Single W and Z boson production properties and asymmetries
aa r X i v : . [ h e p - e x ] M a y FERMILAB-CONF-11-227-E-PPD MAN/HEP/2011/07
Single W and Z boson production properties and asymmetries
Mika Vesterinen
The School of Physics and Astronomy, The University of Manchester,Oxford Road, Manchester, M13 9PL, England.
Recent analyses of single W and Z boson production properties and asymmetries from theCDF and DØ experiments at the Fermilab Tevatron are reported. For W boson production,measurements of the production and lepton charge asymmetries are presented. For Z/γ ∗ production, the following measurements are presented: dσ/dy , (1 /σ )( dσ/dp T ), (1 /σ )( dσ/dφ ∗ η ),lepton angular coefficients, and A F B with extraction of sin θ W and the light quark couplingsto the Z . Most of these measurements are in good agreement with QCD predictions. Production of electroweak vector bosons at hadron colliders provides a rich testing ground forpredictions of the Standard Model. The production cross sections and distributions are sensitiveto higher order QCD corrections, and to the parton distribution functions (PDFs). Leptonic(involving electrons and muons rather than taus) final states are experimentally convenient, dueto the relatively low background rates and straightforward triggering on single (or pairs of) hightransverse momentum, p T , leptons. W boson charge asymmetry The production of W bosons at the Tevatron is mostly via the annihilation of valence lightquarks; for example the annihilation of a u from a proton with a ¯ d from an antiproton toproduce a W + . It is well known that u (¯ u ) quarks tend to carry a larger fraction ( x ) of the p (¯ p ) momentum than d ( ¯ d ) quarks. For the process p ¯ p → W , this implies a preferred boost of W + s along the proton direction, and along the antiproton direction for W − s. The W bosonproduction asymmetry is defined as A ( y W ) = N + ( y W ) − N − ( y W ) N + ( y W ) + N − ( y W ) W |y W C h a r g e A sy mm e t r y data(stat. + syst.) -1 CDF 1 fb = 80.4 W NLO Prediction(CTEQ6.1M) at mPDF uncertainty(CTEQ6.1M) -1 CDF Preliminary Run II 1 fb | W |y W C h a r g e A sy mm e t r y data(stat. + syst.) -1 CDF 1 fb = 80.4 W NNLO Prediction(MRST2006NNLO) at mPDF uncertainty(MRST2006NNLO) -1 CDF Preliminary Run II 1 fb
Figure 1: Comparison of the measured W boson charge asymmetry from CDF with (left) a NLO QCD predictionwith CTEQ 6.6 PDFs, and (right) a NNLO QCD prediction with MRST2008 PDFs. Pseudorapidity0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 A sy mm e t r y -0.1-0.0500.050.10.150.20.250.3 DØ Preliminary < 35 GeV Tl
25 < p > 25 GeV T n p ) -1 (L = 4.9 fb m A ) -1 (L = 0.75 fb e ACTEQ6.6 central valueMRST04NLO central valueCTEQ6.6 uncertainty band l h D i ff e r e n ce -0.1-0.0500.050.1 Pseudorapidity0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 A sy mm e t r y -0.1-0.0500.050.10.150.20.250.30.350.4 DØ Preliminary > 35 GeV Tl p > 25 GeV T n p ) -1 (L = 4.9 fb m A ) -1 (L = 0.75 fb e ACTEQ6.6 central valueMRST04NLO central valueCTEQ6.6 uncertainty band l h D i ff e r e n ce -0.1-0.0500.050.1 Figure 2: Comparison of the measured muon charge asymmetry from DØ with NLO QCD predictions for (left)20 > p T >
35 GeV, and (right) p T >
35 GeV. where y W is the boson rapidity, and is primarily sensitive to the slope of the ratio of u and d quark PDFs as a function of x . Unfortunately, y W is unobservable due to the unknownmomentum of the neutrino along the beam direction. A novel solution suggested by Bodek etal W boson mass, leaving two solutions for y W . Each of these is assigned a weight assuming theknown V − A structure of the weak decay vertex. This method was employed in a measurementby CDF in the W → eν e channel using 1 fb − of data 2. Figure 2 shows that the measured A ( y W ) agrees well with QCD predictions at both NLO and NNLO accuracies.An alternative approach is to measure the asymmetry as a function of the observable leptonpseudorapidity, η l . Unfortunately, the lepton charge asymmetry, A ( η l ), is less sensitive to theproduction asymmetry and thus also the PDFs. The V − A structure of the decay vertex impliesthat the charged lepton tends to head backwards in the W boson rest frame, i.e. cancelling theproduction asymmetry; particularly at low lepton p T and/or large lepton η . Nevertheless, thetwo approaches provide complementary information. The DØ Collaboration recently measured A ( η l ) using 4.9 fb − of data in the W → µν µ channel 3, and compared to NLO QCD predictionsas shown in figure 2. The measurement is performed in two bins of muon p T which partiallydisentangles the production and decay asymmetries. Interestingly, this measurement does notagree so well with the QCD predictions, particularly at larger muon p T and pseudorapidity. pair rapidity - e + e0 0.5 1 1.5 2 2.5 3 pair rapidity - e + e0 0.5 1 1.5 2 2.5 3 / Z ) / d y ( pb ) * g ( s d < 116 GeV/c /Z * g
66 < M s + : measured : NLO CTEQ6.1M prediction (cid:190) pair rapidity - e + e0 0.5 1 1.5 2 2.5 pair rapidity - e + e0 0.5 1 1.5 2 2.5 D a t a / Th e o r y = 35/27, CL=0.168) c NNLO MRST2006E ( = 33/27, CL=0.238) c NNLO MSTW2008E (MSTW2008E 68% C.L. PDFs Uncertainties
Figure 3: Left: measured dσ/dy from CDF compared to a NLO QCD prediction. Right: ratio of the data toNNLO QCD predictions, where the yellow band represents the uncertainty on the prediction due to the PDFs. Z/γ ∗ rapidity distribution The rapidity, y , of the dilepton system in Z/γ ∗ decays is directly related to the x of the twopartons: x , = ( M ll / √ s ) e ± y , where M ll is the dilepton invariant mass, and √ s is the centre ofmass energy of the collider. Events with large rapidity correspond to the annihilation of a low- x parton and a high- x parton. Thus, a measurement of dσ/dy provides additional informationon the PDFs that is complementary to the W charge asymmetry. CDF has measured dσ/dy in the e + e − decay channel using 1 fb − of data 4. Figure 3 shows that the data are in goodagreement with NLO/NNLO QCD predictions, over the full range of probed rapidities. The Z/γ ∗ production cross section is measured as 257 ±
16 pb, also in agreement with NLO/NNLOQCD predictions. Z/γ ∗ transverse momentum distribution At lowest order in
Z/γ ∗ production, the dilepton system has zero momentum transverse to thebeam direction, p T . Higher order QCD corrections include radiation of gluons from the oneor both of the annihilating quarks. Alternatively, one or both of the annihilating quarks canresult from a gluon splitting into a pair of quarks. In addition, the partons may carry someintrinsic transverse momentum within the colliding hadrons. A good understanding of theseeffects is paramount for many physics analyses at hadron colliders; for example the W bosonmass measurement, which relies on a precise prediction of the lepton kinematics for differentmass hypotheses.The DØ Collaboration has recently measured the shape of the p T distribution in the µ + µ − final state using 1.0 fb − of data 5. For p T >
10 GeV, NLO QCD is able to describe the datareasonably well, whilst resummation is needed at lower p T , as implemented at approximateleading-log (LL) in various Monte Carlo event generators, and at next-to-LL in the ResBosprogram 6. Compared to the data, ResBos underestimates the cross section for larger p T ( p T >
50 GeV), and varying levels of agreement are observed for the different event generators.This and other recent measurements of the
Z/γ ∗ p T distribution have been dominated byuncertainties in correcting for detector resolution and efficiency. An alternative approach is tomeasure the distribution of a variable that is less sensitive to these effects, such as a T
7, or morerecently φ ∗ φ ∗ η = tan([( π − ∆ φ ) /
2] sin θ ∗ , where ∆ φ is the azimuthal opening anglebetween the two leptons, and cos θ ∗ = tanh[( η ( − ) − η (+) ) / η ( − ) being the pseudorapidityof the negatively charged lepton. The variable φ ∗ η is sensitive to the same physics as the p T ,but is determined exclusively from lepton angles resulting in far better experimental resolution.Furthermore, φ ∗ η is less correlated than the p T , with efficiencies of typical Z/γ ∗ event selection .911.10.911.1 -1 DØ 7.3 fb data mm ee dataResBos ) ResBos (tuned gResBos (small-x) scale uncertainty ¯ PDF (a) |y| < 1 (b) 1 < |y| < 2(c) |y| > 2 = 25/24 ) mm (ee,2 c = 27/24 ) mm (ee,2 c h * f h * f R a t i o t o R es B o s -2 -1
10 1 -2 -1
10 1
Figure 4: Ratio of measured (1 /σ )( dσ/dφ ∗ η ), and alternative ResBos predictions, to the nominal ResBos prediction.The yellow band around the ResBos prediction represents the uncertainty due to renormalisation and factorisationscale variation added in quadrature with PDF parameter variations. requirements; e.g. on lepton isolation.The DØ Collaboration recently measured (1 /σ ) ( dσ/dφ ∗ η ) using 7.3 fb − of data, in the e + e − and µ + µ − decay channels, and in three bins of dilepton rapidity 9. The measured distri-butions are compared to predictions from the ResBos program in figure 4, with a modest levelof agreement.ResBos includes a non-perturbative form factor which has been tuned to simultaneouslydescribe low- Q Drell-Yan data, and Tevatron Run I
Z/γ ∗ data 10. Floating the g parameter,which controls the width of the form factor, does not substantially improve the agreement, asrepresented by the blue line in figure 4. Recently, the x -dependence of the non perturbativeform factor has received some attention, and an additional “small- x broadening” was suggestedto describe SIDIS data from HERA 11, which would have significant effects at the LHC 12. The | y | > x modification, which is represented by the black line infigure 4. Z/γ ∗ lepton angular distributions and forward-backward asymmetry The angular distributions of the leptons from
Z/γ ∗ decays are often considered in the Collins-Soper frame 13, and are predicted by perturbative QCD 14 to take the following form: dσd cos θdφ ∝ (1 + cos θ )+ A (1 − θ ) + A sin 2 θ cos φ + A sin θ cos 2 φ + A sin θ cos φ + A cos θ + A sin θ sin 2 φ + A sin 2 θ sin φ + A sin θ sin φ where θ and φ are the polar and azimuthal angles respectively 13. The coefficients, A i ,are dependent on the kinematics of the dilepton system; in particular the p T . The A , A , A parameters are calculated to be negligible 14. The A (cos θ ) term generates an asymmetry in thecos θ distribution, and is due to the different couplings of the Z boson to left- and right-handedfermions, whose relative strength is determined by the value of sin θ W .The forward-backward asymmetry is defined as A F B = ( σ F − σ B ) / ( σ F + σ B ) , where σ F and σ B are the cross sections for forward ( θ >
0) and backward ( θ <
0) events respectively.Interference between the Z and the γ ∗ diagrams leads to an enhanced asymmetry for massesaway from the Z pole. At higher invariant masses, A F B is sensitive to the presence of additional
Z P0 10 20 30 40 50 60 70 80 A ) +M /(P : Pqq ) +M /(5P qg : 5PVBP ResummationResBos ResummationPythiaPythia Z+1jetMadgraphDyradFEWZ(NNLO)PowhegData -1 L = 2.1 fb (cid:242)
CDF Preliminary Result with )<116 - e + T Z P0 10 20 30 40 50 60 70 80 A ) +M /(P : Pqq ) +M /(5P qg : 5PVBP ResummationResBos ResummationPythiaPythia Z+1jetMadgraphFEWZ(NNLO)PowhegData -1 L = 2.1 fb (cid:242)
CDF Preliminary Result with )<116 - e + T Z P0 10 20 30 40 50 60 70 80 A -0.08-0.06-0.04-0.0200.020.04 PythiaVBP ResummationResBos ResummationFEWZ(NNLO)PowhegData -1 L = 2.1 fb (cid:242)
CDF Preliminary Result with )<116 - e + T Z P0 10 20 30 40 50 60 70 80 A PythiaVBP ResummationResBos ResummationPowhegFEWZ(NNLO)Data = 0.232 W q sin -1 L = 2.1 fb (cid:242)
CDF Preliminary Result with )<116 - e + Figure 5: Measured angular coefficients as a function of dilepton p T , compared to various QCD predictions. (GeV) ee M
100 1000 F B A -0.500.51
50 70 100 300 500 1000
PYTHIAZGRAD2Statistical uncertaintyTotal uncertainty
DØ 5.0 fb -1 Figure 6: Left: measured A F B compared to Standard Model predictions. Middle and right: measured u and d quark couplings to the Z . gauge bosons. A F B is sensitive to the couplings of the light quarks to the Z , which are relativelypoorly constrained by measurements at LEP.The CDF collaboration have measured A , A , A and A as a function of the dilepton p T ,using 2.1 fb − of data in the e + e − decay channel 15. The data are compared to various QCDpredictions in figure 5. The A parameter (multiplying the cos θ term) is directly related to the A F B , and thus also the value of sin θ W . The A measurement is translated into a measurementof sin θ W = 0 . ± . +0 . − . , where the first uncertainty is experimental and the secondis theoretical.The DØ Collaboration has recently measured A F B as a function of the dilepton invariantmass, using 6.1 fb − of data, in the e + e − channel 16. Figure 6 shows that the measurement is inreasonable agreement with Standard Model predictions. In addition, the couplings of the u and d quarks to the Z are extracted as shown in figure 6. A value of sin θ W is extracted as 0.2309 ± Conclusions
Recent analyses of single W and Z boson production properties and asymmetries from theCDF and DØ experiments at the Fermilab Tevatron are presented. A measurement of the W boson production asymmetry in W → eν e events from CDF is in good agreement with QCDpredictions. Conversely, a measurement of the muon charge asymmetry in W → µν µ eventsfrom DØ is in modest agreement with QCD predictions. The Z/γ ∗ production cross section,and rapidity distribution is measured in the e + e − decay channel by CDF, and agrees well withQCD predictions. The shape of the Z/γ ∗ transverse momentum distribution is measured using1 fb − of data in the µ + µ − decay channel by DØ, in reasonable agreement with various QCDpredictions. The φ ∗ η variable was recently proposed as an alternative variable for studying thetransverse momentum. A measurement of the shape of the φ ∗ η distribution from DØ using7.3 fb − of data, in the e + e − and µ + µ − decay channels is in modest agreement with a state-of-the-art QCD prediction. Four coefficients describing the angular distributions of the decayleptons from Z/γ ∗ decays are studied in the e + e − channel by CDF using 2.1 fb − of data.DØ measures A F B as a function of the dilepton invariant mass, using 5 fb − e + e − decay channel, in agreement with a QCD prediction. This measurement is used to extractsin θ W = 0 . ± . Z boson couplings to u and d quarks. References
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