A Glance into the Future of Particle Physics with Effective Field Theories

Abstract

The experimental results obtained at the LHC mostly agree with the predictions made by the Standard Model of particle physics (SM). However, the need for Beyond the Standard Model (BSM) physics remains solid. But there is no clear path towards a successor for the SM. Hence, we must prepare the tools needed to explore the frontiers of physics thoroughly. In this work, we study one of the main theoretical tools that can be used for such an exploration, Effective Field Theories (EFTs). We show how to use them, study some of their formal aspects and explore the construction of an improved framework. We use the Standard Model Effective Field Theory (SMEFT) to assess the discovery potential of a future experimental tool, the hadron collider FCC-hh. We study the V h production process, with V = W, Z. We consider the channels where the Higgs boson decays to a photon pair and the gauge bosons decay leptonically, which will become available only at the high energies achieved by FCC-hh. The sensitivity of these channels to BSM effects is improved via the measurement of doubly-differential cross-sections. We obtain projected bounds on SMEFT dimension-6 Wilson Coefficients (WCs) and compare them with projections for other future colliders and other processes at FCC-hh. We also interpret our results in terms of anomalous Triple Gauge Couplings and simple UV models. The absence of gauge anomalies is required to preserve the consistency of a Quantum Field Theory. If parameters, such as the WCs in an EFT, generated gauge anomalies for certain values, they would be affected by theoretical constraints. We prove that SMEFT at dimension 6 is free from gauge anomalies coming from triangle diagrams for any value of its WCs. We checked this via the innovative use of bosonic EFT techniques. The bosonic EFT techniques are also used to analyse the relationship in axion EFTs between mixed global-gauge anomalies and axion couplings to vector bosons. They turn out to be unrelated when heavy chiral fermions are integrated out. This fact links axion EFTs to chiral extensions of the SM. For non-abelian gauge bosons, we find IR sum rules whose violation indicate the presence of chiral fields in the UV. We show a minimal phenomenologically relevant extension of the SM with an axion and chiral heavy fermions as an example and evaluate its main constraints. Finally, we explore how revisiting old formalisms can lead to new insights. We introduce the massless helicity spinor and massless scattering amplitudes formalisms and show how they facilitate the computation of the V h production process helicity amplitudes. Then, we present the extension of that formalism to the massive case and discuss how it constitutes an alternative to EFTs as a parametrisation of BSM effects. We study the V V h and V V hh amplitudes, of which we compute the high-energy limit including different BSM contributions.