Reimagining New Physics: Higgs, Flavour, Dark Matter, and Topology Beyond the Standard Model

In 2012 the Large Hadron Collider (LHC) discovered the Higgs boson to complete the Standard Model, our most precise theory of Nature. But the Standard Model provides no account of dark matter, which outweighs all known particles by 5:1. Furthermore, the Higgs is central to two mysteries: the hierarchy problem, whereby the Higgs was found to be much lighter than it should be, and the flavour puzzle, whereby the Higgs gives very different masses to three otherwise identical copies of quarks and leptons (the lightest forming all atomic matter). Before the LHC turned on, theorists were confident it would find particles that solved the hierarchy problem and doubled-up as dark matter, and they put the flavour puzzle aside. But after extensive searches at the LHC and in dark matter direct detection experiments, there is no evidence supporting this paradigm. This project will pioneer new theoretical approaches to solve these problems and develop experimental strategies to test them. 1. Higgs and Flavour: rather than separating the Higgs-centric mysteries of the Standard Model, I will build theories that solve the hierarchy problem and flavour puzzle together. I will do so by merging our best solutions to the hierarchy problem, namely supersymmetry and the composite Higgs, with the idea of non-universal gauge interactions and ultimately electroweak flavour unification - which furthermore explains why there are three copies of particles in the first place. The resulting theories predict new particles that interact strongly with the Higgs and the heaviest quarks and leptons. Experimental constraints on such flavoured particles are currently much weaker than the constraints on the flavour-blind particles favoured pre-LHC. I will collaborate with experimentalists to search for these new particles in data from the LHC and other experiments, as well as exploring their prospects for discovery in future colliders, thereby charting a new “flavoured path” to BSM physics. 2. Higgs and Topology: I will demonstrate how algebraic topology, the abstract mathematics for measuring rigid properties of shapes, provides an untapped way to experimentally probe composite Higgs solutions to the hierarchy problem. While all experimental studies to date constrain geometry, every composite Higgs theory is also characterized by interesting topology, the consequences of which have been barely explored. After using tools from topology to construct a suite of new topological interactions appearing in these theories I will collaborate with experimentalists to design innovative searches for them in the ATLAS detector. I thus hope to demonstrate that topology provides a distinctive way to test compositeness at the LHC and even in cosmology, which I expect to be especially rich for the flavoured composite Higgs theory that I will develop in part (1). 3. Dark Matter and Topology: I apply the same topological tools as in (2) to explore a new topological portal to the dark Universe, that can explain the observed abundance of dark matter as well as its non-observation in direct detection experiments. I will build a complete high-energy theory for this topological portal. With this theory in hand, I aim to establish new experimental paths to discovering dark matter via spectacular signatures in the LHC and electron-positron colliders like Belle-II predicted by the topological portal, for instance involving long-lived particles with distinctive multi-photon decays, that have been so far overlooked in experiments.