NNLO QCD corrections for Drell-Yan p T Z and \( {\phi}_{{}^{\eta}}^{\ast } \) observables at the LHC
Received: October
QCD corrections for Drell-Yan pZ
A. Gehrmann-De Ridder 0 1 2 4
T. Gehrmann 0 1 2
E.W.N. Glover 0 1 3
A. Huss 0 1 4
ETH 0 1
CH- 0 1
Zurich 0 1
Switzerland 0 1
CH- 0 1
Zurich 0 1
Switzerland 0 1
QCD. We compute the 0 1
via Z= 0 1
Open Access 0 1
c The Authors. 0 1
0 distribution measured by the ATLAS
1 University of Durham , Durham, DH1 3LE, U.K
2 Department of Physics, University of Zurich
3 Institute for Particle Physics Phenomenology, Department of Physics
4 Institute for Theoretical Physics
Drell-Yan lepton pairs with nite 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 xed order predictions break down due to that relies on the directions of the leptons. For su ciently small transverse momentum, observable can be measured experimentally with better resolution. We study the distributions up to next-to-next-to-leading order (NNLO) in perturbative distributions for the fully inclusive production of lepton pairs to NNLO and normalise them to the NNLO cross sections for inclusive Z= production. We compare our predictions with the collaboration during LHC operation at 8 TeV. We nd that at moderate to large values of , the NNLO e ects are positive and lead to a substantial improvement in the theory-data comparison compared to next-to-leading order (NLO). At small values of pZT and known large logarithmic enhancements emerge through and we identify the region where resummation is needed. We nd an approximate relationship between the values of pZT and where the large logarithms emerge and nd perturbative consistency between the two
distribution constructed from the energies of the leptons; or through the
-
Kinematics of the angular variable
in the low-pZT regime
The transverse momentum distribution at low p
1 Introduction
Numerical results
Calculational setup
Summary and conclusions
The production of Z-bosons which subsequently decay into a pair of leptons is a Standard
Model benchmark process at hadron colliders. It occurs with a large rate and, due to
nal state signature, can be measured very accurately with small experimental
uncertainties. It has been studied extensively at the LHC by the ATLAS [1, 2], CMS [3, 4]
and LHCb [5, 6] experiments.
When combined with precise theoretical predictions for related observables, there is
the potential for accurate determinations of fundamental parameters of the theory. In
particular, the transverse momentum distribution of the Z-boson has been one of the most
studied observables. The high sensitivity of the pZT spectrum to the distribution of gluons in
the proton makes it a key observable for constraining parton distribution functions (PDF's).
For inclusive Z-production, restricting ourselves to the framework of QCD, corrections
at next-to-next-to-leading order (NNLO) are available [7, 13{15] and the present state
of the art is obtained by combining the NNLO QCD corrections with a resummation of
next-to-next-to-leading logarithmic e ects (NNLL) [16{19]. This combination is necessary
to predict the transverse momentum distribution of the Z-boson at small pZ . In this
perturbative expansion in
s, spoiling the convergence of the xed-order predictions.
The transverse momentum of the Z-boson is caused by the emission of QCD radiation
from the initial state partons. As a consequence,
xed order predictions at O
perturbative QCD, which are NNLO accurate for the inclusive cross section correspond
only to NLO accurate predictions for the transverse momentum distributions. At high
values of pZT, namely above 20 GeV, both ATLAS and CMS observed a tension between the
NLO predictions and their measurements of the pZT distributions presented in the form of
ducial cross sections for a restricted kinematical range of the nal state leptons. Motivated
by this observation, in a recent paper [20], we have used the parton-level event generator
NNLOjet, as described in [21, 22], to predict the Z-boson distributions at large transverse
momentum to NNLO accuracy. We computed the ducial cross section for the production
of a Z-boson at nite transverse momentum fully inclusively on the hadronic nal state. We
found that when the pZT distribution is normalised to the relevant di-lepton cross section,
the NNLO predictions yield an excellent agreement with the measured distributions at
for phenomenology, it is also crucial to have a thorough probe of the low p
ZT domain as well.
We therefore use the NNLOjet code to make predictions in the low transverse momentum
region. As expected, the
xed order description will fail at su ciently small pZT, but it is
also interesting to see exactly where this happens. In particular, we will show that the
xed order perturbative description extends to signi cantly lower pZT than at NLO.
In the small pZT region, the precision of direct measurements of the pZT spectrum using
the standard p
ZT variable is limit (...truncated)