Precision predictions for Higgs differential distributions at the LHC

After the discovery of a Standard-Model-like Higgs boson at the LHC a central aspect of the LHC physics program is to study the Higgs boson's couplings to Standard Model particles in detail in order to elucidate the nature of the Higgs mechanism and to search for hints of physics beyond the Standard Model. This requires precise theory predictions for both inclusive and differential Higgs cross sections. In this thesis we focus on the application of resummation techniques in the framework of Soft-Collinear Effective Theory (SCET) to obtain accurate predictions with reliable theory uncertainties for various observables. We first consider transverse momentum distributions, where the resummation of large logarithms in momentum (or distribution) space has been a long-standing open question. We show that its two-dimensional nature leads to additional difficulties not observed in one-dimensional observables such as thrust, and solving the associated renormalization group equations (RGEs) in momentum space thus requires a very careful scale setting. This is achieved using distributional scale setting, a new technique to solve differential equations such as RGEs directly in distribution space, as it allows one to treat logarithmic plus distributions like ordinary logarithms. We show that the momentum space solution fundamentally differs from the standard resummation in Fourier space by different boundary terms to all orders in perturbation theory and hence provides an interesting and complementary approach to obtain new insight into the all-order perturbative and nonperturbative structure of transverse momentum distributions. Our work lays the ground for a detailed numerical study of the momentum space resummation. We then show that in the case of a discovery of a new heavy color-singlet resonance such as a heavy Higgs boson, one can reliably and model-independently infer its production mechanism by dividing the data into two mutually exclusive jet bins. The method is based on a resummation framework that precisely predicts the jet cut dependence and systematically incorporates theory uncertainties and their correlations among the jet bins. The technique is demonstrated for an example scalar resonance of mass m_X=750 GeV. It can also be applied to and tested in diphoton production which receives contributions from both quark annihilation and gluon fusion. Here, the presence of final state photons requires photon isolation cuts which yield unresummed nonglobal logarithms. As a first step towards the full analysis, we show that these are numerically small and can be incorporated in fixed-order perturbation theory. Vice versa, we find that the jet veto renders contributions from fragmentation photons power suppressed, and thus is a particularly clean channel to study direct diphoton production at the LHC. Lastly, we discuss the resummation of timelike logarithms ln²(-1)= π² in Higgs production, arising in the form factor at timelike momentum transfer. Their resummation is well understood in exclusive cross sections known to factorize. We show how to consistently incorporate the resummation into inclusive cross sections, discussing in detail the validity of the technique and associated uncertainties. The method is first applied to the total cross section in gluon fusion Higgs production at N³LO+N³LL_φ^', where it significantly improves perturbative convergence and reduces perturbative uncertainties by about a factor of two. We also obtain the currently most precise Higgs rapidity spectrum at NNLO+NNLL_φ^' with a similar reduction of uncertainties. The effect is less pronounced in bottom-quark annihilation, but still shows that the resummation of timelike logarithms is a beneficial and viable tool for Higgs production.