Resummation phenomenology and PDF determination for precision QCD at the LHC

With the ongoing Run 3 of the LHC and its upcoming High-Luminosity upgrade, there is a growing need to study observables that can be both experimentally measured and theoretically predicted with high precision. To match the demand for increased precision on the theory side, improvements of fixed-order perturbative predictions, resummation of logarithmic enhancements and accurate determination of proton structure are required. This thesis provides an exploration of the latter two topics. We discuss high-energy logarithms and their resummation techniques, introducing an extension of the HELL formalism (High Energy Large Logarithms) for multi-differential distributions in transverse momentum, rapidity and invariant mass. As a phenomenological study, we apply this framework to heavy-quark pair production at the LHC, studying the kinematics of both a single quark and the final-state pair. Part of the thesis is dedicated to studying an extension of the kt -factorisation framework, which underlies high-energy resummation, to capture next-to-leading logarithmic corrections. To put this hypothesis to the test, we delve into the computation of a NLO off-shell coefficient function. We use Higgs-induced Deep Inelastic Scattering in the limit mt → ∞ as a benchmark process and report a partial result. Beside high-energy logarithms, we consider the determination of transverse-momentum distributions from a high-invariant mass system with additional QCD radiation and exclusive cuts on the final state. Specifically, we focus on HW + associate production with a veto on the leading jet and analyse the Higgs transverse momentum spectrum at NNLO, using qt -subtraction. We complement the fixed order study with NNLL resummation of jet-veto logarithms and linear power correction in ptHW using the RadISH (RADiation off Initial State Hadrons) formalism. Finally, in the last project pertaining to this thesis we consider the problem of Parton Distribution Function determination. We propose a minimal parametrisation guided by physical arguments and investigate its performance in fitting the HERA dataset with NLO QCD theory predictions.