Compositeness above the electroweak scale and a proposed test at LHCb

I review attempts to construct models of partial compositeness from strongly coupled gauge theories. A few minimal assumptions allow one to isolate a small number of representative models. After presenting the main idea, I discuss a recent proposal to detect a light pseudo-scalar, predicted in all these models, at the LHCb detector.

Exploring new possibilities to discover a light pseudo-scalar at LHCb

We study the possibility of observing a light pseudo-scalar a at LHCb. We target the mass region $$2.5\,\mathrm{GeV}\lesssim m_a\lesssim 60\,\mathrm{GeV}$$ 2.5 GeV ≲ m a ≲ 60 GeV and various decay channels, some of which have never been considered before: muon pairs, tau pairs, D meson pairs, and di-photon. We interpret the results in the context of models of 4D Composite Higgs and Partial Compositeness in particular.

Loop-generated neutrino masses in composite Higgs models

We present a composite scotogenic model for neutrino masses, which are generated via loops of ℤ2-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 ℤ2-odd right-handed neutrinos have masses between the TeV and the Planck scales. Additionally, the lightest ℤ2-odd composite scalar may play the role of Dark Matter, either via thermal freeze-out or as an asymmetric relic. This mechanism can be featured in a variety of models based on vacuum misalignment. For concreteness, we demonstrate it in a composite two-Higgs scheme based on the coset SU(6)/Sp(6).

Flavour observables and composite dynamics: leptons

We review lepton flavor physics and corresponding observables in the composite Higgs framework with partial compositeness, considering ‘UV complete’ setups as well as effective and holographic approaches. This includes anarchic flavor setups, scenarios with flavor symmetries, and minimal incarnations of the see-saw mechanism that naturally predict non-negligible lepton compositeness. We focus on lepton flavor violating processes, dipole moments, and on probes of lepton flavor universality, all providing stringent tests of partial compositeness. We discuss the expected size of effects in the different approaches to lepton flavor, which will be useful to understand how a composite lepton sector could look like, given up-to-date experimental constraints.

Neutrino masses from low scale partial compositeness

We consider a class of models in which the neutrinos acquire Majorana masses through mixing with singlet neutrinos that emerge as composite states of a strongly coupled hidden sector. In this framework, the light neutrinos are partially composite particles that obtain their masses through the inverse seesaw mechanism. We focus on the scenario in which the strong dynamics is approximately conformal in the ultraviolet, and the compositeness scale lies at or below the weak scale. The small parameters in the Lagrangian necessary to realize the observed neutrino masses can naturally arise as a consequence of the scaling dimensions of operators in the conformal field theory. We show that this class of models has interesting implications for a wide variety of experiments, including colliders and beam dumps, searches for lepton flavor violation and neutrinoless double beta decay, and cosmological observations. At colliders and beam dumps, this scenario can give rise to striking signals involving multiple displaced vertices. The exchange of hidden sector states can lead to observable rates for flavor violating processes such as μ → eγ and μ → e conversion. If the compositeness scale lies at or below a hundred MeV, the rate for neutrinoless double beta decay is suppressed by form factors and may be reduced by an order of magnitude or more. The late decays of relic singlet neutrinos can give rise to spectral distortions in the cosmic microwave background that are large enough to be observed in future experiments.

Towards a fundamental safe theory of composite Higgs and dark matter

We present a novel paradigm that allows to define a composite theory at the electroweak scale that is well defined all the way up to any energy by means of safety in the UV. The theory flows from a complete UV fixed point to an IR fixed point for the strong dynamics (which gives the desired walking) before generating a mass gap at the TeV scale. We discuss two models featuring a composite Higgs, Dark Matter and partial compositeness for all SM fermions. The UV theories can also be embedded in a Pati–Salam partial unification, thus removing the instability generated by the $$\text{ U }(1)$$ U ( 1 ) running. Finally, we find a Dark Matter candidate still allowed at masses of 260 GeV, or 1.5–2 TeV, where the latter mass range will be covered by next generation direct detection experiments.

A more natural composite Higgs model

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 quartic term from the collective symmetry breaking of the little Higgs mechanism can be realized by the partial compositeness couplings between elementary Standard Model fermions and the composite operators, without introducing new elementary fields beyond the Standard Model and the composite sector. The model contains two Higgs doublets, as well as several additional pseudo-Nambu-Goldstone bosons. To avoid tuning, the extra Higgs bosons are expected to be relatively light and may be probed in the future LHC runs. The deviations of the Higgs couplings and the weak gauge boson couplings also provide important tests as they are expected to be close to the current limits in this model.