Search

We study on-shell scattering amplitudes for continuous-spin particles (CSPs). Poincar\'e invariance, little-group $ISO(2)$ covariance, analyticity, and on-shell factorisation (unitarity) impose stringent conditions on these amplitudes. We solve them by realizing a non-trivial representation for all little-group generators on the space of functions of bi-spinors. The three-point amplitudes are uniquely determined by matching their high-energy limit to that of definite-helicity (ordinary) massless particles. Four-point amplitudes are then bootstrapped using consistency conditions, allowing us to analyze the theory in a very transparent way, without relying on any off-shell Lagrangian formulation. We present several examples that highlight the main features of the resulting scattering amplitudes. We discuss CSP's amplitudes as a new infrared deformation of ordinary massless amplitudes, which is controlled by the scale of the Pauli-Lubanski vector squared, as opposed to the familiar mass deformation. Finally, we explore under which conditions it is possible to relax some assumptions, such as strict on-shell factorisation, analyticity, or others. In particular, we also investigate how continuous-spin particles may couple to gravity and electromagnetism, in a loose version of $S$-matrix principles., Comment: v2: largely improved discussions, new results, new figures, extra appendices, 32 pages (+ references and appendices)

We derive new positivity bounds at finite momentum transfer, assuming a large separation between the mass $m$ of the lightest particle in the effective theory and the mass gap $M$ to new heavy states. Massive gravity parametrically violates these bounds unless the cutoff is within one order of magnitude of the graviton mass $M\lesssim O(10)m$. Non-gravitational effective theories of massive spin-2 particles are similarly bounded., Comment: v2: 8 pages + appendices & references, 3 figures. Typos fixed, references added, discussion on negativity of general spin-2 EFTs included

We study the eikonal scattering of two gravitationally interacting bodies, in the regime of large angular momentum and large center of mass energy. We show that eikonal exponentiation of the scattering phase matrix is a direct consequence of the group contraction $SU(2)\to ISO(2)$, from rotations to the isometries of the plane, in the large angular momentum limit. We extend it to all orders in the scattering angle, and for all masses and spins. The emergence of the classical limit is understood in terms of the continuous-spin representations admitted by $ISO(2)$. We further investigate the competing classical vs quantum corrections to the leading classical eikonal scattering, and find several interesting examples where quantum corrections are more important than Post-Minkowskian's. As a case of study, we analyse the scattering of a photon off a massless neutral scalar field, up to next-to-leading order in the Newton constant, and to leading order in the fine structure constant. We investigate the causal structure of the eikonal regime and establish an infinite set of non-linear positivity bounds, of which positivity of time delay is the simplest., Comment: 32 pages + Appendices and References, 5 Figures, published version

We show how calculable IR loop effects impact positivity bounds in Effective Field Theories with causal and unitary UV completions. We identify infrared singularities which appear in dispersion relations at $|t|\lesssim m^2$. In the massless limit, they weaken two-sided bounds based on crossing symmetry, such as the lower bound on the amplitude for Galileon scattering. For amplitudes that are analytic in $s$ even for large negative $t$, i.e. $|t|\gg m^2$, we propose a new simple analytic approach to dispersive bounds, which are instead insensitive to the singularities, and explicitly compute the finite contributions from loops. Finally we show that the singularity do not affect the bounds based on smearing in impact parameter., Comment: 10 pages, 4 figures; v2: table added, matches journal version

We study causality in gravitational systems beyond the classical limit. Using on-shell methods, we consider the one-loop corrections from charged particles to the photon energy-momentum tensor - the self-stress - that controls the quantum interaction between two on-shell photons and one off-shell graviton. The self-stress determines in turn the phase shift and time delay in the scattering of photons against a spectator particle of any spin in the eikonal regime. We show that the sign of the $\beta$-function associated to the running gauge coupling is related to the sign of time delay at small impact parameter. Our results show that, at first post-Minkowskian order, asymptotic causality, where the time delay experienced by any particle must be positive, is respected quantum mechanically. Contrasted with asymptotic causality, we explore a local notion of causality, where the time delay is longer than the one of gravitons, which is seemingly violated by quantum effects., Comment: v3: added references, fixed numerics in Fig.5, found analytic asymptotic behaviors, matching journal version

We find the complete set of conditions satisfied by the forward $2\to2$ scattering amplitude in unitarity and causal theories. These are based on an infinite set of energy dependent quantities -- the arcs -- which are dispersively expressed as moments of a positive measure defined at (arbitrarily) higher energies. We identify optimal finite subsets of constraints, suitable to bound Effective Field Theories (EFTs), at any finite order in the energy expansion. At tree-level arcs are in one-to-one correspondence with Wilson coefficients. We establish under which conditions this approximation applies, identifying seemingly viable EFTs where it never does. In all cases, we discuss the range of validity in both couplings and energy. We also extend our results to the case of small but finite~$t$. A consequence of our study is that EFTs in which the scattering amplitude in some regime grows in energy faster than $E^6$ cannot be UV-completed., Comment: 15 pages, v2 matches published version

We construct the effective field theory for a single massive higher-spin particle in flat spacetime. Positivity bounds of the S-matrix force the cutoff of the theory to be well below the naive strong-coupling scale, forbid any potential and make therefore higher-derivative operators important even at low energy. As interesting application, we discuss in detail the massive spin-3 theory and show that an extended Galileon-like symmetry of the longitudinal modes, even with spin, emerges at high energy., Comment: 22 pages, 2 figures and 2 appendices; v2 improved discussion, extra appendix and references added

We derive new positivity bounds for scattering amplitudes in theories with a massless graviton in the spectrum in four spacetime dimensions, of relevance for the weak gravity conjecture and modified gravity theories. The bounds imply that extremal black holes are self-repulsive, $M/|Q|<1$ in suitable units, and that they are unstable to decay to smaller extremal black holes, providing an S-matrix proof of the weak gravity conjecture. We also present other applications of our bounds to the effective field theory of axions, $P(X)$ theories, weakly broken galileons, and curved spacetimes., Comment: v4: two more appendices, discussion of Froissart bound extended

Neutral diboson processes are precise probes of the Standard Model (SM) of particle physics, which entail high sensitivity to new physics effects. We identify in terms of dimension-8 effective operators the leading departures from the SM that survive in neutral diboson processes at high-energy, and which interfere with the unsuppressed SM helicity contributions. We describe symmetries and selections rules that single out those operators, both for weakly and strongly coupled physics beyond the SM. Finally, we show that unitarity and causality enforce, via dispersion relations, positivity constraints on the coefficients of these effective operators, reducing the parameter space which is theoretically allowed., Comment: 7 pages, 2 figures

We constrain effective field theories by going beyond the familiar positivity bounds that follow from unitarity, analyticity, and crossing symmetry of the scattering amplitudes. As interesting examples, we discuss the implications of the bounds for the Galileon and ghost-free massive gravity. The combination of our theoretical bounds with the experimental constraints on the graviton mass implies that the latter is either ruled out or unable to describe gravitational phenomena, let alone to consistently implement the Vainshtein mechanism, down to the relevant scales of fifth-force experiments, where general relativity has been successfully tested. We also show that the Galileon theory must contain symmetry-breaking terms that are at most one-loop suppressed compared to the symmetry-preserving ones. We comment as well on other interesting applications of our bounds., Comment: 10 pages + 3 appendices and references, 4 figures; v2: bounds optimized, improved discussion, extended outlook, conclusion unchanged. Extra appendix and references added

We discuss the only two viable realizations of fermion compositeness described by a calculable relativistic effective field theory consistent with unitarity, crossing symmetry and analyticity: chiral-compositeness vs goldstino-compositeness. We construct the effective theory of $\mathcal{N}$ Goldstini and show how the Standard Model can emerge from this dynamics. We present new bounds on either type of compositeness, for quarks and leptons, using dilepton searches at LEP, dijets at the LHC, as well as low-energy observables and precision measurements. Remarkably, a scale of compositeness for Goldstino-like electrons in the 2 TeV range is compatible with present data, and so are Goldstino-like first generation quarks with a compositeness scale in the 10 TeV range. Moreover, assuming maximal $R$-symmetry, goldstino-compositeness of both right- and left-handed quarks predicts exotic spin-1/2 colored sextet particles that are potentially within the reach of the LHC., Comment: 32 pages on how Thomson might have discovered supersymmetry; v2: few typos fixed and comments added

We study the effective theory of a generic class of hidden sectors where supersymmetry is broken together with an approximate R-symmetry at low energy. The light spectrum contains the gravitino and the pseudo-Nambu-Goldstone boson of the R-symmetry, the R-axion. We derive new model-independent constraints on the R-axion decay constant for R-axion masses ranging from GeV to TeV, which are of relevance for hadron colliders, lepton colliders and B-factories. The current bounds allow for the exciting possibility that the first sign of SUSY will be the R-axion. We point out its most distinctive signals, providing a new experimental handle on the properties of the hidden sector and a solid motivation for searches of axion-like particles., Comment: 7 pages, 2 figures. v2: typos fixed, appendix added. v3: R-axion as motivation for ALP phenomenological studies made explicit, minor clarifications. Accepted for publication on PRL

We derive positivity bounds for scattering amplitudes of particles with arbitrary spin using unitarity, analyticity and crossing symmetry. The bounds imply the positivity of certain low-energy coefficients of the effective action that controls the dynamics of the light degrees of freedom. We show that low-energy amplitudes strictly softer than $O(p^4)$ do not admit unitary ultraviolet completions unless the theory is free. This enforces a bound on the energy growth of scattering amplitudes in the region of validity of the effective theory. We discuss explicit examples including the Goldstino from spontaneous supersymmetry breaking, and the theory of a spin-1/2 fermion with a shift symmetry., Comment: 28 pages + refs and 3 appendices, 2 figures; v2: extra refs, improved discussions, typos fixed, accepted on JHEP

We study the conditions for a new scalar resonance to be observed first in diphotons at the LHC Run-2. We focus on scenarios where the scalar arises either from an internal or spacetime symmetry broken spontaneously, for which the mass is naturally below the cutoff and the low-energy interactions are fixed by the couplings to the broken currents, UV anomalies, and selection rules. We discuss the recent excess in diphoton resonance searches observed by ATLAS and CMS at 750 GeV, and explore its compatibility with other searches at Run-1 and its interpretation as Goldstone bosons in supersymmetry and composite Higgs models. We show that two candidates naturally emerge: a Goldstone boson from an internal symmetry with electromagnetic anomalies, and the scalar partner of the Goldstone of supersymmetry breaking: the sgoldstino. The dilaton from conformal symmetry breaking is instead disfavoured by present data, in its minimal natural realization., Comment: 18 pages + refs, 2 figures. v2: typos corrected, references added, discussions extended and three new plots. Conclusion unchanged. v3: published version

The appearance of the light Higgs boson at the LHC is difficult to explain, particularly in light of naturalness arguments in quantum field theory. However light scalars can appear in condensed matter systems when parameters (like the amount of doping) are tuned to a critical point. At zero temperature these quantum critical points are directly analogous to the finely tuned standard model. In this paper we explore a class of models with a Higgs near a quantum critical point that exhibits non-mean-field behavior. We discuss the parametrization of the effects of a Higgs emerging from such a critical point in terms of form factors, and present two simple realistic scenarios based on either generalized free fields or a 5D dual in AdS space. For both of these models we consider the processes $gg\to ZZ$ and $gg\to hh$, which can be used to gain information about the Higgs scaling dimension and IR transition scale from the experimental data., Comment: 25p+ appendix, 3 figures; v2: references added, minor improvements, match published version

We derive rigorous bounds on corrections to Einstein gravity using unitarity and analyticity of graviton scattering amplitudes. In $D\geq 4$ spacetime dimensions, these consistency conditions mandate positive coefficients for certain quartic curvature operators. We systematically enumerate all such positivity bounds in $D=4$ and $D=5$ before extending to $D\geq 6$. Afterwards, we derive positivity bounds for supersymmetric operators and verify that all of our constraints are satisfied by weakly-coupled string theories. Among quadratic curvature operators, we find that the Gauss-Bonnet term in $D\geq 5$ is inconsistent unless new degrees of freedom enter at the natural cutoff scale defined by the effective theory. Our bounds apply to perturbative ultraviolet completions of gravity., Comment: 26 pages

Vacuum energy changes during cosmological phase transitions and becomes relatively important at epochs just before phase transitions. For a viable cosmology the vacuum energy just after a phase transition must be set by the critical temperature of the next phase transition, which exposes the cosmological constant problem from a different angle. Here we propose to experimentally test the properties of vacuum energy under circumstances different from our current vacuum. One promising avenue is to consider the effect of high density phases of QCD in neutron stars. Such phases have different vacuum expectation values and a different vacuum energy from the normal phase, which can contribute an order one fraction to the mass of neutron stars. Precise observations of the mass of neutron stars can potentially yield information about the gravitational properties of vacuum energy, which can significantly affect their mass-radius relation. A more direct test of cosmic evolution of vacuum energy could be inferred from a precise observation of the primordial gravitational wave spectrum at frequencies corresponding to phase transitions. While traditional cosmology predicts steps in the spectrum determined by the number of degrees of freedom both for the QCD and electroweak phase transitions, an adjustment mechanism for vacuum energy could significantly change this. In addition, there might be other phase transitions where the effect of vacuum energy could show up as a peak in the spectrum., Comment: 28 pages, LaTeX, 7 figures

Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the scattering amplitudes in the IR to total cross sections integrated all the way up to the UV. Exploiting the group structure of the symmetry, we systematically determine all the independent sum rules and positivity conditions on the expansion coefficients. For effective field theories the amplitudes in the IR are calculable and hence the sum rules set constraints on the parameters of the effective Lagrangian. We clarify the impact of gauging on the sum rules for Goldstone bosons in spontaneously broken gauge theories. We discuss explicit examples that are relevant for WW-scattering, composite Higgs models, and chiral perturbation theory. Certain sum rules based on custodial symmetry and its extensions provide constraints on the Higgs boson coupling to the electroweak gauge bosons., Comment: 50 pages, 5 figures, 5 appendices; several typos fixed, discussions improved, references added; results unchanged

We present an overview of composite Higgs models in light of the discovery of the Higgs boson. The small value of the physical Higgs mass suggests that the Higgs quartic is likely loop generated, thus models with tree-level quartics will generically be more tuned. We classify the various models (including bona fide composite Higgs, little Higgs, holographic composite Higgs, twin Higgs and dilatonic Higgs) based on their predictions for the Higgs potential, review the basic ingredients of each of them, and quantify the amount of tuning needed, which is not negligible in any model. We explain the main ideas for generating flavor structure and the main mechanisms for protecting against large flavor violating effects, and present a summary of the various coset models that can result in realistic pseudo-Goldstone Higgses. We review the current experimental status of such models by discussing the electroweak precision, flavor and direct search bounds, and comment on UV completions and on ways to incorporate dark matter., Comment: 58 Pages, 5 Figures, 5 Tables. Invited review article accepted for publication in The European Physical Journal C

We study the effective Lagrangian, at leading order in derivatives, that describes the propagation of density and metric fluctuations in a fluid composed by an arbitrary number of interacting components. Our results can be applied to any situation in cosmology where different species have non-gravitational interactions. In time-dependent backgrounds, such as FLRW, the quadratic action can only be diagonalized at fixed time slices and flavour mixing is unavoidable as time flows. In spite of this, the fluid can be interpreted at the level of the linear equations of motion as an ensemble of individual interacting species. We show that interactions lead to anisotropic stresses that depend on the mixing terms in the quadratic action for perturbations. In addition to the standard entrainment among different components, we find a new operator in the effective action that behaves as a cosmological constant when it dominates the dynamics., Comment: 1+19 pages. Minor changes. Matches JCAP version

We present an effective non-relativistic theory of self-interacting dark matter. We classify the long range interactions and discuss how they can be generated from quantum field theories. Generic dark sectors can generate singular potentials. We show how to consistently renormalize such potentials and apply this to the calculation of the Sommerfeld enhancement of dark matter interactions. We explore further applications of this enhancement to astrophysical probes of dark matter including the core vs. cusp problem., Comment: 25 pages, 6 figures

We describe the cosmological dynamics of perfect fluids within the framework of effective field theories. The effective action is a derivative expansion whose terms are selected by the symmetry requirements on the relevant long-distance degrees of freedom, which are identified with comoving coordinates. The perfect fluid is defined by requiring invariance of the action under internal volume-preserving diffeomorphisms and general covariance. At lowest order in derivatives, the dynamics is encoded in a single function of the entropy density that characterizes the properties of the fluid, such as the equation of state and the speed of sound. This framework allows a neat simultaneous description of fluid and metric perturbations. Longitudinal fluid perturbations are closely related to the adiabatic modes, while the transverse modes mix with vector metric perturbations as a consequence of vorticity conservation. This formalism features a large flexibility which can be of practical use for higher order perturbation theory and cosmological parameter estimation., Comment: Matches JCAP version

We examine the possibility that the recently discovered 125 GeV higgs like resonance actually corresponds to a dilaton: the Goldstone boson of scale invariance spontaneously broken at a scale f. Comparing to LHC data we find that a dilaton can reproduce the observed couplings of the new resonance as long as f ~ v, the weak scale. This corresponds to the dynamical assumption that only operators charged under the electroweak gauge group obtain VEVs. The more difficult task is to keep the mass of the dilaton light compared to the dynamical scale, Lambda ~ 4 pi f, of the theory. In generic, non-supersymmetric theories one would expect the dilaton mass to be similar to Lambda. The mass of the dilaton can only be lowered at the price of some percent level (or worse) tuning and/or additional dynamical assumptions: one needs to suppress the contribution of the condensate to the vacuum energy (which would lead to a large dilaton quartic coupling), and to allow only almost marginal deformations of the CFT., Comment: 30 pages, 4 figures; v2: references added, typos fixed, discussions clarified, accepted for publication in EPJC

The spontaneous breaking of linearly realized N=1 supersymmetry implies the existence of a pseudo-Goldstone fermion, the goldstino, and of its complex scalar superpartner, the sgoldstino. The latter has generically sizable tree-level couplings to Standard Model gauge bosons while its couplings to SM fermions are suppressed. We consider a light sgoldstino, with a mass around 1 TeV, that mixes with a SM-like Higgs scalar at around 125 GeV. We show that such a mixing can enhance the Higgs to di-photon signal rate while evading all the relevant experimental bounds and without significantly affecting the other decay channels., Comment: 8 pages, 6 figures and 1 table

The coupling of a composite Higgs to the standard model fields can deviate substantially from the standard model values. In this case perturbative unitarity might break down before the scale of compositeness is reached, which would suggest that additional composites should lie well below this scale. In this paper we account for the presence of an additional spin 1 custodial triplet of rhos. We examine the implications of requiring perturbative unitarity up to the compositeness scale and find that one has to be close to saturating certain unitarity sum rules involving the Higgs and the rho couplings. Given these restrictions on the parameter space we investigate the main phenomenological consequences of the spin 1 triplet. We find that they can substantially enhance the Higgs di-photon rate at the LHC even with a reduced Higgs coupling to gauge bosons. The main existing LHC bounds arise from di-boson searches, especially in the experimentally clean channel where the charged rhos decay to a W-boson and a Z, which then decay leptonically. We find that a large range of interesting parameter space with 700 GeV < m(rho) < 2 TeV is currently experimentally viable., Comment: 37 pages, 12 figures; v4: sum rule corrected, conclusions unchanged

We propose that the fermionic superpartner of a weak-scale Goldstone boson can be a natural WIMP candidate. The p-wave annihilation of this `Goldstone fermion' into pairs of Goldstone bosons automatically generates the correct relic abundance, whereas the XENON100 direct detection bounds are evaded due to suppressed couplings to the Standard Model. Further, it is able to avoid indirect detection constraints because the relevant s-wave annihilations are small. The interactions of the Goldstone supermultiplet can induce non-standard Higgs decays and novel collider phenomenology., Comment: 25 pages, 6 figures. References added, minor typos corrected. Submitted to JHEP

Neutrino oscillation experiments are known to be sensitive to Non-Standard Interactions (NSIs). We extend the NSI formalism to include one-loop effects. We discuss universal effects induced by corrections to the tree level W exchange, as well as non-universal effects that can arise from scalar charged current interactions. We show how the parameters that can be extracted from the experiments are obtained from various loop amplitudes, which include vertex corrections, wave function renormalizations, mass corrections as well as box diagrams. As an illustrative example, we discuss NSIs at one loop in the Minimal Supersymmetric Standard Model (MSSM) with generic lepton flavor violating sources in the soft sector. We argue that the size of one-loop NSIs can be large enough to be probed in future neutrino oscillation experiments., Comment: 27 pages, 4 figures

The Higgs boson may dominantly decay to 4 light jets through a light pseudo-scalar intermediary: h -> 2 eta -> 4j, making reconstruction at the LHC particularly challenging. We explore the phenomenology of such "Buried Higgs" scenarios in which the primary discovery channel of the Higgs is in cascade decays of superpartners. QCD backgrounds that would otherwise overwhelm the Higgs decay are suppressed by the requirement of high p_T jets and large missing transverse momentum that are the typical signatures of TeV scale supersymmetry. Utilizing jet substructure techniques, we find that for buried Higgses in the 100-120 GeV range, a 5-sigma discovery can be expected with roughly 10-25 inverse fb of data at E_CM = 14 TeV. For lighter Higgs bosons, the signal is contaminated by hadronically decaying W bosons, and discovery remains an unsolved challenge., Comment: 10 pages, 7 figures, references added

We show that the low-energy dynamics of anyons in (1+1)-dimensions with the smallest number of derivatives and C, P and T symmetric interactions, are dual to the sine-Gordon model for bosonic fields. We discuss in particular the Tomonaga-Luttinger, Thirring and Schwinger models, as well as their deformation by relevant and marginal operators. In the presence of electromagnetic interactions, the mass of the meson from anyon confinement and the chiral anomaly get corrected by the statistical parameter., Comment: 17+1 pages, extra appendix, typos fixed

We investigate Luttinger junctions of quantum wires away from criticality. The one-body scattering matrix, corresponding to the off-critical boundary conditions at the junction, admits in general antibound and/or bound states. Their contribution to the theory is fixed by causality. The presence/absence of bound states determines the existence of two different regimes with inequivalent physical properties. A scattering matrix without bound states defines an isolated equilibrium system. Bound states instead drive the system away from equilibrium, giving raise to non-trivial incoming or outgoing energy flows in the junction. We derive in both regimes and in explicit form the electromagnetic conductance tensor, pointing out the different impact of bound and antibound states., Comment: LaTex, 9 pages, 1 figure

We present a simple supersymmetric model where the dominant decay mode of the lightest Higgs boson is h->2eta->4c where eta is a light pseudoscalar and c is the charm quark. For such decays the Higgs mass can be smaller than 100 GeV without conflict with experiment. Together with the fact that both the Higgs and the pseudoscalar eta are pseudo-Goldstone bosons, this resolves the little hierarchy problem., Comment: 6 pages, 2 figures

We explore the possibility to break time reversal invariance at the junction of quantum wires. The universal features in the bulk of the wires are described by the anyon Luttinger liquid. A simple necessary and sufficient condition for the breaking of time reversal invariance is formulated in terms of the scattering matrix at the junction. The phase diagram of a junction with generic number of wires is investigated in this framework. We give an explicit classification of those critical points which can be reached by bosonization and study the interplay between their stability and symmetry content., Comment: Extended version (Appendices C and D and some references added, typos corrected) to appear in Phys. Rev. B

We present an extension of the MSSM where the dominant decay channel of the Higgs boson is a cascade decay into a four-gluon final state. In this model the Higgs is a pseudo-Goldstone boson of a broken global symmetry SU(3)-> SU(2). Both the global symmetry breaking and electroweak symmetry breaking are radiatively induced. The global symmetry breaking pattern also implies the existence of a light (few GeV) pseudo-Goldstone boson eta which is a singlet under the standard model gauge group. The h -> eta eta branching fraction is large, and typically dominates over the standard h -> b b decay. The dominant decay of eta is into two gluons, while the decays to photons, taus or lighter standard model flavors are suppressed at the level of 10^(-4) or more. With h-> 4 jets as the dominant decay, the Higgs could be as light as 78 GeV without being detected at LEP, while detection at the LHC is extremely challenging. However many of the super- and global symmetry partners of the standard model particles should be easily observable at the LHC. Furthermore, the LHC should be able to observe a "wrong Higgs" that is a 300-400 GeV heavy Higgs-like particle with suppressed couplings to W and Z that by itself does not account for electroweak precision observables and the unitarity of WW scattering. At the same time, the true Higgs is deeply buried in the QCD background., Comment: 19+1 pages, 13 figures, added references, accepted in PRD

We present an extended study of anyonic Luttinger liquids wires jointing at a single point. The model on the full line is solved with bosonization and the junction of an arbitrary number of wires is treated imposing boundary conditions that preserve exact solvability in the bosonic language. This allows to reach, in the low momentum regime, some of the critical fixed points found with the electronic boundary conditions. The stability of all the fixed points is discussed., Comment: 16 pages, 2 figures, typos corrected, Refs added

We investigate the idea of the Higgs doublet as a pseudo-Goldstone boson in perturbative extensions of the Standard Model, motivated by the desire to ameliorate its hierarchy problem without conflict with the electroweak precision data. Two realistic supersymmetric models with global SU(3) symmetry are proposed, one for large and another for small values of tan\beta. The two models demonstrate two different mechanisms for EWSB and the Higgs mass generation. Their experimental signatures are quite different. Our constructions show that a pseudo-Goldstone Higgs doublet in perturbative extensions is just as plausible as in non-perturbative ones., Comment: 16pp, typos corrected, phenomenological discussion expanded

The variety of ideas put forward in the context of a "composite" picture for the Higgs boson calls for a simple and effective description of the related phenomenology. Such a description is given here by means of a "minimal" model and is explicitly applied to the example of a Higgs-top sector from an SO(5) symmetry. We discuss the spectrum, the ElectroWeak Precision Tests, B-physics and naturalness. We show the difficulty to comply with the different constraints. The extended gauge sector relative to the standard SU(2)xU(1), if there is any, has little or no impact on these considerations. We also discuss the relation of the "minimal" model with its "little Higgs" or "holographic" extensions based on the same symmetry., Comment: 22 pp; v3: Small corrections, version to be published in Phys. Rev. D