Precision studies of soft-collinear QCD dynamics in the presence of heavy quarks

The discovery of the Higgs boson in 2012 marked a milestone in confirming the Standard Model (SM) of particle physics, yet the SM remains incomplete, failing to account for phenomena such as gravity, dark matter, and the matter–antimatter asymmetry in the universe. This motivates precision studies of collider processes, where more accurate theoretical predictions are needed to match the increasing experimental precision. Key challenges arise from Quantum Chromodynamics (QCD), which demands both calculations to high loop-orders in the perturbative regime and a careful separation of perturbative and non-perturbative dynamics. This thesis is split into two parts, each addressing issues in one of these categories.
In the first part of this thesis, we present an all-order analysis of double-logarithmic corrections to the soft-overlap contribution in heavy-to-light transition form factors at large hadronic recoil. We focus on $B_c \to \eta_c$ transitions in a perturbative non-relativistic setup, treating both the bottom and charm quarks as heavy, with the hierarchy $m_b \gg m_c \gg \Lambda_{\rm QCD}$. Our diagrammatic analysis identifies two independent sources of double logarithms: soft-gluon effects, described by standard exponential Sudakov factors, and rapidity-ordered soft-quark configurations, which generate a novel set of coupled integral equations. These equations capture the intricate interplay between soft-quark and soft-gluon dynamics at the double-logarithmic level. As an independent consistency check, we employ a bare factorization formula within Soft-Collinear Effective Theory. Although endpoint-divergent convolution integrals prevent its use for resumming logarithmic corrections with renormalization group methods, its structure enables us to derive logarithmic corrections up to the two-loop level. By computing the only unknown contribution, we confirm the correctness of the integral equations to this order. While a closed-form solution of the integral equations remains currently elusive, we provide iterative expressions for the double-logarithmic series and derive the asymptotic behavior of the soft-overlap form factor at infinite recoil, showing that the Sudakov suppression is slightly weakened by the combined effects of soft quarks and soft gluons.
In the second part of this thesis, we study the phase-space integral of the double-emission soft limit of generic QCD amplitudes with massless and massive emitters at an arbitrary angle to each other. This is a necessary ingredient to extend the nested soft-collinear subtraction scheme to cases with massive final states at hadron colliders. We employ integration-by-parts identities and the differential equations method to obtain an analytic expression for the expansion around the small-velocity limit of the massive emitter, which is an important cross-check for the exact calculation with full dependence on the velocity.