Production asymmetry of D(s) from 600-GeV/c Sigma- and pi- beam

The SELEX collaboration Kaya, M ; Alkhazov, G ; Atamantchouk, A.G ; et al.
Phys.Lett.B 558 (2003) 34-40, 2003.
Inspire Record 613961 DOI 10.17182/hepdata.41958

The production of $D_s^-$ relative to $D_s^+$ as a function of $x_F $ with 600 GeV/c $\Sigma^-$ beam is measured in the interval $0.15 < x_F < 0.7$ by the SELEX (E781) experiment at Fermilab. The integrated charge asymmetries with 600 GeV/c $\Sigma^-$ beam ($0.53\pm0.06$) and $\pi^-$ beam ($0.06\pm0.11$) are also compared. The results show the $\Sigma^-$ beam fragments play a role in the production of $D_s^-$, as suggested by the leading quark model.

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Hadronic Production of $\Lambda_c$ from 600-GeV/c $\pi^-, \Sigma^-$ and $p$ Beams

The SELEX collaboration Garcia, F.G. ; Alkhazov, G. ; Atamantchouk, A.G. ; et al.
Phys.Lett.B 528 (2002) 49-57, 2002.
Inspire Record 562836 DOI 10.17182/hepdata.26997

We present data from Fermilab experiment E781 (SELEX) on the hadroproduction asymmetry for anti-Lambda_c compared to Lambda_c+ as a function of xF and pt2 distributions for Lambda_c+. These data were measured in the same apparatus using incident pi-, sigma- beams at 600 GeV/c and proton beam at 540 GeV/c. The asymmetry is studied as a function of xF. In the forward hemisphere with xF >= 0.2 both baryon beams exhibit very strong preference for producing charm baryons rather than charm antibaryons, while the pion beam asymmetry is much smaller. In this energy regime the results show that beam fragments play a major role in the kinematics of Lambda_c formation, as suggested by the leading quark picture.

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Measurement of the Sigma- Charge Radius by Sigma- Electron Elastic Scattering

The SELEX collaboration Gough Eschrich, Ivo M. ; Kruger, H. ; Simon, J. ; et al.
Phys.Lett.B 522 (2001) 233-239, 2001.
Inspire Record 558329 DOI 10.17182/hepdata.42898

The Sigma^- mean squared charge radius has been measured in the space-like Q^2 range 0.035-0.105 GeV^2/c^2 by elastic scattering of a Sigma^- beam off atomic electrons. The measurement was performed with the SELEX (E781) spectrometer using the Fermilab hyperon beam at a mean energy of 610 GeV/c. We obtain <r^2> = (0.61 +/- 0.12 (stat.) +/- 0.09 (syst.)) fm^2. The proton and pi^- charge radii were measured as well and are consistent with results of other experiments. Our result agrees with the recently measured strong interaction radius of the Sigma^-.

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Measurement of inclusive differential cross sections for $\upsilon_{1S}$ production in $p \bar{p}$ collisions at $\sqrt{s}$ = 1.96-TeV

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Rev.Lett. 94 (2005) 232001, 2005.
Inspire Record 676877 DOI 10.17182/hepdata.51525

We present measurements of the inclusive production cross sections of the Upsilon(1S) bottomonium state in ppbar collisions at sqrt(s) = 1.96 TeV. Using the Upsilon(1S) to mu+mu- decay mode for a data sample of 159 +- 10 pb^-1 collected by the D0 detector at the Fermilab Tevatron collider, we determine the differential cross sections as a function of the Upsilon(1S) transverse momentum for three ranges of the Upsilon(1S) rapidity: 0 < |y| < 0.6, 0.6 < |y| < 1.2, and 1.2 < |y| < 1.8.

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Measurement of the $W W$ production cross section in $p\bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Rev.Lett. 94 (2005) 151801, 2005.
Inspire Record 1650063 DOI 10.17182/hepdata.42037

A change in estimated integrated luminosity (from 226 pb$^{-1} to 257 pb$^{-1}$ leads to a corrected value for ${\sigma (p \bar p \to Z) \cdot}$Br${(Z \to \tau \tau)}$ of $209\pm13(stat.)\pm16(syst.)\pm13(lum) pb.

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Measurement of the $p$ - $\bar{p} \to W \gamma$ + $X$ cross section at $\sqrt{s}$ = 1.96-TeV and $W W \gamma$ anomalous coupling limits

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Rev.D 71 (2005) 091108, 2005.
Inspire Record 679253 DOI 10.17182/hepdata.42778

The WWgamma triple gauge boson coupling parameters are studied using p-pbar -> l nu gamma + X (l = e,mu) events at sqrt(s) = 1.96 TeV. The data were collected with the DO detector from an integrated luminosity of 162 pb^{-1} delivered by the Fermilab Tevatron Collider. The cross section times branching fraction for p-pbar -> W(gamma) + X -> l nu gamma + X with E_T^{gamma} > 8 GeV and Delta R_{l gamma} > 0.7 is 14.8 +/- 1.6 (stat) +/- 1.0 (syst) +/- 1.0 (lum) pb. The one-dimensional 95% confidence level limits on anomalous couplings are -0.88 < Delta kappa_{gamma} < 0.96 and -0.20 < lambda_{gamma} < 0.20.

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First measurement of $\sigma$ ($p \bar{p} \to Z^{)}$ . Br ($Z \to \tau \tau^{)}$ at $\sqrt{s}$ = 1.96- TeV

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Rev.D 71 (2005) 072004, 2005.
Inspire Record 666357 DOI 10.17182/hepdata.50921

We present a measurement of the cross section for $Z$ production times the branching fraction to $\tau$ leptons, $\sigma \cdot$Br$(Z\to \tau^+ \tau^-)$, in $p \bar p$ collisions at $\sqrt{s}=$1.96 TeV in the channel in which one $\tau$ decays into $\mu \nu_{\mu} \nu_{\tau}$, and the other into $\rm {hadrons} + \nu_{\tau}$ or $e \nu_e \nu_{\tau}$. The data sample corresponds to an integrated luminosity of 226 pb$^{-1}$ collected with the D{\O}detector at the Fermilab Tevatron collider. The final sample contains 2008 candidate events with an estimated background of 55%. From this we obtain $\sigma \cdot$Br$(Z \to \tau^+ \tau^-)=237 \pm 15$(stat)$\pm 18$(sys)$ \pm 15$(lum) pb, in agreement with the standard model prediction.

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Measurement of gamma + b + X and gamma + c + X production cross sections in p anti-p collisions at s**(1/2) = 1.96-TeV

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Rev.Lett. 102 (2009) 192002, 2009.
Inspire Record 810425 DOI 10.17182/hepdata.42739

First measurements of the differential cross sections for the inclusive production of a photon in association with a heavy quark (c, b) jet are presented, covering photon transverse momenta 30-150 GeV, photon rapidities | y_gamma| < 1.0, jet rapidities |y_jet| < 0.8, and jet transverse momenta pT_jet > 15 GeV. The results are based on an integrated luminosity of 1 fb^-1 in ppbar collisions at sqrt(s)=1.96 TeV recorded with the D0 detector at the Fermilab Tevatron Collider. The results are compared with next-to-leading order perturbative QCD predictions.

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Measurement of the $t \bar{t}$ production cross section in $p \bar{p}$ collisions at $\sqrt{s}$ = 1.96-TeV using kinematic characteristics of lepton + jets events

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Rev.D 76 (2007) 092007, 2007.
Inspire Record 750966 DOI 10.17182/hepdata.42702

We present a measurement of the top quark pair production cross section in ppbar collisions at sqrt(s)=1.96 TeV utilizing 425 pb-1 of data collected with the D0 detector at the Fermilab Tevatron Collider. We consider the final state of the top quark pair containing one high-pT electron or muon and at least four jets. We exploit specific kinematic features of ttbar events to extract the cross section. For a top quark mass of 175 GeV, we measure sigma_ttbar = 6.4 +1.3-1.2(stat} +/- 0.7(syst)+/- 0.4(lum) pb in good agreement with the standard model prediction.

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Measurement of dijet azimuthal decorrelations at central rapidities in $p\bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Rev.Lett. 94 (2005) 221801, 2005.
Inspire Record 659398 DOI 10.17182/hepdata.19397

Correlations in the azimuthal angle between the two largest transverse momentum jets have been measured using the D0 detector in pp-bar collisions at a center-of-mass energy sqrt(s)=1.96 TeV. The analysis is based on an inclusive dijet event sample in the central rapidity region corresponding to an integrated luminosity of 150 pb-1. Azimuthal correlations are stronger at larger transverse momenta. These are well-described in perturbative QCD at next-to-leading order in the strong coupling constant, except at large azimuthal differences where soft effects are significant.

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Measurements of differential cross sections of Z/gamma*+jets+X events in proton anti-proton collisions at s**(1/2) = 1.96-TeV

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Lett.B 678 (2009) 45-54, 2009.
Inspire Record 815094 DOI 10.17182/hepdata.51854

We present cross section measurements for Z/gamma*+jets+X production, differential in the transverse momenta of the three leading jets. The data sample was collected with the D0 detector at the Fermilab Tevatron proton anti-proton collider at a center-of-mass energy of 1.96 TeV and corresponds to an integrated luminosity of 1 fb-1. Leading and next-to-leading order perturbative QCD predictions are compared with the measurements, and agreement is found within the theoretical and experimental uncertainties. We also make comparisons with the predictions of four event generators. Two parton-shower-based generators show significant shape and normalization differences with respect to the data. In contrast, two generators combining tree-level matrix elements with a parton shower give a reasonable description of the the shapes observed in data, but the predicted normalizations show significant differences with respect to the data, reflecting large scale uncertainties. For specific choices of scales, the normalizations for either generator can be made to agree with the measurements.

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Measurement of the $t \bar{t}$ production cross-section in $p \bar{p}$ collisions using dilepton events

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Rev.D 76 (2007) 052006, 2007.
Inspire Record 752236 DOI 10.17182/hepdata.42700

We present a measurement of the ttbar pair production cross section in ppbar collisions at sqrt(s) = 1.96 TeV utilizing approximately 425 pb-1 of data collected with the D0 detector. We consider decay channels containing two high pT charged leptons (either e or \mu) from leptonic decays of both top-daughter W bosons. These were gathered using four sets of selection criteria, three of which required that a pair of fully identified leptons (i.e., e\mu, ee, or \mu\mu) be found. The fourth approach imposed less restrictive criteria on one of the lepton candidates and required that at least one hadronic jet in each event be tagged as containing a b quark. For a top quark mass of 175 GeV, the measured cross section is 7.4 +/-1.4(stat} +/- 1.0(syst) pb.

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Measurement of dijet angular distributions at s**(1/2) = 1.96-TeV and searches for quark compositeness and extra spatial dimensions

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Rev.Lett. 103 (2009) 191803, 2009.
Inspire Record 824127 DOI 10.17182/hepdata.52427

We present the first measurement of dijet angular distributions in ppbar collisions at sqrt{s}=1.96TeV at the Fermilab Tevatron Collider. The measurement is based on a dataset corresponding to an integrated luminosity of up to 0.7fb-1 collected with the D0 detector. Dijet angular distributions have been measured over a range of dijet masses, from 0.25TeV to above 1.1TeV. The data are in good agreement with the predictions of perturbative QCD and are used to constrain new physics models including quark compositeness, large extra dimensions, and TeV-1 scale extra dimensions. For all models we set the most stringent direct limits to date.

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Dependence of the $t\bar{t}$ Production Cross Section on the Transverse Momentum of the Top Quark

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Lett.B 693 (2010) 515-521, 2010.
Inspire Record 842641 DOI 10.17182/hepdata.54975

We present a measurement of the differential cross section for $t\bar{t}$ events produced in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV as a function of the transverse momentum ($p_T$) of the top quark. The selected events contain a high-$p_T$ lepton ($\ell$), four or more jets, and a large imbalance in $p_T$, and correspond to 1 fb${}^{-1}$ of integrated luminosity recorded with the D0 detector. Each event must have at least one candidate for a $b$ jet. Objects in the event are associated through a constrained kinematic fit to the $t\bar{t}\to WbW\bar{b} \to \ell\nu b q\bar{q}'\bar{b}$ process. Results from next-to-leading-order perturbative QCD calculations agree with the measured differential cross section. Comparisons are also provided to predictions from Monte Carlo event generators using QCD calculations at different levels of precision.

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Measurement of the ratios of the Z/gamma* + >= n jet production cross sections to the total inclusive Z/gamma* cross section in p anti-p collisions at s**(1/2) = 1.96-TeV

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Lett.B 658 (2008) 112-119, 2008.
Inspire Record 724239 DOI 10.17182/hepdata.42763

We present a study of events with Z bosons and jets produced at the Fermilab Tevatron Collider in ppbar collisions at a center of mass energy of 1.96 TeV. The data sample consists of nearly 14,000 Z/G* -> e+e- candidates corresponding to the integrated luminosity of 0.4 fb-1 collected using the D0 detector. Ratios of the Z/G* + >= n jet cross sections to the total inclusive Z/G* cross section have been measured for n = 1 to 4 jet events. Our measurements are found to be in good agreement with a next-to-leading order QCD calculation and with a tree-level QCD prediction with parton shower simulation and hadronization.

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Measurement of the Dijet Invariant Mass Cross Section in $p\bar{p}$ Collisions at $\sqrt{s}=1.96$ TeV

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Lett.B 693 (2010) 531-538, 2010.
Inspire Record 846483 DOI 10.17182/hepdata.54666

The inclusive dijet production double differential cross section as a function of the dijet invariant mass and of the largest absolute rapidity of the two jets with the largest transverse momentum in an event is measured in proton anti-proton collisions at sqrt{s} = 1.96 TeV using 0.7 fb^{-1} integrated luminosity collected with the D0 detector at the Fermilab Tevatron Collider. The measurement is performed in six rapidity regions up to a maximum rapidity of 2.4. Next-to-leading order perturbative QCD predictions are found to be in agreement with the data.

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Measurement of Direct Photon Pair Production Cross Sections in $p\bar{p}$ Collisions at $\sqrt{s}=1.96$ TeV

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Lett.B 690 (2010) 108-117, 2010.
Inspire Record 846997 DOI 10.17182/hepdata.54534

We present a measurement of direct photon pair production cross sections using 4.2 fb-1 of data collected with the D0 detector at the Fermilab Tevatron proton-antiproton Collider. We measure single differential cross sections as a function of the diphoton mass, the transverse momentum of the diphoton system, the azimuthal angle between the photons, and the polar scattering angle of the photons, as well as the double differential cross sections considering the last three kinematic variables in three diphoton mass bins. The results are compared with different perturbative QCD predictions and event generators.

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Measurement of the photon$+b$-jet production differential cross section in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Acharya, B.S. ; et al.
Phys.Lett.B 714 (2012) 32-39, 2012.
Inspire Record 1095100 DOI 10.17182/hepdata.61739

We present measurements of the differential cross section dsigma/dpT_gamma for the inclusive production of a photon in association with a b-quark jet for photons with rapidities |y_gamma|< 1.0 and 30<pT_gamma <300 GeV, as well as for photons with 1.5<|y_gamma|< 2.5 and 30< pT_gamma <200 GeV, where pT_gamma is the photon transverse momentum. The b-quark jets are required to have pT>15 GeV and rapidity |y_jet| < 1.5. The results are based on data corresponding to an integrated luminosity of 8.7 fb^-1, recorded with the D0 detector at the Fermilab Tevatron $p\bar{p}$ Collider at sqrt(s)=1.96 TeV. The measured cross sections are compared with next-to-leading order perturbative QCD calculations using different sets of parton distribution functions as well as to predictions based on the kT-factorization QCD approach, and those from the Sherpa and Pythia Monte Carlo event generators.

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Measurement of the $t\bar{t}$ cross section using high-multiplicity jet events

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Rev.D 82 (2010) 032002, 2010.
Inspire Record 837547 DOI 10.17182/hepdata.52975

We present a measurement of the ttbar cross section using high-multiplicity jet events produced in ppbar collisions at sqrt{s}=1.96 TeV. These data were recorded at the Fermilab Tevatron collider with the D0 detector. Events with at least six jets, two of them identified as b jets, were selected from a 1 fb-1 data set. The measured cross section, assuming a top quark mass of 175 GeV/c^2, is 6.9 \pm 2.0 pb, in agreement with theoretical expectations.

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Measurement of $\sigma(p\bar{p} \to Z + X)$ Br($Z \to \tau^+ \tau^-$) at $\sqrt{s}$ = 1.96-TeV

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Lett.B 670 (2009) 292-299, 2009.
Inspire Record 792818 DOI 10.17182/hepdata.42676

We present a measurement of the cross section for Z boson production times the branching fraction to tau lepton pairs sigma(ppbar -> Z + X) Br(Z -> tau+ tau-) in proton-antiproton collisions at center of mass energy 1.96 TeV. The measurement is performed in the channel in which one tau lepton decays into a muon and neutrinos, and the other tau lepton decays hadronically or into an electron and neutrinos. The data sample corresponds to an integrated luminosity of 1.0 inverse fb collected with the D0 detector at the Fermilab Tevatron Collider. The sample contains 1511 candidate events with an estimated 20% background from jets or muons misidentified as tau leptons. We obtain sigma Br = 240 +/- 8 (stat) +/- 12 (sys) +/- 15 (lum) pb, which is consistent with the standard model prediction.

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Measurement of differential $Z / \gamma^{*}$ + jet + $X$ cross sections in $p \bar{p}$ collisions at $\sqrt{s}$ = 1.96-TeV

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Lett.B 669 (2008) 278-286, 2008.
Inspire Record 792812 DOI 10.17182/hepdata.49090

We present new measurements of differential cross sections for Z/gamma*(->mumu)+jet+X production in a 1 fb-1 data sample collected with the D0 detector in proton anti-proton collisions at sqrt{s}=1.96 TeV. Results include the first measurements differential in the Z/gamma* transverse momentum and rapidity, as well as new measurements differential in the leading jet transverse momentum and rapidity. Next-to-leading order perturbative QCD predictions are compared to the measurements, and reasonable agreement is observed, except in the region of low Z/gamma* transverse momentum. Predictions from two event generators based on matrix elements and parton showers, and one pure parton shower event generator are also compared to the measurements. These show significant overall normalization differences to the data and have varied success in describing the shape of the distributions.

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Model-independent measurement of the $W$ boson helicity in top quark decays at D0

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Rev.Lett. 100 (2008) 062004, 2008.
Inspire Record 767094 DOI 10.17182/hepdata.47072

We present the first model-independent measurement of the helicity of $W$ bosons produced in top quark decays, based on a 1 fb$^{-1}$ sample of candidate $t\bar{t}$ events in the dilepton and lepton plus jets channels collected by the D0 detector at the Fermilab Tevatron $p\bar{p}$ Collider. We reconstruct the angle $\theta^*$ between the momenta of the down-type fermion and the top quark in the $W$ boson rest frame for each top quark decay. A fit of the resulting \costheta distribution finds that the fraction of longitudinal $W$ bosons $f_0 = 0.425 \pm 0.166 \hbox{(stat.)} \pm 0.102 \hbox{(syst.)}$ and the fraction of right-handed $W$ bosons $f_+ = 0.119 \pm 0.090 \hbox{(stat.)} \pm 0.053 \hbox{(syst.)}$, which is consistent at the 30% C.L. with the standard model.

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Measurement of the ratio of the $p \bar{p} \to W^+ c^-$ jet cross section to the inclusive $p \bar{p} \to W +$ jets cross section

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Lett.B 666 (2008) 23-30, 2008.
Inspire Record 781444 DOI 10.17182/hepdata.42740

We present a measurement of the fraction of inclusive $W$+jets events produced with net charm quantum number $\pm1$, denoted $W$+$c$-jet, in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV using approximately 1~fb$^{-1}$ of data collected by the D0 detector at the Fermilab Tevatron Collider. We identify the $W$+jets events via the leptonic $W$ boson decays. Candidate $W$+$c$-jet events are selected by requiring a jet containing a muon in association with a reconstructed $W$ boson and exploiting the charge correlation between this muon and $W$ boson decay lepton to perform a nearly model-independent background subtraction. We measure the fraction of $W$+$c$-jet events in the inclusive $W$+jets sample for jet $p_{T}>20$ GeV and pseudorapidity $|\eta|<2.5$ to be 0.074$\pm0.019$(stat.)$\pm^{0.012}_{0.014}$(syst.), in agreement with theoretical predictions. The probability that background fluctuations could produce the observed fraction of $W$+$c$-jet events is estimated to be $2.5\times 10^{-4}$, which corresponds to a 3.5 $\sigma$ statistical significance.

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Measurement of the shape of the boson transverse momentum distribution in $p \bar{p} \to Z / \gamma^{*} \to e^+ e^- + X$ events produced at $\sqrt{s}$=1.96-TeV

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Rev.Lett. 100 (2008) 102002, 2008.
Inspire Record 769689 DOI 10.17182/hepdata.50920

We present a measurement of the shape of the Z/gamma* boson transverse momentum (qT) distribution in ppbar -> Z/gamma* -> ee+X events at a center-of-mass energy of 1.96 TeV using 0.98 fb-1 of data collected with the D0 detector at the Fermilab Tevatron collider. The data are found to be consistent with the resummation prediction at low qT, but above the perturbative QCD calculation in the region of qT>30 GeV/c. Using events with qT<30 GeV/c, we extract the value of g2, one of the non-perturbative parameters for the resummation calculation. Data at large boson rapidity y are compared with the prediction of resummation and with alternative models that employ a resummed form factor with modifications in the small Bjorken x region of the proton wave function.

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Measurement of the electron charge asymmetry in $p \bar{p} \to W + X \to e \nu + X$ events at $\sqrt{s}$ = 1.96-TeV

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Rev.Lett. 101 (2008) 211801, 2008.
Inspire Record 791230 DOI 10.17182/hepdata.42683

We present a measurement of the electron charge asymmetry in ppbar->W+X->enu+X events at a center of mass energy of 1.96 TeV using 0.75 fb-1 of data collected with the D0 detector at the Fermilab Tevatron Collider. The asymmetry is measured as a function of the electron transverse momentum and pseudorapidity in the interval (-3.2, 3.2) and is compared with expectations from next-to-leading order calculations in perturbative quantum chromodynamics. These measurements will allow more accurate determinations of the proton parton distribution functions.

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