The $q_T$ and $Δφ$ spectra in W and Z production at the LHC at N$^3$LL'+N$^2$LO

Wan-Li Ju; Marek Schönherr

Paper

The $q_T$ and $Δφ$ spectra in W and Z production at the LHC at N$^3$LL'+N$^2$LO

Abstract

The production of weak gauge bosons,

and

, are at the core of the LHC precision measurement program. Their transverse momentum spectra as well as their pairwise ratios are key theoretical inputs to many high-precision analyses, ranging from the

mass measurement to the determination of parton distribution functions. Owing to the different properties of the

and

boson and the different accessible fiducial regions for their measurement, a simple one-dimensional correlation is insufficient to capture the differing vector and axial-vector dynamics of the produced lepton pair. We propose to correlate them in two observables, the transverse momentum

of the lepton pair and its azimuthal separation

. Both quantities are purely transverse and therefore accessible in all three processes, either directly or by utilising the missing transverse momentum of the event. We calculate all the single-differential

and

as well as the double-differential

spectra for all three processes at N

LL'+N

LO accuracy, resumming small transverse momentum logarithms in the soft-collinear effective theory approach and including all singlet and non-singlet contributions. Using the double-differential cross sections we build the pairwise ratios

and determine their uncertainties assuming fully correlated, partially correlated, and uncorrelated uncertainties in the respective numerators and denominators. In the preferred partially correlated case we find uncertainties of less than 1% in most phase space regions and up to 3% in the lowest

region.