Synergies between effective field theories: global analyses of the Minimal Flavour Violating SMEFT and subleading NLO analysis of $b\to s\gamma$ transitions

Abstract

The Standard Model (SM) of particle physics, despite its remarkable predictive power, is widely recognised as incomplete. Effective Field Theories (EFTs) provide a systematic framework to explore physics beyond the SM, both through searches for new heavy particles within the Standard Model Effective Field Theory (SMEFT) and through precision studies at low energy using the Soft-Collinear Effective Theory (SCET). A central theme of this thesis is the consistent inclusion of higher-order effects, specifically Next-to-Leading Order (NLO) corrections and Renormalisation Group Evolution (RGE), which are essential for achieving reliable theoretical predictions and for connecting different energy scales. In the SMEFT part of this work, I developed and critically assessed a global analysis that combines theoretical and experimental information across multiple observables. Unlike purely data-driven approaches, this analysis was performed within a flavour-symmetric UV-inspired framework. Building on this foundation, I systematically incorporated NLO corrections and RGE effects, showing their significant impact on Wilson coefficient determinations, their correlations, and ultimately the interpretation of new physics constraints. In the flavour-physics sector, I investigated the inclusive decay $\bar{B}\to X_s\gamma$ within SCET. In this context, I focused on the non-local contributions, which appear only at the NLO in $1/m_b$, and currently constitute one of the largest sources of uncertainty in this inclusive decay rate. In particular, the numerically dominant non-local contribution arises from the interference of the two electroweak operators $Q_1^q$ and $Q_{7\gamma}$. To this end, I computed previously unknown $\mathcal{O}(\alpha_s)$ corrections to the functions entering the factorisation theorem of this non-local contribution. Important advances include the determination and analysis of the RGE of the non-perturbative soft function $g_{17}$, enabling the resummation of large logarithms, as well as the computation of the NLO (two-loop) $\bar{n}$-jet function. These technically demanding calculations not only improve the theoretical predictions but also provide novel insights into the structure of SCET factorisation. Together, these results significantly enhance the precision and scope of EFT analyses, both in constraining new physics through global fits and in improving the precision of key flavour observables predictions.