Fundamental Composite Dynamics: A Review

Abstract

We introduce fundamental gauge theories that can be employed to construct informed composite bright and dark extensions of the Standard Model, within and beyond the standard paradigms. The gap between theory and experiments is bridged by providing predictions and ways to test them, for example, at the Fermi scale and via precision flavor experiments. We will review time-honoured paradigms from (walking) technicolor to composite Goldstone Higgs and discuss their features and differences. Standard model fermion mass generation in composite models will also be discussed along with the challenges and opportunities that it offers. To be concrete and pedagogical we will concentrate on minimal constructions featuring strongly coupled gauge theories supporting the global symmetry breaking pattern SU(4)/Sp(4). The most minimal underlying 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 first principle lattice results to predict the massive spectrum for models of composite (Goldstone) Higgs dynamics and strongly interacting dark matter, of immediate impact for current and future experimental searches. Because composite dynamics embraces a rich spectrum of theories with dynamics ranging from QCD-like behaviour to (near) conformal one, we also report here the state-of-the-art of numerical and analytic properties of several strongly coupled theories including their spectrum, phase diagrams and, when applicable, their (near) conformal data.

Gauge hierarchy from electroweak vacuum metastability

“…As θ 0 appears also in the Higgs' couplings to SM gauge bosons, reproducing the pure SM in the limit θ 0 → 0, it is in principle accessible to experiments. Indeed, the continuing agreement of experimental data with the pure SM can be translated to the upper bound sin θ 0 0.2 [72,73]. Evidently, compositeness replaces the fine-tuning of the hierarchy problem with another apparent fine-tuning between X t and X m .…”

A Flavor Change Study based on Dyson-Schwinger Equation

“…In other words, the Higgs mechanism may have a dynamic mechanism, and the Higgs boson should be composite (see, e.g., Refs. [7][8][9][10]). In order to ensure the hierarchical structure of quarks, charged leptons, and neutrinos that match the strengths of the corresponding interactions, the Higgs boson needs to participate in all the three kind interactions, so it can only be composed of quarks.…”

Charging the Walking U(N)$\times$U(N) Higgs Theory as a Complex CFT

“…The latter behaviour has been invoked in the literature for models of dynamical electroweak symmetry breaking [8][9][10]. Lattice methods have been employed to establish walking as summarised in Ref [11]. Another way to discuss walking is via the emergence of two complex zeros of the beta-function in the near-conformal phase [3,12].…”