Multi-scalar critical theories: first steps for a non perturbative functional renormalization group analysis

In this work the fundamental ideas to study properties of QFTs with the functional Renormalization Group are presented and some examples illustrated. First the Wetterich equation for the effective average action and its flow in the local potential approximation (LPA) for a single scalar field is derived. This case is considered to illustrate some techniques used to solve the RG fixed point equation and study the properties of the critical theories in D dimensions. In particular the shooting methods for the ODE equation for the fixed point potential as well as the approach which studies a polynomial truncation with a finite number of couplings, which is convenient to study the critical exponents. We then study novel cases related to multi field scalar theories, deriving the flow equations for the LPA truncation, both without assuming any global symmetry and also specialising to cases with a given symmetry, using truncations based on polynomials of the symmetry invariants. This is used to study possible non perturbative solutions of critical theories which are extensions of known perturbative results, obtained in the epsilon expansion below the upper critical dimension.

Embedding Starobinsky inflation in string compactifications

A period of accelerated expansion of the primordial universe, known as inflation, represents the standard paradigm for the early universe cosmology. While inflation agrees with observational constraints, a complete understanding of its physical origin is not available yet. This suggests the necessity of an embedding into a more fundamental theory. String theory is arguably the best-developed candidate for an ultra-violet (UV) complete theory of gravity and string compactifications could provide a natural framework for addressing this issue. The aim of this thesis work is to investigate the potential embedding of Starobinsky inflation in effective field theories arising in string compactifications. In particular, we focus on two main objectives. The first one is the evaluation of Yukawa-like couplings in f (R)-theories of gravity with fermions, more specifically in the context of Starobinsky inflation. The second goal is understanding if any of the moduli which naturally arise in string compactifications has the right form of this coupling and displays the correct scalar potential, as needed for a possible identification with the scalar field driving Starobinsky inflation.

Phenomenology of top-philic axion-like particles

Axion like particles (ALPs), i.e., pseudo-scalar bosons interacting via derivative couplings, are a generic feature of many new physics scenarios, including those addressing the strong-CP problem and/or the existence of dark matter. Their phenomenology is very rich, with a wide range of scales and interactions being directly probed at very different experiments, from accelerators to observatories. In this thesis, we explore the possibility that ALPs might indirectly affect precision collider observables. In particular, we consider an ALPs that preferably couple to the top quark (top-philic) and we study new-physics 1- loop corrections to processes involving top quarks in the final state. Our study stems from the simple, yet non-trivial observation that 1-loop corrections are infrared finite even in the case of negligible ALP masses and therefore can be considered on their own. We compute the 1-loop corrections of new physics analytically in key cases involving top quark pair production and then implement and validate a fully general next-to-leading-order model in MadGraph5_aMC@NLO that allows to compute virtual effects for any process of interest. A detailed study of the expected sensitivity to virtual ALPs in ttbar production at the LHC is performed.