Drell-Yan lepton pairs are produced in the process pp → γ^{*}/Z + X, with the subsequent decay of the γ^{*}/Z into lepton pairs. We present a measurement of the Δσ/ΔP_{T} differential cross section using 2.1 fb^{-1} of CDF Run II data in the e^{+}e^{-} channel. The cross section presented is measured in P_{T} bins of variable width and is the averge cross section in the bin: Δσ/ΔP_{T}. The measurements are for dielectrons in a mass range of 66—116 GeV/c^{2}, for all boson rapidities and decay electron phase space, and √s = 1.96 TeV.
Introduction
The measurement is an extension of our 2.1 fb^{-1}
Drell-Yan dielectron process measurements of
dσ/dy [Phys. Lett. B692 232 (2010)]
and electron angular distribution coefficients
[Phys. Rev. Lett. 106, 241801 (2011)]. Analysis
details are available on the CDF EWK
web page (under
W/Z Cross Sections and Asymmetries).
The Δσ/ΔP_{T} measurement uses
the exact same dataset and nearly identical analysis methods
used in the decay electron angular distribution measurement
because the data is understood well and the simulation of
the data is tuned well.
The Data
The electron candidates used in this analysis can be in
either the CDF central (C) or the forward end plug (P)
calorimeters. The central and plug calorimeters
cover the range, |η_{det}|<1.1 and
1.1<|η_{det}|<3.5 respectively. Each
electron is required to have an associated track and pass
standard CDF electron selection and fiducial cuts. Three
electron-pair topology categories are used with the following
kinematic selections.
Data Driven Measurement
The fully corrected measurement of the differential cross section
requires corrections for the detector acceptance, A, and electron
selection and reconstruction efficiencies, ε. The combined
A×ε is calculated with a simulation of the physics
and detector that also unfolds detector resolution effects. Because of
detector resolution smearing, the correct modeling of the physics
and detector are important.
The simulation modeling is data driven. The modeling starts with the Pythia 6.2 simulation of pp → γ^{*}/Z (→ ee) + X (at tree level) followed by parton showering. PHOTOS 2.0 adds final state QED radiation to charged particle vertices. This is then followed by the full CDF detector simulation. All data efficiencies, both global and η_{det} dependent, as well as time-dependent, are measured and incorporated into the simulation. Both the physics and detector models are tuned (iteratively) so that the simulated, reconstructed event distributions match the data.
The tuning of Pythia's γ^{*}/Z dσ/dy and
the decay angular distributions are from our previous measurements
using the 2.1 fb^{-1} data. The simulated, reconstructed
event P_{T} distribution that pass all
analysis cuts disagrees with the data, so we tune the underlying
Pythia P_{T} so that it does.
The simulation's calorimetric energy scales and resolutions
are important for the measurement, and are tuned to the data.
The tuning is from our dσ/dy and electron angular decay
distribution analyses. The energy scales and resolutions in the
simulation are tuned against the data's dielectron mass
(M_{ee}) and electron E_{T} distributions.
As the backgrounds are very small, they are not subtracted
out.
The statistical precision of the data tightly constrains calorimetry modeling uncertainties. The systematic shifts in A×ε from global variations in the simulation energy scales and resolutions allowed by the data are small: Under 0.3%. The simulation statistical uncertainties (√N) are larger in all P_{T} bins.
The systematic uncertainties in each P_{T} bin from the propagation of efficiency measurement uncertainties are flat and about 1% over 0<P_{T}<20 GeV/c, and slowly decreasing after that. They are also 100% correlated across all bins.
The differential cross section that we measure is Δσ/ΔP_{T}, or the average cross section in a P_{T} bin of width ΔP_{T}. The cross section in a P_{T} bin is calculated using: Δσ = N / ( L × (A×ε) ), where N is the background subtracted event count, and L is the integrated luminosity. For this measurement, L = 2057 pb^{-1}, and it has a 5.8% systematic uncertainty. The A×ε calcuated with the tuned simulation ranges from 0.2 at P_{T}=0 GeV/c to 0.3 at high P_{T}. As P_{T} increases, the electrons become more central, their E_{T} get larger and their acceptance increases. The A×ε includes the measured electron identification, tracking, and other efficiences, but uncertainties from it are kept and presented separately from the (simulation) statistical uncertainties because they are correlated.
The Δσ/ΔP_{T} versus P_{T} is shown on the left. The black data uncertainties plotted for each point include the data statistical uncertainty, the A×ε statistical uncertainty, and and the 1% efficiency measurement uncertainty, all combined in quadrature. No luminosity uncertainties are included. The horizontal "error bars" represent the extent of the bin. The red ResBos calculation is straight out of the box: 041511 (10.15.09cp) using the resummation and yk grids. The ResBos total cross section is 254 pb. |
An ASCII table of the measurement is here; the uncertainties are split into the data and simulation statistical (stat) and 100% correlated efficiency systematic (syst) uncertainties. The 5.8% luminosity uncertainty is not included.
The statistical uncertainty of √N from the bin cross section formula is inadequate with the large smearing at low P_{T} and it is estimated with the simulation. The 1/(A×ε) bin-by-bin unfolding is a two step procedure: A scaling correction then an acceptance correction. The scaling correction is on reconstructed events, and it rescales the events reconstructed in a P_{T} bin into reconstructed events produced in the bin. The scaling uncertainities from physics and detector modeling mismatches between the simulation and the data has been mitigated by the tuning of both so that the reconstructed simulation data matches the real data. Denote ρ as the scaling factor that takes the number of reconstructed events in a bin, N_{r}, and rescales it to the number number of reconstructed events produced in the bin, N_{g}.
The set of produced events is subject to statistical fluctuations. The sets of events migrating into and out of a bin are also subject to statistical fluctuations. These fluctuations are different. As the number of produced events and the number of migrating events are not measured, the simulation is used along with a model for fluctuations for an estimate of the overall "statistical" uncertainty.
Within the context of the simulation, the event smearing across
bins can be described by the number of events produced in a bin
that stay in a bin, n_{g}, the events that migrate out,
n_{o}, and events produced in neighboring bins that
migrate in, n_{i}:
N_{g} = n_{g} + n_{o}
N_{r} = n_{g} + n_{i}.
The event sets corresponding to n_{g}, n_{o}, and
n_{i} are statistically independent. The set corresponding
to n_{g} is common to both N_{g} (produced events)
and N_{r} (observed events).
The scaling correction prediction for N_{g} is:
N_{g}^{(p)} = ρ N_{r}
= ρ(n_{g} + n_{i}),
where the prediction is denoted with a (p) superscript. Both
N_{g} and N_{g}^{(p)} have uncertainties
from statistical fluctuations in their event sets. The method to
estimate the overall bin uncertainty combines the expected
uncertainty on the events produced in the bin, N_{g}, with
the expected uncertainty on the estimate of produced events,
N_{g}^{(p)}. However, as both have n_{g} in
common, it must be removed from the combination to avoid double
counting. The model for combining the fluctuations is:
δN_{g}' = δN_{g}^{(p)} +
δN_{g} -
δn_{g}
= δρ N_{r} +
δn_{o}
= δρn_{g} +
δρn_{i} +
δn_{o}.
The last two terms, δρn_{i} and δn_{o}
induce interbin correlations as events migrating into a bin have
migrated out of another bin. Denote the statistical variance of a
quantity as δ^{2} followed by the variable. The
variance of N_{g}' is:
δ^{2}N_{g}' =
ρ^{2}δ^{2}n_{g} +
ρ^{2}δ^{2}n_{i} +
δ^{2}n_{o} ,
where δ^{2}N_{g}' is the estimate of the
overall bin uncertainty of the method.
With Poisson statistics (δ^{2}n = n), the variance can
be rewritten in this form:
δ^{2}N_{g}' =
N_{g} +
(ρ^{2}-1)n_{g} +
ρ^{2}n_{i} .
The measured cross section of the bin is combined with
δ^{2}N_{g}' in its fractional form,
√[δ^{2}N_{g}']/N_{g} ,
for the estimate of the cross section "statistical"
uncertainty of a bin used in the cross section plots
and tables.
The ratio of the data to the ResBos prediction is shown
below:
Due to the large inter-bin smearing at low P_{T},
interpreting the significance of the data-to-prediction
comparison there is difficult. At large P_{T}
(above 40 GeV/c), the smearing is predominantly among
nearest neighbor P_{T} bins so the data-to-prediction
comparison shown has much less correlations from smearing. The
40 < P_{T} < 90 GeV/c region is where the
the ResBos resummed, asymptotic, and perturbative cross
sections are matched.