NNLO QCD corrections for Drell-Yan $p_T^Z$ and $φ^*$ observables at the LHC

A. Gehrmann-De Ridder; T. Gehrmann; E. W. N. Glover; A. Huss; T. A. Morgan

Paper

NNLO QCD corrections for Drell-Yan $p_T^Z$ and $φ^*$ observables at the LHC

Abstract

Drell-Yan lepton pairs with finite transverse momentum are produced when the vector boson recoils against (multiple) parton emission(s), and is determined by QCD dynamics. At small transverse momentum, the fixed order predictions break down due to the emergence of large logarithmic contributions. This region can be studied via the

distribution constructed from the energies of the leptons, or through the

distribution that relies on the directions of the leptons. For sufficiently small transverse momentum, the

observable can be measured experimentally with better resolution. We study the small

and

distributions up to next-to-next-to-leading order (NNLO) in perturbative QCD. We compute the

distributions for the fully inclusive production of lepton pairs via

to NNLO and normalise them to the NNLO cross sections for inclusive

production. We compare our predictions with the

distribution measured by the ATLAS collaboration during LHC operation at 8 TeV. We find that at moderate to large values of

, the NNLO effects are positive and lead to a substantial improvement in the theory-data comparison compared to next-to-leading order (NLO). At small values of

and

, the known large logarithmic enhancements emerge through and we identify the region where resummation is needed. We find an approximate relationship between the values of

and

where the large logarithms emerge and find perturbative consistency between the two observables.