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Register a new userThe high energy fate of the minimal Goldstone Higgs
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We consider a minimal model where the Higgs boson arises as an elementary pseudo-Nambu-Goldstone boson. The model is based on an extended scalar sector with global SO(5)/SO(4) symmetry. To achieve the correct electroweak symmetry breaking pattern, the model is augmented either with an explicit symmetry breaking term or an extra singlet scalar field. We consider separately both of these possibili- ties. We fit the model with the known particle spectrum at the electroweak scale and extrapolate to high energies using renormalization group. We find that the model can remain stable and perturbative up to the Planck scale provided that the heavy beyond Standard Model scalar states have masses in a narrow interval around 3 TeV.
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We consider the renormalizable $SO(5)/SO(4)$ $sigma$-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 predictions for photonic signals in axion searches for all models discussed. Because of the constraints imposed on the exotic fermion sector by the Standard Model fermion masses, the expected range of allowed axion-photon couplings turns out to be generically narrowed with respect to that of standard invisible axion models, impacting the experimental quest.
The transition between the broken and unbroken phases of massive gauge theories, namely the rearrangement of longitudinal and Goldstone degrees of freedom that occurs at high energy, is not manifestly smooth in the standard formalism. The lack of smoothness concretely shows up as an anomalous growth with energy of the longitudinal polarization vectors, as they emerge in Feynman rules both for real on-shell external particles and for virtual particles from the decomposition of the gauge field propagator. This makes the characterization of Feynman amplitudes in the high-energy limit quite cumbersome, which in turn poses peculiar challenges in the study of Electroweak processes at energies much above the Electroweak scale. We develop a Lorentz-covariant formalism where polarization vectors are well-behaved and, consequently, energy power-counting is manifest at the level of individual Feynman diagrams. This allows us to prove the validity of the Effective W Approximation and, more generally, the factorization of collinear emissions and to compute the corresponding splitting functions at the tree-level order. Our formalism applies at all orders in perturbation theory, for arbitrary gauge groups and generic linear gauge-fixing functionals. It can be used to simplify Standard Model loop calculations by performing the high-energy expansion directly on the Feynman diagrams. This is illustrated by computing the radiative corrections to the decay of the top quark.
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 the Standard Model. We will analyze the minimal underlying realization in terms of fundamental strongly coupled gauge theories supporting the flavor symmetry breaking pattern SU(4)/Sp(4) $sim$ SO(6)/SO(5). The most minimal fundamental description consists of an SU(2) gauge theory with two Dirac fermions transforming according to the fundamental representation of the gauge group. This minimal choice enables us to use recent first principle lattice results to make the first predictions for the massive spectrum for models of composite (Goldstone) Higgs dynamics. These results are of the upmost relevance to guide searches of new physics at the Large Hadron Collider.
Most of the analysis of composite Higgs have focussed on the Minimal Composite Higgs Model, based on the coset SO(5)$times$U(1)$_X$/SO(4)$times$U(1)$_X$. We consider a model based on the coset of simple groups SO(7)/SO(6), with SO(4)$times$U(1)$_X$ embedded into SO(6). This extension of the minimal model leads to a new complex pNGB that has hypercharge and is a singlet of SU(2)$_L$, with properties mostly determined by the pattern of symmetry breaking and a mass of order TeV. Composite electroweak unification also leads to new bosonic and fermion resonances with exotic charges, not present in the minimal model. The lightest of these resonances is stable, and in some cases could provide candidates for dark matter. A new rich phenomenology is expected at LHC.
Recently a new class of theories of electroweak symmetry breaking have been constructed. These models, based on deconstruction and the physics of theory space, provide the first alternative to weak-scale supersymmetry with naturally light Higgs fields and perturbative new physics at the TeV scale. The Higgs is light because it is a pseudo-Goldstone boson, and the quadratically divergent contributions to the Higgs mass are cancelled by new TeV scale ``partners of the {em same} statistics. In this paper we present the minimal theory space model of electroweak symmetry breaking, with two sites and four link fields, and the minimal set of fermions. There are very few parameters and degrees of freedom beyond the Standard Model. Below a TeV, we have the Standard Model with two light Higgs doublets, and an additional complex scalar weak triplet and singlet. At the TeV scale, the new particles that cancel the 1-loop quadratic divergences in the Higgs mass are revealed. The entire Higgs potential needed for electroweak symmetry breaking--the quartic couplings as well as the familiar negative mass squared--can be generated by the top Yukawa coupling, providing a novel link between the physics of flavor and electroweak symmetry breaking.
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