Soft Threshold Limit of Drell-Yan Angular Distributions

Abstract

The angular distribution of the final state leptons in the Drell-Yan process plays a key role for testing the QCD dynamics of Z/W bosons production and for measuring the values of masses and couplings of the EW sector of the SM. This angular distribution is in one to one correspondence to the set of of production cross sections for vector bosons of definite helicity (helicity cross sections) which feature sensitivity to soft and collinear QCD radiation. In this thesis, we calculate radiative corrections to the helicity cross sections up to next-to-next-to leading order (NNLO) in the strong coupling, focusing on the emission of a single and double gluon from the initial state quark-antiquark pair. We then study the behavior of these corrections in the soft threshold limit, where the dilepton pir invariant mass approaches the available center of mass energy. Finally, we use Soft-Collinear Effective Theory (SCET) to derive soft factorization theorems for Drell-Yan helicity cross sections ranging from the leading-power (LP) to the next-to-next-to-leading power (NNLP) in the soft expansion, perturbatively evaluate the relevant subleading soft functions, and perform a comparison to our expanded full-QCD results.