Peering from the Parapet of Perturbative QFT

Abstract

Modern experiments such as the Large Hadron Collider probe new physics through precise measurements that over-constrain Standard Model parameters to sub-percent accuracy, alongside broad searches for beyond-Standard-Model signals. Central to these efforts is perturbation theory, which approximates quantum field theory computations as series expansions in small parameters. Although the complete result lies in the full series, only the first few terms are computationally accessible, raising the question: when can perturbative predictions be trusted, and what alternatives exist when they fail? In this dissertation, we demonstrate that effective field theories (EFTs) can restore convergence by resumming perturbative series to all orders in the coupling. We illustrate this approach with examples from backward scattering in gauge theories, and the extraction of the strong coupling constant using heavy jet mass distribution from electron-positron colliders. Furthermore, by leveraging precision experimental data, we refine power counting in bottom-up flavor EFTs, imposing strong constraints on UV models of the SM flavor hierarchy. Finally, we address the breakdown of perturbation theory--manifested in non-convergent asymptotic series—-by interpreting diagrammatic renormalons as saddle points of the effective action, thereby developing a new probe into their existence via the path integral.