Factorization and resummation for precision physics at the LHC

The LHC precision program aims to more thoroughly test the Standard Model of particle physics than ever before. Precise theory predictions for realistic experimental observables are a key ingredient in this program. Experimental observables that are sensitive to radiation in the soft and/or collinear limit of Quantum Chromodynamics often admit a factorization into simpler pieces that encode the dynamics at different scales. Factorization in turn enables the use of the renormalization group to predict, at fixed order, or resum, to all orders in perturbation theory, contributions from large logarithms that can dominate the cross section. In this thesis we derive new factorization results for hadronic collisions using the language of Soft-Collinear Effective Theory. These results extend and improve existing resummation methods, in particular towards a more detailed description of the final state. We extend the standard jet p${}_T$ (jet veto) resummation into a systematic framework that accounts for a finite jet rapidity cut up to which jets are reconstructed, as required by the finite detector acceptance in experiments. We also consider the case of a step in the veto parameter at some value of rapidity, which is of experimental relevance to avoid the increased contamination from unsuppressed pile-up beyond the reach of the tracking detectors. We next consider the production cross section for a Z boson differential in the Z boson transverse momentum p${}_T^Z$ and the 0-jettiness event shape T${}_0$. We perform, for the first time, the simultaneous analytic resummation of all large logarithms in both p${}_T^Z$ and T${}_0$ at NNLL+NLO, and present the first analytic predictions for a Sudakov peak in two independent resolution variables in pp collisions. We present and prove a generalization of the classic soft threshold factorization theorem that holds in the limit where only one proton is probed at a large momentum fraction by the hard process and collinear radiation into the final state is kinematically still allowed. This is a much weaker limit than the standard soft limit of taking both momentum fractions to one. At the partonic level, the new factorization theorem captures all singular terms in the partonic cross section, including in particular off-diagonal partonic channels. As a first illustrative example of its many applications, we use it to derive a nontrivial set of terms in the N${}^3$LO Drell-Yan rapidity spectrum. Using consistency relations with known soft matrix elements that in part arise from our new factorization theorem, we derive the leading eikonal terms at third order in perturbation theory for the q${}_T$ and T${}_0$ beam functions. Finally, we show how to perform the resummation of so-called fiducial power corrections in p${}_T^Z$ or p${}_T^W$ that arise from experimental measurements on the decay products of a Z or W boson. We find an improved agreement with precision ATLAS and CMS measurements of the p${}_T^Z$ and ${\varphi }^{\ast }$ spectrum when including the resummation of these power corrections in cutting-edge N${}^3$LL+NNLO predictions. Using the same approach, we present the first analytically resummed result for the lepton p${}_T^{\ell }$ spectrum in W decays at N${}^3$LL+NNLO.