Multi-differential resummation for the LHC

Differential measurements at the LHC involve many physical scales set by the hard production process and soft or collinear QCD dynamics. When these scales are widely separated, the perturbative series becomes dominated by logarithms of their ratios. Precise (or sometimes even just physical) theory predictions require the resummation of these large logarithms to all orders. In this talk I will provide an overview of the challenges encountered when extending the resummation program to multi-differential observables, and of the new insights one gains into the infrared structure of QCD. I will first briefly review single-differential resummation methods, focusing on TMD factorization and the transverse momentum (qT) of electroweak gauge bosons at hadron colliders as a key application. I will then discuss the extension to the simultaneous measurement of qT and the beam thrust (or 0-jettiness) event shape, and explain how it gives rise to a 2D Sudakov emission spectrum. In the second half of the talk I will show how treating a very basic QCD quantity (the Drell-Yan rapidity spectrum) in a multi-differential spirit leads to surprising new insight into its all-order perturbative structure, and generalizes the classic QCD result of threshold (or soft-gluon) resummation.