existence of vector meson fields.
In the extra dimensional scenarios with gauge fields in the bulk, the Kaluza-Klein (KK) gauge bosons can induce Nambu-Jona-Lasinio (NJL) type attractive four-fermion interactions, which can break electroweak symmetry dynamically with accompanying composite Higgs fields. We consider a possibility that electroweak symmetry breaking (EWSB) is triggered by both a fundamental Higgs and a composite Higgs arising in a dynamical symmetry breaking mechanism induced by a new strong dynamics. The resulting Higgs sector is a partially composite two-Higgs doublet model with specific boundary conditions on …
In this note we analyse the prospects of a future electron-positron collider in testing a particular realisation of a composite Higgs model encompassing partial compositeness, namely, the 4-Dimensional Composite Higgs Model. We study the main Higgs production channels for three possible energy stages and different luminosity options of such a machine and confront our results to the expected experimental accuracies in the various Higgs decay channels accessible herein and, for comparison, also at the Large Hadron Collider.
The composite Higgs scenario, in which the Higgs emerges as a composite pseudo-Nambu-Goldstone boson, is extensively reviewed in these Notes. The material is presented in a pedagogical fashion, with great emphasis on the conceptual and technical foundations of the construction. A comprehensive summary of the flavor, collider and electroweak precision phenomenology is also presented.
In the extra dimensional scenarios with gauge fields in the bulk, the Kaluza-Klein (KK) gauge bosons can induce Nambu-Jona-Lasinio (NJL) type attractive four-fermion interactions, which can break electroweak symmetry dynamically with accompanying composite Higgs fields. We consider a possibility that electroweak symmetry breaking (EWSB) is triggered by both a fundamental Higgs and a composite Higgs arising in a dynamical symmetry breaking mechanism induced by a new strong dynamics. The resulting Higgs sector is a partially composite two-Higgs doublet model with specific boundary conditions on …
In the context of Composite Higgs Models we consider the realisation of an extended Higgs sector with two Higgs doublets arising as pseudo Nambu-Goldstone bosons from a $\textrm{SO}(6) \to \textrm{SO}(4) \times \textrm{SO}(2)$ breaking. The properties of the Higgses are obtained in terms of the fundamental parameters of the composite sector, such as masses, Yukawa and gauge couplings of the new spin-1/2 and spin-1 resonances. After computing the Higgs potential from the explicit breaking of the $\textrm{SO}(6)$ global symmetry by the partial compositeness of fermions and gauge bosons, the main…
In composite Higgs models the Higgs boson arises as a pseudo-Goldstone boson from a strongly-interacting sector. Fermion mass generation is possible through partial compositeness accompanied by the appearance of new heavy fermionic resonances. The Higgs couplings to the Standard Model (SM) particles and between the Higgs bosons themselves are modified with respect to the SM. Higgs pair production is sensitive to the trilinear Higgs self-coupling but also to anomalous couplings like the novel 2-Higgs-2-fermion coupling emerging in composite Higgs models. The QCD corrections to SM Higgs boson pa…
We present a new class of composite Higgs models where an adjustable tree-level Higgs quartic coupling allows for a significant reduction in the tuning of the Higgs potential. Our 5D warped space implementation is the first example of a holographic composite Higgs model with a tree-level quartic. It is inspired by a 6D model where the quartic originates from the Tr [A_5,A_6]^2 term of the gauge field strength, the same model that led to the original little Higgs construction of Arkani-Hamed, Cohen, and Georgi. Beyond the reduction of the tuning and the standard composite Higgs signatures, the …
Composite Higgs models involving partial compositeness of Standard Model fermions typically require the introduction of fermionic partners which are relatively light in realistic scenarios. In this paper, we analyze the role of these light custodian fermions in the phenomenology of the composite Higgs models and show that they significantly modify couplings of the Higgs field. We focus on the coupling to gluons in particular, which is of central importance for Higgs production at the LHC. We show that this coupling can be increased as well as decreased depending on the SM fermion embedding in …
We explore the Higgs-Z-photon coupling in the Minimal Composite Higgs Model with vector and axial resonances. The electroweak precision measurement, i.e. S and T, is estimated for this model. We calculate the signal strength for Higgs decay into Z-photon and notable enhancement is found in certain EWPT allowed parameter region.
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 an…
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.
