We study the flavor structure of 5D warped models that provide a dual description of a composite pseudo-Goldstone Higgs. We first carefully re-examine the flavor constraints on the mass scale of new physics in the standard Randall-Sundrum-type scenarios, and find that the KK gluon mass should generically be heavier than about 21 TeV. We then compare the flavor structure of the composite Higgs models to those in the RS model. We find new contributions to flavor violation, which while still are suppressed by the RS-GIM mechanism, will enhance the amplitudes of flavor violations. In particular, there is a kinetic mixing term among the SM fields which (although parametrically not enhanced) will make the flavor bounds even more stringent than in RS. This together with the fact that in the pseudo-Goldstone scenario Yukawa couplings are set by a gauge coupling implies the KK gluon mass to be at least about 33 TeV. For both the RS and the composite Higgs models the flavor bounds could be stronger or weaker depending on the assumption on the value of the gluon boundary kinetic term. These strong bounds seem to imply that the fully anarchic approach to flavor in warped extra dimensions is implausible, and there have to be at least some partial flavor symmetries appearing that eliminate part of the sources for flavor violation. We also present complete expressions for the radiatively generated Higgs potential of various 5D implementations of the composite Higgs model, and comment on the 1-5 percent level tuning needed in the top sector to achieve a phenomenologically acceptable vacuum state.
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.
We consider a model of dynamical electroweak symmetry breaking with a partially composite Goldstone Higgs. The model is based on a strongly-interacting fermionic sector coupled to a fundamental scalar sector via Yukawa interactions. The SU(4) x SU(4) global symmetry of these two sectors is broken to a single SU(4) via Yukawa interactions. Electroweak symmetry breaking is dynamically induced by condensation due to the strong interactions in the new fermionic sector which further breaks the global symmetry SU(4) to Sp(4). The Higgs boson arises as a partially composite state which is an exact Go…
We discuss the well-known phenomenon of spontaneous symmetry breaking for a linear sigma model for scalar and pseudoscalar mesons based on the meson composite structure and the normalization of the quantum states. To test our formulation and validate our approach we give another proof of the Goldstone theorem and derive the corresponding mass eigenstates of the theory. We briefly describe the possible wave function of a meson that leads to the adequate mass eigenstates.
This is an introduction to theories where the Higgs is a composite Nambu-Goldstone boson of a new strongly-interacting dynamics not much above the weak scale. A general discussion is presented based on the pattern of global symmetries at low energy, and the analogy with the QCD pion is analyzed. The last part of the lectures shows how a composite Higgs can emerge as the hologram of a 5-dimensional gauge field.
We study the bosonic excitations in the favorite cubic three flavor crystalline LOFF phases of QCD. We calculate in the Ginzburg-Landau approximation the masses of the eight pseudo Nambu-Goldstone Bosons (NGB) present in the low energy theory. We also compute the decay constants of the massless NGB Goldstones associated to superfluidity as well as those of the eight pseudo NGB. Differently from the corresponding situation in the Color-Flavor-Locking phase, we find that meson condensation phases are not expected in the present scenario.
In $\XQM$, a quark can emit Goldstone bosons. The flavor symmetry breaking in the Goldstone boson emission process is used to intepret the nucleon flavor-spin structure. In this paper, we study the inner structure of constituent quarks implied in $\XQM$ caused by the Goldstone boson emission process in nucleon. From a simplified model Hamiltonian derived from $\XQM$, the intrinsic wave functions of constituent quarks are determined. Then the obtained transition probabilities of the emission of Goldstone boson from a quark can give a reasonable interpretation to the flavor symmetry breaking in …
We pursue a possibility that a pseudo-Nambu-Goldstone boson is lurking around or below the intermediate scale. To this end we consider an anomaly-free global flavor symmetry, and construct models where the pseudo-Nambu-Goldstone boson is coupled preferentially to leptons. The experimental and astrophysical bounds derived from couplings to photons and nucleons are significantly relaxed. If sufficiently light, the pseudo-Nambu-Goldstone boson contributes to dark matter, and interestingly, it generally decays into photons through couplings arising from threshold corrections. We show that the rece…
We investigate the color-singlet order parameters and the quark description of the Nambu-Goldstone (NG) bosons in the color-flavor locked (CFL) phase. We put emphasis on the NG boson (phason) called ``H'' associated with the $\mathrm{U_B(1)}$ symmetry breaking. We qualitatively argue the nature of H as the second sound in the hydrodynamic regime. We articulate, based on a diquark picture, how the structural change of the condensates and the associated NG bosons occurs continuously from hadronic to CFL quark matter if the quark-hadron continuity is realized. We sharpen the qualitative differenc…
The mechanism where flavor symmetry is broken spontaneously is discussed within a scalar QCD model with effective three-meson couplings. For sufficiently large coupling the model is unstable with respect to quantum loops from mesonic vacuum polarization. It is argued that color and gluons naturally can account for the Goldstone degrees of freedom expected when flavor symmetry is spontaneously broken.
We study the flavor change effects using the Dyson-Schwinger (DS) equation in a multi-flavor system. By taking the Electroweak interaction as perturbation into conditions, the $\text{SU(4)}_\text{L}\rightarrow\text{SU(2)}_\text{L}\otimes\text{SU(2)}_\text{L}\rightarrow\text{SO(2)}_\text{L}\otimes\text{SO(2)}_\text{L}$ symmetry breaking chain is studied. Under this symmetry breaking pattern fermion masses are split, and we can identify the fermions with different masses as different generations. Quark mass spectrum is then given. Meanwhile, there are a total of fifteen Goldstones but only four …
We calculate the axial current decay constants of taste non-Goldstone pions and kaons in staggered chiral perturbation theory through next-to-leading order. The results are a simple generalization of the results for the taste Goldstone case. New low-energy couplings are limited to analytic corrections that vanish in the continuum limit; certain coefficients of the chiral logarithms are modified, but they contain no new couplings. We report results for quenched, fully dynamical, and partially quenched cases of interest in the chiral SU(3) and SU(2) theories.
At very high densities, QCD is in the color-flavor locked phase, which is a color-superconducting phase. The diquark condensates break chiral symmetry in the same way as it is broken in vacuum QCD and gives rise to an octet of pseudo-Goldstone bosons and a superfluid mode. The lightest of these are the charged and neutral kaons. For energies below the superconducting gap, the kaons are described by an $O(2)\times O(2)$-symmetric effective scalar field theory with chemical potentials. We use this effective theory to study Bose-condensation of kaons and their properties as functions of the tempe…
We calculate the masses of taste non-Goldstone pions and kaons in staggered chiral perturbation theory through next-to-leading order in the standard power counting. The results can be used to quantitatively understand taste violations in existing lattice data generated with staggered fermions and to extract the $u$, $d$, and $s$ quark masses and Gasser-Leutwyler parameters from the experimentally observed spectrum. The expressions for the non-Goldstone masses contain low-energy couplings unique to the non-Goldstone sector. With two exceptions these enter as coefficients of analytic terms; all …
We propose a new way of breaking the Goldstone symmetry in composite Higgs models, restoring the global symmetry in the mixings between the elementary and composite fermions by completing the former to full representations of this symmetry. The Goldstone symmetry is in turn broken softly by vector-like mass terms in the {\it elementary} sector only. The resulting softened explicit breaking allows for a light Higgs boson, as found at the LHC, and a heavy top quark, without the need of light top partners around the Goldstone scale $f \sim {\rm TeV} \ll m_{\rm comp.}$, which remain elusive at the…
It is shown that a Nambu-Goldstone (NG) field may be coherently produced by a large number of particles in spite of the fact that the NG bosons do not couple to flavor conserving scalar densities like $\barψψ$. If a flavor oscillation process takes place the phases of the pseudo-scalar or flavor violating densities of different particles do not necessarily cancel each other. The NG boson gets a macroscopic source whenever the total (spontaneously broken) quantum number carried by the source particles suffers a net increase or decrease in time. If the lepton numbers are spontaneously broken suc…
The properties of the pseudoscalar Goldstone bosons in the color-flavor locked phase at moderate densities are studied within a model of the Nambu--Jona-Lasinio type. The Goldstone bosons are constructed explicitly by solving the Bethe-Salpeter equation for quark-quark scattering in random phase approximation. Main focus of our investigations are (i) the weak decay constant in the chiral limit, (ii) the masses of the flavored (pseudo-) Goldstone bosons for non-zero but equal quark masses, (iii) their masses and effective chemical potentials for non-equal quark masses, and (iv) the onset of kao…
General flavor changing interactions for a Goldstone boson (GB) to fermions due to a spontaneous global $U(1)_G$ symmetry breaking are discussed. This GB may be the Axion, solving the strong QCD CP problem, if there is a QCD anomaly for the $U(1)_G$ charge assignments for quarks. Or it may be the Majoron in models from lepton number violation in producing seesaw Majorana neutrino masses if the symmetry breaking scale is much higher than the electroweak scale. It may also, in principle, play the roles of Axion and Majoron simultaneously as far as providing solution for the strong CP problem and…
We compute the correction to the muon magnetic moment in theories where the Higgs is a pseudo-Goldstone boson and leptons are partially composite. Using a general effective lagrangian we show that in some regions of parameters a sizable new physics contribution to the magnetic moment can be obtained from composite fermions that could explain the 3.5$σ$ experimental discrepancy from the Standard Model prediction. This effect depends on the derivative interactions of the Higgs that do not modify the coupling of the Higgs to leptons and it does not require extremely light fermions, allowing to ea…
The hierarchy of fermion masses in the standard model may arise via the breaking of discrete gauge symmetries. The renormalizable interactions of the flavor-symmetry-breaking potential can have accidental global symmetries that are spontaneously broken, leading to pseudo-goldstone bosons that may drive inflation. We consider two-field, axion-monodromy inflation models in which the inflaton is identified with a linear combination of pseudo-goldstone bosons of the flavor sector. We show that the resulting models are nontrivially constrained by current cosmological data as well as the requirement…
In this talk, I will present the status of lepton flavor physics in composite Higgs models with partial compositeness in the light of recent data in the lepton sector. I will consider anarchic flavor setups, scenarios with flavor symmetries, and minimal incarnations of the see-saw mechanism that naturally predict non-negligible lepton compositeness. The focus will be on lepton flavor violating processes, dipole moments, and on probes of lepton flavor universality, all providing stringent tests of partial compositeness. The expected size of effects in the different approaches to lepton flavor a…
We discuss the connection between the top quark, naturalness and flavor in composite Higgs models. The phenomenological features of the top quark and the associated fermionic partners are presented. The main realizations of the flavor structure, in particular the anarchic partial compositeness scenario and its possible modifications, are also briefly reviewed.
We introduce a scalar-less anomaly free chiral gauge theory that serves as natural ultraviolet completion of models of fundamental composite (Goldstone) Higgs dynamics. The new theory is able to generate the top mass and furthermore features a built-in protection mechanism that naturally suppresses the bottom mass. At low energies the theory predicts new fractionally charged fermions, and a number of four-fermion operators that, besides being relevant for the generation of the top mass, also lead to an intriguing phenomenology for the new states predicted by the theory.
In a two-flavor color superconductor, the SU(3)_c gauge symmetry is spontaneously broken by diquark condensation. The Nambu-Goldstone excitations of the diquark condensate mix with the gluons associated with the broken generators of the original gauge group. It is shown how one can decouple these modes with a particular choice of 't Hooft gauge. We then explicitly compute the spectral density for transverse and longitudinal gluons of adjoint color 8. The Nambu-Goldstone excitations give rise to a singularity in the real part of the longitudinal gluon self-energy. This leads to a vanishing gluo…
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…
A schematic NJL-type model is employed to investigate kaon and pion condensation in deconfined quark matter in the color-flavor locked (CFL) phase, explicitly referring to quark degrees of freedom. To that end we allow for non-vanishing pseudoscalar diquark condensates in addition to the scalar ones which constitute the CFL phase. Color neutrality is ensured by the appropriate choice of color chemical potentials. The dependence of the free energy in the Goldstone condensed phases on quark masses and charge chemical potentials is found to be in good qualitative -- in most cases also quantitativ…
The flavor protection in composite Higgs models with partial compositeness is known to be insufficient. We explore the possibility to alleviate the tension with CP odd observables by assuming that flavor or CP are symmetries of the composite sector, broken by the coupling to Standard Model fields. One realization is that the composite sector has a flavor symmetry SU(3) or SU(3)_U x SU(3)_D which allows us to realize Minimal Flavor Violation. We show how to avoid the previously problematic tension between a flavor symmetric composite sector and electro-weak precision tests. Some of the light qu…
Partial compositeness is a key ingredient of models where the electroweak symmetry is broken by a composite Higgs state. Recently, a UV completion of partial compositeness was proposed, featuring a new strongly coupled gauge interaction as well as new fundamental fermions and scalars. We work out the full flavor structure of the minimal realization of this idea and investigate in detail the consequences for flavor physics. While CP violation in kaon mixing represents a significant constraint on the model, we find many viable parameter points passing all precision tests. We also demonstrate tha…
We point out that Higgs rates into gauge bosons can be significantly modified in composite pseudo Nambu--Goldstone boson (pNGB) Higgs models if quarks belonging to the first two generation are relatively composite objects as well. Although the lightness of the latter a priori screen them from the electroweak symmetry breaking sector, we show, in an effective two-site description, that their partners can lead to order one shifts in radiative Higgs couplings to gluons and photons. Moreover, due to the pseudo-Goldstone nature of the Higgs boson, the size of these corrections is completely control…
We consider the phase diagram of QCD at very high baryon density and at zero temperature in the presence of a strong magnetic field. The state of matter at such high densities and low temperatures is believed to be a phase known as the color-flavor locked phase which breaks color and electromagnetic gauge invariance leaving a linear combination of them unbroken. Of the 9 quarks (three flavors and three colors), five are neutral under this unbroken generator and four are oppositely charged. In the presence of a magnetic field corresponding to the unbroken generator however, the properties of th…
The masses of the pseudo-Nambu-Goldstone bosons in the color superconducting phase of dense QCD with two light flavors are estimated by making use of the Cornwall-Jackiw-Tomboulis effective action. Parametrically, the masses of the doublet and antidoublet bosons are suppressed by a power of the coupling constant as compared to the value of the superconducting gap. This is qualitatively different from the mass expression for the singlet pseudo-Nambu-Goldstone boson, resulting from non-perturbative effects. It is argued that the (anti-) doublet pseudo-Nambu-Goldstone bosons form colorless [with …
We consider the phenomenology of a composite technicolor model proposed recently by Georgi. Composite technicolor interactions produce four-quark operators in the low energy theory that contribute to flavor changing neutral current processes. While we expect operators of this type to be induced at the compositeness scale by the flavor-symmetry breaking effects of the preon mass matrices, the Georgi model also includes operators from higher scales that are not GIM-suppressed. Since these operators are potentially large, we study their impact on flavor changing neutral currents and CP violation …
We study, via first principles lattice simulations, the nonperturbative dynamics of $SU(2)$ gauge theory with two fundamental Dirac flavors. The model can be used simultaneously as a template for composite Goldstone boson dark matter and for breaking the electroweak symmetry dynamically. We compute the form factor, allowing us to estimate the associated electromagnetic charge radius. Interestingly we observe that the form factor obeys vector meson dominance even for the two color theory. We finally compare the model predictions with dark matter direct detection experiments. We find that the co…
Similarly to the previously studied case of inclusive $t\bar t$ production we consider the inclusive $t\bar b$ production in $e^+e^-$, gluon~gluon and photon~photon collisions. We show how it is sensitive to new physics, connected to the charged Goldstone sector and possibly generated by Higgs and/or top quark compositeness.
We present a framework to study the interactions among Nambu-Goldstone bosons (NGB), pseudo-NGB (pNGBs) and gauge bosons in Composite Higgs (CH) models at high energies, including operators of order $\mathcal{O}(p^4)$ and $\mathcal{O}(p^2g^2)$ in the chiral expansion and topological terms. The set of (p)NGBs comprises the longitudinal modes of electroweak bosons, the Higgs boson, and possibly other scalar states from the dynamical spontaneous electroweak symmetry breaking. The framework is implemented in a collider simulation tool especially suited for the study of Goldstone Boson Scattering (…
We show that a composite-field (diatom) Goldstone state is expected in a dilute Bose gas for temperatures between the Bose gas critical temperature where the atom Bose-Einstein condensate appears and the temperature where superfluidity sets in. The presence of superfluidity is tied to the existence of a U(1) charge-two diatom condensate in the system. By promoting the global U(1) symmetry of the theory to a gauge symmetry, we find that the mass of the gauge particle generated through the Anderson-Higgs mechanism is related to the superfluid density via the Meissner effect and the superfluid de…
The appearance of a light composite $0^+$ scalar resonance in nearly conformal gauge-fermion theories motivates further study of the low energy structure of these theories. To this end, we present a nonperturbative lattice calculation of s-wave scattering of Goldstone bosons in the maximal-isospin channel in SU(3) gauge theory with $N_f=8$ light, degenerate flavors. The scattering phase shift is measured both for different values of the underlying fermion mass and for different values of the scattering momentum. We examine the effect of a light flavor-singlet scalar (reported in earlier studie…
The assumption of anarchic quark flavor puts serious stress on composite Higgs models: flavor bounds imply a tuning of a few per-mille (at best) in the Higgs potential. Composite twin Higgs (CTH) models significantly reduce this tension by opening up a new region of parameter space, obtained by raising the coupling among the composites close to the strong coupling limit $g_* \sim 4π$, thereby raising the scale of composites to around 10 TeV. This does not lead to large tuning in the Higgs potential since the leading quantum corrections are canceled by the twin partners (rather than the composi…
We consider supersymmetric models in which a (pseudo) Goldstone supermultiplet plays the role of the messenger of supersymmetry breaking. Such models lead to a highly predictive form of flavor and CP conserving soft terms, particularly the soft scalar masses and trilinear couplings vanish at the scale where the (approximate) global symmetry is spontaneously broken. We discuss also the possibility for realizing this scheme in supergravity models derived from string theories.
We compute the 1-loop correction to the electroweak observables from spin-1 resonances in SO(5)/SO(4) composite Higgs models. The strong dynamics is modeled with an effective description comprising the Nambu-Goldstone bosons and the lowest-lying spin-1 resonances. A classification is performed of the relevant operators including custodially-breaking effects from the gauging of hypercharge. The 1-loop contribution of the resonances is extracted in a diagrammatic approach by matching to the low-energy theory of Nambu-Goldstone bosons. We find that the correction is numerically important in a sig…
In these proceedings we discuss a flavor-safe explanation of the anomaly found in $R_K= {\cal B}(B \to K μ^+ μ^-)/{\cal B}(B \to K e^+ e^-)$ by LHCb, within the framework of composite Higgs models. We present a model featuring a non-negligible degree of compositeness for all three generations of right-handed leptons, which leads to a violation of lepton-flavor universality in neutral current interactions while other constraints from quark- and lepton-flavor physics are met. Moreoever, the particular embedding of the lepton sector considered in this setup provides a parametrically enhanded cont…
We discuss flavor violation in large N Composite Higgs models. We focus on scenarios in which the masses of the standard model fermions are controlled by hierarchical mixing parameters, as in models of Partial Compositeness. We argue that a separation of scales between flavor and Higgs dynamics can be employed to parametrically suppress dipole and penguin operators, and thus effectively remove the experimental constraints arising from the lepton sector and the neutron EDM. The dominant source of flavor violation beyond the standard model is therefore controlled by 4-fermion operators, whose Wi…
We consider the renormalizable $SO(5)/SO(4)$ $σ$-model, in which the Higgs particle has a pseudo-Nambu-Goldstone boson character, and explore what the minimal field extension required to implement the Peccei-Quinn symmetry (PQ) is, within the partial compositeness scenario. It turns out that the minimal model does not require the enlargement of the exotic fermionic sector, but only the addition of a singlet scalar: it is sufficient that the exotic fermions involved in partial compositeness and the singlet scalar become charged under Peccei-Quinn transformations. We explore the phenomenological…
Composite Higgs models can trivially satisfy precision-electroweak and flavour constraints by simply having a large spontaneous symmetry breaking scale, f > 10 TeV. This produces a 'split' spectrum, where the strong sector resonances have masses greater than 10 TeV and are separated from the pseudo Nambu-Goldstone bosons, which remain near the electroweak scale. Even though a tuning of order 10^{-4} is required to obtain the observed Higgs boson mass, the big hierarchy problem remains mostly solved. Intriguingly, models with a fully-composite right-handed top quark also exhibit improved gauge …
We calculate the coupling between a vector resonance and two Goldstone bosons in $SU(2)$ gauge theory with $N_f=2$ Dirac fermions in the fundamental representation. The considered theory can be used to construct a minimal Composite Higgs models. The coupling is related to the width of the vector resonance and we determine it by simulating the scattering of two Goldstone bosons where the resonance is produced. The resulting coupling is $g_{\rm{VPP}}=7.8\pm 0.6$, not far from $g_{ρππ}\simeq 6$ in QCD. This is the first lattice calculation of the resonance properties for a minimal UV completion. …
The properties of pseudoscalar bosonic excitations in the color-flavor locked phase at moderate densities are studied within a model of the Nambu--Jona-Lasinio type. Our previous analysis is extended to Goldstone bosons with hidden flavor and to higher-lying modes which stay massive in the chiral limit. The bosons are constructed explicitly by solving the Bethe-Salpeter equation for quark-quark scattering in random phase approximation. The masses and weak decay constants of the Goldstone bosons are found in good agreement with predictions from the low-energy effective theory. In the non-Goldst…
We should be taking advantage of recent gains in our nonperturbative understanding of supersymmetric gauge theories to find the ``standard'' model of of dynamical supersymmetry breaking, and possibly of flavor as well. As an illustration of the possibilities for understanding the flavor hierarchy, I describe a realistic, renormalizable, supersymmetric model with a compositeness scale of $\sim 1-3$ TeV for the top quark, the left handed bottom quark, and the up-type Higgs. The top-Higgs Yukawa coupling is a dynamically generated strong interaction effect, and is naturally large, while the other…
We present preliminary results for the chiral behavior of charged pseudo-Goldstone-boson masses and decay constants. These are obtained in simulations with N_f=2+1 flavors of tree-level, O(a)-improved Wilson sea quarks. In these simulations, mesons are composed of either valence quarks discretized in the same way as the sea quarks (unitary simulations) or of overlap valence quarks (mixed-action simulations). We find that the chiral behavior of the pseudoscalar meson masses in the mixed-action calculations cannot be explained with continuum, partially-quenched chiral perturbation theory. We sho…
The SU(2) gauge theory with two massless Dirac flavors constitutes the building block of several models of Technicolor. Furthermore it has also been used as a template for the construction of a natural light asymmetric, or mixed type, dark matter candidate. We use explicit lattice simulations to confirm the pattern of chiral symmetry breaking by determining the Goldstone spectrum and therefore show that the dark matter candidate can, de facto, be constituted by a complex Goldstone boson. We also determine the phenomenologically relevant spin-one and spin-zero isovector spectrum and demonstrate…
We consider a vector-like gauge theory of fermions that confines at the multi-TeV scale, and that realizes the Higgs particle as a composite Goldstone boson. The weak interactions are embedded in the unbroken subgroup $Sp(4)$ of a spontaneously broken $SU(4)$ flavour group. The meson resonances appear as poles in the two-point correlators of fermion bilinears, and include the Goldstone bosons plus a massive pseudoscalar $η'$, as well as scalars, vectors and axial vectors. We compute the mass spectrum of these mesons, as well as their decay constants, in the chiral limit, in the approximation w…
We explore the up flavor structure of composite pseudo Nambu-Goldstone-boson Higgs models, where we focus on the flavor anarchic minimal $SO(5)$ case. We identify the different sources of flavor violation in this framework and emphasise the differences from the anarchic Randall-Sundrum scenario. In particular, the fact that the flavor symmetry does not commute with the symmetries that stabilize the Higgs potential may constrain the flavor structure of the theory. In addition, we consider the interplay between the fine tuning of the model and flavor violation. We find that generically the tunin…
We present a model which connects the neutral current B anomalies with composite Higgs models. The model is based on the minimal fundamental composite Higgs model with $SU(4)/Sp(4)$ coset. The strong dynamics spontaneously break the symmetry and introduce five Nambu-Goldstone bosons. Four of them become the Standard Model Higgs doublet and the last one, corresponding to the broken local $U(1)'$ symmetry, is eaten by the gauge boson. This leads to an additional TeV-scale $Z'$ boson, which can explain the recent B anomalies. The experimental constraints and allowed parameter space are discussed …
A pseudo-Nambu Goldstone Boson (pNGB) arising from the breaking of a global symmetry ($G\rightarrow H$) can be one of the most promising candidates for the quintessence model, to explain the late-time acceleration of our universe. Motivated from the Composite Higgs scenario, we have investigated the case where the pNGB associated with $SO(N)/ SO(N-1)$ develops a potential through its couplings with the particles that do not form the complete representations of $G$. The Coleman Weinberg (CW) potential is generated via the external particles in the loop which are linked with the strongly interac…
We discuss the phenomenology of composite Higgs models that naturally produce a Standard Model-like Higgs boson with a mass of $126$ GeV. The effective theory below the compositeness scale is weakly coupled in these models, and the goldstone sector acts as a portal between the third generation of quarks and a hidden gauge sector. The addition of hidden-sector fermions gives rise to a calculable effective scalar potential with a naturally light scalar resonance. The generic prediction of these theories is the existence of additional pseudo-Nambu Goldstone bosons with electroweak-scale cross sec…
We study the light scalar resonance sector of a composite Higgs model UV embedding based on the coset $SU(4)/Sp(4)$. Beyond the Higgs multiplet, the pseudo Nambu-Goldstone sector of this model contains Standard Model singlets which couple to the Standard Model gauge bosons through Wess-Zumino-Witten anomaly terms. They can thus be produced in gluon fusion and decay into either gluons or pairs of electroweak gauge bosons $WW$, $ZZ$, $Zγ$, or $γγ$. In this letter we show that one of the pseudo Nambu-Goldstone boson states has appropriate couplings in order to explain a di-boson excess in the $WW…
Partial compositeness as a theory of flavor in the lepton sector is assessed. We begin presenting the first systematic analysis of neutrino mass generation in this context, and identifying the distinctive mass textures. We then update the bounds from charged lepton flavor and CP violating observables. We put forward a $U(1)^3\times CP$ symmetry of the composite sector, in order to allow the new physics to be not far above the TeV scale. This hypothesis effectively suppresses the new contributions to the electron EDM and $μ\to eγ$, by far the most constraining observables, and results in a nove…
The Bethe-Salpeter equations for diquarks with the quantum numbers of the Nambu-Goldstone bosons are analyzed in the color-flavor locked phase of cold dense QCD with three quark flavors. The decay constants and the velocities of the Nambu-Goldstone bosons are calculated in the Pagels-Stokar approximation. It is also shown that, in contrast to the case of dense QCD with two flavors, there are no massive radial excitations with quantum numbers of the Nambu-Goldstone bosons in the color-flavor locked phase. The role of the Meissner effect in the pairing dynamics of diquarks is explained.
A natural composite Higgs demands the presence of light resonances at the TeV scale, that in general are in conflict with bounds from flavor and CP violation. We propose a composite model with a Froggatt-Nielsen mechanism, that offers new possibilities for the origin of flavor. We analyse the interplay of partial compositeness and the horizontal U(1) symmetry in achieving the quark masses and mixing angles. We study the contributions to $ΔF=2$ 4-fermion operators, as well as to $ΔF=1$ and neutron dipole operators. We find scenarios in which the contribution to Left-Right and Right-handed opera…
We present a new class of models of lepton flavor in the composite Higgs framework. Following the concept of minimality, they lead to a rich phenomenology in good agreement with the current experimental picture. Because of a unification of the right-handed leptons, our scenario is very predictive and can naturally lead to a violation of lepton-flavor universality in neutral current interactions. We will show that, in particular, the anomaly in $R_K= {\cal B}(B \to K μ^+ μ^-)/{\cal B}(B \to K e^+ e^-)$, found by LHCb, can be addressed, while other constraints from quark- and lepton-flavor physi…
