The transverse momentum (PT) of W and Z bosons produced in proton-antiproton collisions is coupled to the associated production of one or more gluons or quarks. At low transverse momentum, multiple soft gluon emission is expected to dominate the cross section. In this regime, soft gluon resummation techniques must be used to make reliable QCD predictions. At high transverse momentum, standard perturbative QCD is expected to be applicable. Prescriptions have been proposed for matching the predictions at high and low PT in order to provide a prediction for all PT. In the calculation by Arnold and Kaufmann (AK), next-to-leading order QCD is matched with a resummed calculation at low PT. Two parameters, g1 and g2, are introduced to account for non-perturbative effects. The Ladinsky and Yuan (LY) calculation matches leading order QCD with the resummed region, and introduces an additional non-perturbative parameter, g3.

Also see:
Ratio of W and Z pt differential cross sections

In addition to the individual W and Z pt measurements described below, we have recently studied the  ratio of differential cross sections for W and Z boson production.  Ratios between W and Z observables can be calculated reliably using perturbative QCD. Using the ratio of differential cross sections reduces the experimental and theoretical uncertainties.

See our measurement of this ratio in the following paper:

Measurement of the ratio of differential cross sections for W and Z boson production as a function of transverse momentum
Phys. Lett. B {517}  299 (2001)
FERMILAB-Pub-01/212-E, hep-ex/0107012. PS 

The following plots show our results on the  W and Z boson differential cross sections dsigma/dpT .
(Click on the plot to get the postscript file).

W boson PT distributions - Run 1b data

Results are described in the following paper:

Differential Cross Section for W Boson Production as a Function of Transverse Momentum in pbarp Collisions at sqrt(s)=1.8 TeV
Phys. Lett. B513, 292 (2001)
FERMILAB-Pub-00/268-E, hep-ex/0010026. PS
 

	The differential cross section as a function of W pT compared to the resummation calculations of Ladinsky-Yuan, Arnold-Kauffman (b-space resummation), and Ellis-Veseli (qT-space resummation). The published values of the non-perturbative function parameters are used in this comparison. The uncertainties shown are stat+syst (except for a 4.4% overall normalization uncertainty due to the uncertainty in integrated luminosity). (Data/Theory - 1) plots for the three theoretical prodictions. The best agreement is with the Ladinsky-Yuan prediction; however when the EV and AK non-perturbative functions are fit to the data we expect they might describe the data equally well.
	A comparison of the data to the resummed Ladinsky-Yuan calulation over the full range of W pT. The data points show only statistical errors. The fractional systematic uncertainty, shown as the band in the lower plot, does not include an overall 4.4% normalization uncertainty in integrated luminosity.
	Background fractions with respect to the number of observed candidate events in the CC region as a function of the transverse momentum.

W boson PT distributions - Run 1a data

Our results from Run 1a are summarized here.
 

Z Boson PT distributions

Our latest results, using Run 1b data, are described in the following two publications:

Measurement of the inclusive differential cross section for Z bosons as a function of transverse momentum produced in p\bar{p} collisions at sqrt{s}=1.8 TeV
Phys. Rev. D {61}, 032004 (2000) PDF (Copyright by the APS)
FERMILAB PUB-99/197-E, hep-ex/9907009 PS

Differential production cross section of Z bosons as a function of transverse momentum at sqrt(s)=1.8 TeV
Phys. Rev. Lett. {84} 2792 (2000) PDF (Copyright by the APS)
FNAL ?, hep-ex/9909020 PS
 

Comparison of our unsmeared data with theoretical predictions are shown below. We extract a new values of the non-perturbative parameters g_1, g_2, and g_3, which describe the form of the Sudakov form factor for the low-pT region of Z production. The measurement is primarily most sensitive to the g_2 parameter and we obtain

	The differential cross section as a function of pT compared to the resummation calculations of Ladinsky-Yuan, Davies-Webber-Stirling (b-space resummation) and Ellis-Veseli (qT-space resummation). The published values of the non-perturbative function parameters are used in this comparison. The uncertainties shown are stat+syst (except for a 4.4% overall normalization uncertainty due to the uncertainty in integrated luminosity).
	(Data/Theory - 1) plots for the three theoretical prodictions. The best agreement is with the Ladinsky-Yuan prediction; however when the DWS and EV non-perturbative functions are fit to the data we expect they might describe the data equally well.
	A comparison of the data to the resummed (LY) and fixed order (order-alpha_s^2) calulations over the full range of Z pT.
	As this (Data/Theory - 1) plot shows, the LY prediction agrees well with the data, but the fixed-order-alpha_s^2 perturbative QCD prediction shows strong disageement with the data due to the divergence of the calculation at pT=0 and contributions from soft gluon emission, which is not accounted for in the calculation.

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