DOI 10.1393/ncc/i2010-10531-3 Colloquia: LaThuile09
Study of hard QCD at the Tevatron
M. Begelfor the D0 and CDF Collaborations
Brookhaven National Laboratory - Upton, NY 11973, USA
(ricevuto il 10 Novembre 2009; pubblicato online il 18 Gennaio 2010)
Summary. — Recent measurements of photon, jet, and boson+jet production
from the CDF and D0 Collaborations are presented. NLO pQCD describes most of the results except for the shapes of inclusive isolated photon and γ+jet differential cross-section measurements. Calculations involving matrix elements matched to parton showers agree with the data except at low pT. Limits on several exotic
models are set based on dijet distributions.
PACS 13.85.Qk – Inclusive production with identified leptons, photons, or other nonhadronic particles.
PACS 13.87.-a – Jets in large-Q2 scattering.
Large-pT processes in hadronic interactions originate in the hard scattering of partons.
Measurements of boson and jet production test next-to-leading–order (NLO) perturba-tive QCD (pQCD) calculations and constrain parton distribution functions (PDF) [1, 2]. Jet production is also sensitive to the presence of new physical phenomena including quark compositeness, large extra-dimensions, and resonances that decay with jets in the final state. Measurements of the production of vector bosons with associated jets test NLO pQCD as well as models used to describe backgrounds to other processes such as t¯t, single top quark production, and searches for the Higgs boson and new physical
phenomena.
Direct photons are produced primarily through q ¯q annihilation (q ¯q → γg) and
quark-gluon Compton-like scattering (qg → γq). Direct photons were therefore con-sidered an important sample for extracting information about the gluon PDF. Unfor-tunately, direct photons have been excluded from global PDF fits for most of the past decade due to differences between NLO pQCD and many experimental results [3]. The inclusive isolated-photon cross-sections from D0 [4] and CDF [5] are presented in fig. 1 as a function of photon pT. Overlayed on the data are the results from the NLO pQCD
calculation jetphox [6]. While the prediction agrees with the data within uncertainties, the shape is different. This is similar to the shape seen in previous measurements from D0 and CDF as well as from many other direct photon experiments [3]. The differences between theory and data are more obvious in comparisons of theory with the measure-ments of photon+jet production from D0 [7] shown in fig. 2. Here, as in the inclusive photon measurements, NLO pQCD [6] basically agrees with data within uncertainties
c
(GeV) γ T p 0 50 100 150 200 250 Data / Theory 0.4 0.6 0.8 1 1.2 1.4 (GeV) γ T p 0 50 100 150 200 250 Data / Theory 0.4 0.6 0.8 1 1.2 1.4
ratio of data to theory CTEQ6.1M PDF uncertainty scale dependence ) γ T and 2p γ T =0.5p f μ = F μ = R μ (
DØ
300 -1 L = 380 pb [GeV/c] T Photon p 50 100 150 200 250 300 350 400 data/theory 0.6 0.8 1 1.2 1.4 1.6 1.8 [GeV/c] T Photon p 50 100 150 200 250 300 350 400 data/theory 0.6 0.8 1 1.2 1.4 1.6 1.8 CDF Run II PreliminaryRatio to pQCD NLO JETPHOX systematic uncertainty (theory corrected for UE contributions) CTEQ6.1M PDF uncertainties scale dependence γ T =2p μ and γ T =0.5p μ
|<1.0 and iso<2.0 GeV, R=0.4
γ
η |
-1 L=2.5 fb
Fig. 1. – Ratio of data to NLO pQCD for the inclusive production of isolated photons.
Ratio of cross sections: Data/Theory 0.2
0.4 0.6 0.8 1 1.2 1.4 1.6 DØ -1 = 1 fb int L | < 1 γ |y > 15 GeV T jet p > 0 jet y ⋅ γ | < 0.8, y jet |y jet > 0 y ⋅ γ | < 2.5, y jet 1.5 < |y 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 < 0 jet y ⋅ γ | < 0.8, y jet |y 30 100 200
7.8% is overall normalization uncertainty
(GeV)
γ T
p (GeV)γT
p
ratio of data to theory (JETPHOX) theor. scale uncertainty CTEQ6.5M PDF uncertainty ratio of MRST04 to CTEQ6.5M ratio of Alekhin02 to CTEQ6.5M ratio of ZEUS05 to CTEQ6.5M
< 0 jet y ⋅ γ | < 2.5, y jet 1.5 < |y 30 100 cross sections 1 DØ -1 = 1 fb int L | < 1 γ |y > 15 GeV T jet p > 0) jet y ⋅ γ | < 0.8, y jet D(|y < 0) jet y ⋅ γ | < 0.8, y jet D(|y Ratio of differential 1 10 > 0) jet y ⋅ γ | < 2.5, y jet D(1.5 < |y > 0) jet y ⋅ γ | < 0.8, y jet D(|y > 0) jet y ⋅ γ | < 2.5, y jet D(1.5 < |y < 0) jet y ⋅ γ | < 0.8, y jet D(|y > 0) jet y ⋅ γ | < 2.5, y jet D(1.5 < |y < 0) jet y ⋅ γ | < 2.5, y jet D(1.5 < |y 10 < 0) jet y ⋅ γ | < 2.5, y jet D(1.5 < |y > 0) jet y ⋅ γ | < 0.8, y jet D(|y jet dy γ dy γ T dp σ 3 d D = 30 100 200 pγT (GeV) < 0) jet y ⋅ γ | < 2.5, y jet D(1.5 < |y < 0) jet y ⋅ γ | < 0.8, y jet D(|y data 0 μ = 0.5 μ theory, 0 μ = μ theory, 0 μ = 2.0 μ theory, 30 100
Fig. 2. – Production of γ+jet events as a function of pγT from D0. Left: ratio of data-to-theory for four rapidity regions. Right: comparison of theory to data for ratios of rapidity regions.
though the discrepancies in the data-to-theory shapes in fig. 2 (left) are similar to those in fig. 1 and other photon measurements [3]. The γ+jet cross-sections were measured in four regions that combined the central-rapidity photons with both central- and forward-rapidity jets. Many systematic uncertainties cancel in ratios of one region to another in both data and theory. These comparisons are shown in fig. 2 (right). NLO pQCD clearly disagrees with the measurements for several of the ratios of one region to another.
Jet production is also dependent on the gluon PDF and jet data have supplanted photons in the global PDF fits [1, 2]. CDF and D0 have recently published precision measurements of the inclusive jet cross-section as a function of pT in multiple rapidity
0.5 1.0 1.5 |y| < 0.4 DØ Run II -1 L = 0.70 fb = 0.7 cone R 50 100 200 300 0.0 0.5 1.0 1.5 1.2 < |y| < 1.6
NLO scale uncertainty
0.4 < |y| < 0.8 T = p F μ = R μ NLO pQCD +non-perturbative corrections 50 100 200 300 1.6 < |y| < 2.0
CTEQ6.5M with uncertainties MRST2004 0.8 < |y| < 1.2 Data Systematic uncertainty 50 100 200 300 2.0 < |y| < 2.4 (GeV) T p data / theory (GeV) T p data / theory (GeV) T p data / theory (GeV) T p data / theory (GeV) T p data / theory (GeV) T p data / theory 0.5 1 1.5 2 2.5 3 3.5 |y|<0.1 50 100150 200 0.8 1 1.2 1.1<|y|<1.6 50 100150200 0.8 1 1.2 Data / Theory 0.5 1 1.5 2 2.5 3 3.5 0.1<|y|<0.7 50 100 150200 0.8 1 1.2 (GeV/c) JET T p 50 100 150 200 250 300 350 400 450 1.6<|y|<2.1 50 100 150 0.8 1 1.2 (GeV/c) JET T p 0 100 200 300 400 500 600 700 0.5 1 1.5 2 2.5 3 3.5 0.7<|y|<1.1 50 100150200 0.8 1 1.2 ) / NLO -1 CDF Data (1.13 fb PDF Uncertainty MRST 2004 / CTEQ6.1M Systematic uncertainty Including hadronization and UE
=0.75 merge Midpoint: R=0.7, f ] 2 [GeV/c jj m 200 400 600 800 1000 1200 1400 Data / Theory 0.5 1 1.5 2 2.5 3 ) / NLO pQCD, CTEQ6.1M -1 CDF Run II Data (1.13 fb Systematic uncertainties PDF uncertainty (CTEQ6.1M) σ (MRST2004) / σ ) 0 μ ( σ ) / 0 μ (2 x σ
Fig. 3. – Ratio of data to NLO pQCD for inclusive jet (top and lower left) and dijet production (lower right).
bins [8, 9]. Ratios of the data to the NLO pQCD calculation (nlojet++ [10] calculated with fastnlo [11]) are shown in fig. 3. NLO pQCD agrees very well with the data. Uncertainties from recent CTEQ PDF [2] are shown in fig. 3 as the lines. The data systematic uncertainties, shown by the shaded bands and dominated by the energy scale calibration, are smaller than the PDF uncertainties for inclusive jet production. These data have already significantly impacted the current round of global PDF fits [1].
CDF has also measured the differential cross-section for dijet production as a function of the dijet mass [12]. As shown in fig. 3 (lower right), the NLO pQCD calculation [10,11] agrees with the data. No significant evidence of a dijet mass resonance was observed, so exclusion limits were placed on a variety of exotic models including the production of
W and Z bosons as shown in fig. 4 (left). Angular distributions are also sensitive to the presence of new physical phenomena. D0 has compared the shapes of the χdijet =
exp|y1− y2| distribution binned as a function of the dijet mass [13]. This is compared
with NLO pQCD in fig. 4 (right) and with several additional models including one for quark compositeness and two for extra dimensions. The standard model expectation agrees with the data and so limits were placed on the potential new physics.
Z+jet events are produced through diagrams analogous to those for direct photon
production except that the hard scale, Q2, is dominated by the mass of the Z boson.
Characteristics of Z+jet events therefore provide useful tests of NLO pQCD, particu-larly for the emission of multiple jets. Additionally, since Z+jet events form an impor-tant background in studies of t¯t production and in searches for the Higgs boson or for
A (pb) ⋅ B ⋅σ -1 10 1 10 2 10 3 10 95% C.L. limits W’ A (pb) ⋅ B ⋅σ -1 10 1 10 2 10 95% C.L. limits Z’ A (pb) ⋅ B ⋅σ -1 10 1 10 2 10 95% C.L. limits RS graviton T8 ρ ] 2 Mass [GeV/c 400 600 800 1000 1200 1400 A (pb) ⋅ B ⋅σ -2 10 -1 10 1 10 2 10 95% C.L. limits * q Axigluon/Coloron diquark 6 E 0 0.05 0.1 0.25 < Mjj/TeV < 0.3 1/ σdijet d σ /d χdijet 0 0.05 0.1 0.3 < Mjj/TeV < 0.4 0 0.05 0.1 0.4 < Mjj/TeV < 0.5 0.5 < Mjj/TeV < 0.6 0 0.05 0.1 0.6 < Mjj/TeV < 0.7 0.7 < Mjj/TeV < 0.8 0 0.05 0.1 0.8 < Mjj/TeV < 0.9 0.9 < Mjj/TeV < 1.0 0 0.05 0.1 5 10 15 1.0 < Mjj/TeV < 1.1 5 10 15 Mjj/TeV > 1.1 χdijet = exp(|y1-y2|) DØ preliminary Standard Model Quark Compositeness ADD Lg. Extra Dim.
TeV-1 Extra Dim. Λ=2.56TeV (λ=+1) Ms=1.55TeV (GRW)
Mc=1.41TeV
Fig. 4. – Left: exclusion limits for resonant production in the dijet decay channel. Right: angular distribution, χdijet = exp|y1−y2|, binned as a function of dijet mass. Overlayed are comparisons
with NLO pQCD and several new physics models.
alpgen[14] or sherpa [15] that match tree-level matrix elements with parton shower Monte Carlo (MEPS) [16]. Differential cross-section measurements have recently been published by the CDF and D0 Collaborations [17,18] as shown in fig. 5. The NLO pQCD calculation (MCFM [19]) reproduces the jet multiplicity and the pT and rapidity spectra
of both the Z-boson and the jets. Alpgen and sherpa do not compare as well with data, particularly at low pT.
W +jet events also provide useful tests of NLO pQCD calculations and MEPS models.
The higher statistics in W +jet events compared to Z+jet events is particularly useful for detailed comparisons at higher jet multiplicities or with the properties of dijets in events containing at least two jets. These are shown for CDF data [20] in fig. 6. NLO pQCD [19] compares well with the jet multiplicity and pT distributions (fig. 6 (top-left and right)),
however, the MEPS calculations (SMPR [21] and alpgen which is denoted as MLM) do not compare as favorably in the low pT regime. Alpgen does generally reproduce the
characteristics of the leading two jets in W +jets events that have at least two jets. This is shown in fig. 6 (left-center and left-bottom) which display the dijet mass and angular separation (ΔR =(Δφ)2+ (Δη)2). This indicates that alpgen provides a reasonable
mix of gluon-splitting (peak at low ΔR) and uncorrelated diagrams (peak near π). D0 and CDF have also explored the production of vector bosons with associ-ated heavy-flavor jets. Both collaborations have recently published measurements of
W + c jet production which probes the strange content of the proton [22, 23].
Re-sults from NLO pQCD calculations agree with these measurements. CDF measured the W + c cross-section as 9.8± 2.8+1.4−1.8± 0.6 pb compared to an NLO pQCD
expecta-) [fb] -e + e → * γ BR(Z/ × jets N σ 2 10 3 10 4 10 5 10 -1 CDF Data L = 1.7 fb Systematic uncertainties NLO MCFM CTEQ6.1M corrected to hadron level
=1.3 sep (Z), R 2 T + p 2 Z = M 2 0 μ /2 0 μ = μ ; 0 μ = 2 μ NLO scale NLO PDF uncertainties LO MCFM hadron level jets N ≥ 1 2 3 Ratio to LO 1 1.2 1.4 1.6 1.8 [fb/(GeV/c)] jet T /dp σ d -1 10 1 10 2 10 3 10 4 10 5 10 20) × 1 jet inclusive ( ≥ ) + -e + e → *( γ Z/ 2 jets inclusive ≥ ) + -e + e → *( γ Z/ -1 CDF Data L = 1.7 fb Systematic uncertainties NLO MCFM CTEQ6.1M Corrected to hadron level
=1.3 sep (Z), R 2 T + p 2 Z = M 2 0 μ /2 0 μ = μ ; 0 μ = 2 μ PDF uncertainties Data / Theory 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 1 jet inclusive ≥ ) + -e + e → *( γ Z/ [GeV/c] jet T p 30 100 200 Data / Theory 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 jets inclusive ≥ ) + -e + e → *( γ Z/ (pb / GeV) Z T /dpσ d -2 10 -1 10 1 Data NLO pQCD + corr. Z T p ⊕ Z = M F μ = R μ CTEQ6.6M PDF ALPGEN Z T p ⊕ Z = M F μ = R μ CTEQ6.1M PDF -1 DØ Run II, L=1.0 fb ) + jet + X μ μ → *( γ Z/ | < 1.7 μ < 115 GeV, |y μ μ 65 < M | < 2.8 jet > 20 GeV, |y jet T =0.5, p cone R (GeV) Z T p 0 20 40 60 80 100 120 140 160 180 200 Ratio 0.5 1 1.5 2 2.5 Data / ALPGEN NLO pQCD / ALPGEN Scale and PDF unc.
SHERPA / ALPGEN PYTHIA / ALPGEN | (pb) Z /d|yσ d 2 4 6 8 10 12 14 16 18 20 Data NLO pQCD + corr. Z T p ⊕ Z = M F μ = R μ CTEQ6.6M PDF ALPGEN Z T p ⊕ Z = M F μ = R μ CTEQ6.1M PDF -1 DØ Run II, L=1.0 fb ) + jet + X μ μ → *( γ Z/ | < 1.7 μ < 115 GeV, |y μ μ 65 < M | < 2.8 jet > 20 GeV, |y jet T =0.5, p cone R | Z |y 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Ratio 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Data / ALPGEN NLO pQCD / ALPGEN Scale and PDF unc.
SHERPA / ALPGEN PYTHIA / ALPGEN
0
Fig. 5. – Differential cross-sections for Z+jets production. Upper left: jet multiplicity; upper right: jet pT; lower left: Z pT; lower right: Z rapidity.
Theory σ / Data σ 1 2 MLM uncertainty CDF II / MLM SMPR uncertainty CDF II / SMPR CDF II / MCFM MCFM Scale uncertainty MCFM PDF uncertainty
Inclusive Jet Multiplicity (n)
0 1 2 3 4 n-1 σ /n σ R = 0.05 0.1 0.15 CDF IIMCFM MLM SMPR Theory σ / Data σ Theory σ / Data σ Theory σ / Data σ 0.5 1 1.5 0.5 1
1.5 CDF II / MCFM Scale uncertainty PDF uncertainty
0.5 1 1.5 0.5 1 1.5 CDF II / MLM Scale uncertainty (GeV) T First Jet E 50 100 150 200 250 300 350 0.5 1 1.5 (GeV) T First Jet E 50 100 150 200 250 300 350 0.5 1 1.5 CDF II / SMPR Scale uncertainty 0.5 1 1.5 2 0.5 1 1.5
2 CDF II / MCFM Scale uncertainty PDF uncertainty
0.5 1 1.5 2 0.5 1 1.5 2 CDF II / MLM Scale uncertainty (GeV) T Second Jet E 20 40 60 80 100 120 140 160 180 0.5 1 1.5 2 (GeV) T Second Jet E 20 40 60 80 100 120 140 160 180 0.5 1 1.5 2 CDF II / SMPR Scale uncertainty 1 2 3 1 2 3 CDF II / MLM Scale uncertainty (GeV) T Third Jet E 20 30 40 50 60 70 80 1 2 3 (GeV) T Third Jet E 20 30 40 50 60 70 80 1 2 3 CDF II / SMPR Scale uncertainty ] 2 ) [GeV/c 2 -jet 1
Di-jet Invariant Mass M(jet
0 100 200 300 400 500 )] 2 [pb/(5GeV/cjj /dM σ d -3 10 -2 10 -1 10
1 (W→eν) + ≥ 2 jets CDF Run II Preliminary
CDF Data -1 dL = 320 pb ∫ W kin: e≥ 20[GeV]; |ηe| ≤ 1.1 T E 30[GeV] ≥ ν T ]; E 2 20[GeV/c ≥ W T M
Jets: jet≥ 15[GeV]
T
|<2.0; E η JetClu R=0.4; | hadron level; no UE correction
LO Alpgen + PYTHIA normalized to Data σ Total ) 2 -jet 1 R(jet Δ Di-jet 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 [pb/0.2]jj R Δ /d σ d 0.5 1 1.5 2 2.5 3 3.5 CDF Run II Preliminary 2 jets ≥ ) + ν e → (W CDF Data -1 dL = 320 pb ∫ W kin: e≥ 20[GeV]; |ηe| ≤ 1.1 T E 30[GeV] ≥ ν T ]; E 2 20[GeV/c ≥ W T M
Jets: jet≥ 15[GeV]
T
|<2.0; E η JetClu R=0.4; | hadron level; no UE correction
LO Alpgen + PYTHIA
normalized to Data
σ
Total
Fig. 6. – Ratio of data-to-theory for W +jets production as a function of jet multiplicity (upper left) and jet pT (right). Differential distributions in the mass and angular separation between
the jets in W +dijet events are displayed in the center left and lower left.
tion of 11+1.4−3.0pb [19] while D0 measured the ratio with respect to W +jet production of 0.074± 0.019+0.012−0.014 compared to 0.044± 0.003 from alpgen.
D0 has recently published the differential cross-section for the production of a direct photon with associated c and b jets [24]. These measurements are shown in ratio with NLO pQCD expectations in fig. 7 (left). Theoretical expectations agree with the γ + b jet data, but disagree at high pT for γ + c jet. The uncertainties are large, but this is
suggestive of an intrinsic charm component in the proton. The b content of the proton can also be probed by Z +b jet events [25,26]. Differential cross-sections from CDF are shown in fig. 7 (right) binned in the pT of the Z boson and in the jet pT. Theoretical expectations
roughly agree with the data; pythia provides the best description of the data. Both collaborations have published ratios of the Z + b jet to Z+jet cross-sections; NLO pQCD is slightly higher than the measurement. CDF reports (2.11± 0.33 ± 0.34)% compared
Data / Theory 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 = 1.0 fb -1 int DØ, L |yjet| < 0.8 > 0 jet y γ y | < 1.0 γ |y > 15 GeV jet T p + b + X γ Data / Theory 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 data / theory CTEQ6.6M PDF uncertainty IC BHPS / CTEQ6.6M IC sea-like / CTEQ6.6M Scale uncertainty 40 60 80 100 120 140 0.5 1 1.5 2 2.5 3 3.5 > 0 jet y γ y + c + X γ 40 60 80 100 120 140 0.5 1 1.5 2 2.5 3 3.5 < 0 jet y γ y + b + X γ (GeV) γ T p 40 60 80 100 120 140 < 0 jet y γ y + c + X γ (GeV) γ T p 40 60 80 100 120 140 [GeV] Z T P 0 10 20 30 40 50 60 70 80 90 100 ] -1 (Z) [ GeV σ ) / T Z (Z+ b jet) /d P σ (d 10 20 30 40 50 60 70 80 90 -6 10 × CDF Data PYTHIA incl. ALPGEN MCFM MCFM +Had.Corr. Z+ b jet. CDF RUN II Preliminary
=1.96 TeV s -1 L ~ 2.0 fb >20 GeV jet T E |<1.5 jet η | [GeV] jet T E 20 30 40 50 60 70 80 90 100 ] -1 (Z) [ GeV σ ) / T jet (Z+ b jet) /d E σ (d 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 -3 10 × CDF Data PYTHIA incl. ALPGEN MCFM MCFM +Had.Corr. Z+ b jet. CDF RUN II Preliminary
=1.96 TeV s -1 L ~ 2.0 fb >20 GeV jet T E |<1.5 jet η |
Fig. 7. – Left: ratio of data to NLO pQCD for γ + b jet (upper) and γ + c jet (lower) production. Right: differential cross-section for the production of Z + b jet as a function of the Z pT (upper)
and jet pT (lower).
to NLO pQCD [19] at (1.77± 0.27)% while D0 reports (2.3 ± 0.4+0.2−0.8)% compared to (1.8± 0.4)%. CDF has also measured the production of b-jets in association with a W boson [27]. The b jets are typically produced through a gluon splitting diagram: g→ b¯b. CDF measures a cross-section of 2.74± 0.27 ± 0.42 pb compared to the expectation from alpgenof 0.78 pb—a significant difference.
Recent Tevatron results on boson and jet production were presented. Differences between results from NLO pQCD [6] and the measured inclusive isolated photon cross-sections [4, 5] were similar to those seen with other photon experiments [3]. The disagreement was larger with the γ+jet measurement [7]. NLO pQCD [10,11] agreed very well with both the inclusive jet [7, 8] and dijet [12] differential cross-sections. Limits on several exotic models were set based on the dijet mass and χdijet[13] distributions. NLO
pQCD also reproduced the characteristics of Z+jet [17,18] and W +jet events [20]; matrix-element plus parton shower Monte Carlo performed less favorably [14, 15, 21]. NLO pQCD [19] reproduced the W +c jet production [22,23] and γ +b jet pT distributions [24],
but did not compare as favorably with the γ +c jet [24] or Z +b jet [25,26] measurements.
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