Composite Higgs theory

I review the idea of realizing the Higgs as a composite pseudo-Nambu-Goldstone boson of a new strongly-interacting sector and collect major constraints on the parameter space of minimal models. Besides limits from electroweak precision tests, LHC searches for resonances and bounds due to Higgs-coupling modifications will be discussed in detail. Finally, the issue of light top partners in these models will be explored, including ways to avoid them which lead to interesting implications for flavor observables.Comment: 12 pages, 5 figures, Proceedings of ALPS2018: An Alpine LHC Physics Summi

On the connectedness of Deligne-Lusztig varieties

We give a criterion which determines when a union of one-dimensional Deligne-Lusztig varieties has a connected closure. We also obtain a new, short proof of the connectedness criterion for Deligne-Lusztig varieties due to Lusztig.Comment: v2: Revised Section 3, added Section 4. 6 page

Lepton Flavor and Non-Universality from Minimal Composite Higgs Setups

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 $R_K= {\cal B}(B \to K \mu^+ \mu^-)/{\cal B}(B \to K e^+ e^-)$, found by LHCb, can be addressed, while other constraints from quark- and lepton-flavor physics are met. In fact, the minimal structure of the setup allows for the implementation of a very powerful flavor protection, which avoids the appearance of new sources of flavor-changing neutral currents to very good approximation. Finally, the new lepton sector provides a parametrically enhanced correction to the Higgs mass, such that the need for ultra-light top partners is weakened considerably, linking the mass of the latter with the size of the neutrino masses.Comment: 5 pages, 3 figures; v2: matches version published in Physical Review Letters, for some slightly extended discussions see v