授業ではやれませんでしたが標準模型の検証 - osaka...

授業ではやれませんでしたが...

標準模型の検証

実験屋の独り言

４元ベクトルを触るだけなら実験屋不要‣ プログラミング言語の初歩で十分๏ 学部生でもできる

‣ 真にオリジナリティのある解析は稀４元ベクトルが正しいかどうか‣ バイアスがないか‣ 精度を理解できているか検出器較正後，既知のプロセスで確認

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標準模型の測定の動機

人類未踏のエネルギー領域に標準模型が適用可能かどうか‣ SUSYなど多くの過程で強い相互作用が支配的๏ Scale 依存性๏ PDFヒッグスや新しい物理の探索の背景事象‣ 昨日のシグナルは今日のバックグラウンドUnderlying event の理解

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ジェット生成断面積 (1)

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Page 12 of 59 Eur. Phys. J. C (2011) 71: 1512

ergy scales. The dijet measurements have been made in aregion where the sensitivity to the parton distributions is re-duced, and thus primarily test the structure of the QCD ma-trix element. The comparison is made for two different Rparameters, showing that the level of agreement is robustunder different soft corrections, as well as under the evolu-tion of the perturbative cross section with R. For both in-clusive and dijet measurements, the theory agrees well withthe data, validating this perturbative QCD approach in a newkinematic regime.

Acknowledgements We deeply thank everybody at CERN involvedin operating the LHC in such a superb way during this initial high-energy data-taking period. We acknowledge equally warmly all thetechnical and administrative staff in the collaborating institutions with-out whom ATLAS could not be operated so efficiently.

We acknowledge the support of ANPCyT, Argentina; YerevanPhysics Institute, Armenia; ARC and DEST, Australia; Bundesminis-terium für Wissenschaft und Forschung, Austria; National Academy ofSciences of Azerbaijan; State Committee on Science & Technologiesof the Republic of Belarus; CNPq and FINEP, Brazil; NSERC, NRC,and CFI, Canada; CERN; CONICYT, Chile; NSFC, China; COL-

CIENCIAS, Colombia; Ministry of Education, Youth and Sports of theCzech Republic, Ministry of Industry and Trade of the Czech Republic,and Committee for Collaboration of the Czech Republic with CERN;DNRF, DNSRC and the Lundbeck Foundation, Denmark; EuropeanCommission, through the ARTEMIS Research Training Network;IN2P3-CNRS and CEA-DSM/IRFU, France; Georgian Academy ofSciences; BMBF, DFG, HGF and MPG, Germany; Ministry of Edu-cation and Religion, through the EPEAEK program PYTHAGORASII and GSRT, Greece; ISF, MINERVA, GIF, DIP, and Benoziyo Cen-ter, Israel; INFN, Italy; MEXT, Japan; CNRST, Morocco; FOM andNWO, Netherlands; The Research Council of Norway; Ministry ofScience and Higher Education, Poland; GRICES and FCT, Portugal;Ministry of Education and Research, Romania; Ministry of Educationand Science of the Russian Federation and State Atomic Energy Cor-poration ROSATOM; JINR; Ministry of Science, Serbia; Departmentof International Science and Technology Cooperation, Ministry of Ed-ucation of the Slovak Republic; Slovenian Research Agency, Ministryof Higher Education, Science and Technology, Slovenia; Ministerio deEducación y Ciencia, Spain; The Swedish Research Council, The Knutand Alice Wallenberg Foundation, Sweden; State Secretariat for Edu-cation and Science, Swiss National Science Foundation, and Cantonsof Bern & Geneva, Switzerland; National Science Council, Taiwan;TAEK, Turkey; The STFC, the Royal Society and The LeverhulmeTrust, United Kingdom; DOE and NSF, United States of America.

Fig. 9 Inclusive jet double-differential cross section as a function ofpT, for different bins of rapidity |y|. The results are shown for jets iden-tified using the anti-kt algorithm with R = 0.4. The data are comparedto leading-logarithmic parton-shower MC simulations, normalised tothe measured cross section by the factors shown in the legend, fixedto give the best normalisation to the inclusive jet measurements. The

bands indicate the total systematic uncertainty on the data. The errorbars indicate the statistical uncertainty, which is calculated as 1/

√N ,

where N is the number of entries in a given bin. The insets along theright-hand side show the ratio of the data to the various MC simula-tions

Eur. Phys. J. C (2011) 71: 1512 Page 13 of 59

Fig. 10 Inclusive jet double-differential cross section as a function ofpT, for different bins of rapidity |y|. The results are shown for jets iden-tified using the anti-kt algorithm with R = 0.6. The data are comparedto leading-logarithmic parton-shower MC simulations, normalised tothe measured cross section by the factors shown in the legend, fixedto give the best normalisation to the inclusive jet measurements. The

bands indicate the total systematic uncertainty on the data. The errorbars indicate the statistical uncertainty, which is calculated as 1/

√N ,

where N is the number of entries in a given bin. The insets along theright-hand side show the ratio of the data to the various MC simula-tions

複雑なアクティビティなのでジェットそのものの理解が簡単ではない : スケールと分解能シミュレーションのチューンが必要‣ 形は合うが，大きさは合わない

ジェット生成断面積 (2)

NLOだとよく合う5


Fig. 13 Inclusive jetdifferential cross section as afunction of jet pT integratedover the full region |y| < 2.8 forjets identified using the anti-ktalgorithm with R = 0.4. Thedata are compared to NLOpQCD calculations to whichsoft QCD corrections have beenapplied. The error bars indicatethe statistical uncertainty on themeasurement, and the shadedbands indicate the quadratic sumof the systematic uncertainties,dominated by the jet energyscale uncertainty. The statisticaluncertainty is calculated as1/

√N , where N is the number

of entries in a given bin. There isan additional overall uncertaintyof 11% due to the luminositymeasurement that is not shown.The theory uncertainty shown isthe quadratic sum ofuncertainties from the choice ofrenormalisation andfactorisation scales, partondistribution functions, αs (MZ),and the modelling of soft QCDeffects, as described in the text

Fig. 14 Inclusive jetdifferential cross section as afunction of jet pT integratedover the full region |y| < 2.8 forjets identified using the anti-ktalgorithm with R = 0.6. Thedata are compared to NLOpQCD calculations to whichsoft QCD corrections have beenapplied. The uncertainties on thedata and theory are shown asdescribed in Fig. 13


Fig. 13 Inclusive jetdifferential cross section as afunction of jet pT integratedover the full region |y| < 2.8 forjets identified using the anti-ktalgorithm with R = 0.4. Thedata are compared to NLOpQCD calculations to whichsoft QCD corrections have beenapplied. The error bars indicatethe statistical uncertainty on themeasurement, and the shadedbands indicate the quadratic sumof the systematic uncertainties,dominated by the jet energyscale uncertainty. The statisticaluncertainty is calculated as1/

√N , where N is the number

of entries in a given bin. There isan additional overall uncertaintyof 11% due to the luminositymeasurement that is not shown.The theory uncertainty shown isthe quadratic sum ofuncertainties from the choice ofrenormalisation andfactorisation scales, partondistribution functions, αs (MZ),and the modelling of soft QCDeffects, as described in the text

Fig. 14 Inclusive jetdifferential cross section as afunction of jet pT integratedover the full region |y| < 2.8 forjets identified using the anti-ktalgorithm with R = 0.6. Thedata are compared to NLOpQCD calculations to whichsoft QCD corrections have beenapplied. The uncertainties on thedata and theory are shown asdescribed in Fig. 13

W/Z

クォーク対への崩壊を使うのは難しい‣ W→lν，Z→ll๏ BR(W→lν）は？๏ isolation && high pT✓20GeV前後✓isolationを要求する理由？

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FIG. 2. Top: Distribution of the electron transverse energy ET in the selected W → eν candidate events after all cuts forpositive (left) and negative (right) charge. Bottom: Transverse mass distributions for W+ (left) and W− (right) candidates.The simulation is normalised to the data. The QCD background shapes are taken from background control samples (top) orMC simulation with relaxed electron identification criteria (bottom) and are normalised to the total number of QCD events asdescribed in the text.

N B CW/Z AW/Z

W+ 77885 5130 ± 350 0.693 ± 0.012 0.478 ± 0.008W− 52856 4500 ± 240 0.706 ± 0.014 0.452 ± 0.009W± 130741 9610 ± 590 0.698 ± 0.012 0.467 ± 0.007Z 9725 206 ± 64 0.618 ± 0.016 0.447 ± 0.009

TABLE IV. Number of observed candidates N and expectedbackground events B, efficiency and acceptance correction fac-tors for the W and Z electron channels. Efficiency scale fac-tors used to correct the simulation for differences between dataand MC are included in the reported CW/Z factors. The givenuncertainties are the quadratic sum of statistical and system-atic components. The statistical uncertainties on the CW/Zand AW/Z factors are negligible.

AW/Z correction factors used, where the uncertainties onAW/Z are obtained from Tab. II. The cross sections forall channels are reported in Tab. V with fiducial and totalvalues and the uncertainties due to data statistics, lumi-nosity, further experimental systematic uncertainties andthe acceptance extrapolation in case of the total crosssections.Table VI presents the sources of systematic uncertain-

ties in all channels. Apart from the luminosity contri-bution of 3.4%, the W cross sections are measured withan experimental uncertainty of 1.8% to 2.1%, where themain contributions are due to electron reconstruction andidentification as well as missing transverse energy perfor-mance related to the hadronic recoil [47].The Z cross section is measured, apart from the lu-

minosity contribution, with an experimental precision of

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FIG. 2. Top: Distribution of the electron transverse energy ET in the selected W → eν candidate events after all cuts forpositive (left) and negative (right) charge. Bottom: Transverse mass distributions for W+ (left) and W− (right) candidates.The simulation is normalised to the data. The QCD background shapes are taken from background control samples (top) orMC simulation with relaxed electron identification criteria (bottom) and are normalised to the total number of QCD events asdescribed in the text.

N B CW/Z AW/Z

W+ 77885 5130 ± 350 0.693 ± 0.012 0.478 ± 0.008W− 52856 4500 ± 240 0.706 ± 0.014 0.452 ± 0.009W± 130741 9610 ± 590 0.698 ± 0.012 0.467 ± 0.007Z 9725 206 ± 64 0.618 ± 0.016 0.447 ± 0.009

TABLE IV. Number of observed candidates N and expectedbackground events B, efficiency and acceptance correction fac-tors for the W and Z electron channels. Efficiency scale fac-tors used to correct the simulation for differences between dataand MC are included in the reported CW/Z factors. The givenuncertainties are the quadratic sum of statistical and system-atic components. The statistical uncertainties on the CW/Zand AW/Z factors are negligible.

AW/Z correction factors used, where the uncertainties onAW/Z are obtained from Tab. II. The cross sections forall channels are reported in Tab. V with fiducial and totalvalues and the uncertainties due to data statistics, lumi-nosity, further experimental systematic uncertainties andthe acceptance extrapolation in case of the total crosssections.Table VI presents the sources of systematic uncertain-

ties in all channels. Apart from the luminosity contri-bution of 3.4%, the W cross sections are measured withan experimental uncertainty of 1.8% to 2.1%, where themain contributions are due to electron reconstruction andidentification as well as missing transverse energy perfor-mance related to the hadronic recoil [47].The Z cross section is measured, apart from the lu-

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FIG. 3. Dielectron invariant mass mee (left) and rapidity yZ distribution (right) for the central Z → ee analysis. The simulationis normalised to the data. The QCD background shapes are taken from a background control sample and normalised to the resultof the QCD background fit.

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FIG. 4. Dielectron invariant mass mee (left) and rapidity yZ distribution (right) for the forward Z → ee analysis. Thesimulation is normalised to the data. The QCD background shapes are taken from a background control sample and normalisedto the result of the QCD background fit.

2.7%. This is dominated by the uncertainty on the elec-tron reconstruction and identification efficiency.

The theoretical uncertainties on CW/Z are evaluatedby comparisons of Mc@Nlo and PowHeg Monte Carlosimulations and by testing the effect of different PDFsets, as described in Sec. III for the acceptances. Thetotal theoretical uncertainty is found to be 0.6% for CWand 0.3% for CZ .

The theoretical uncertainty on the extrapolation fromthe fiducial region to the total phase space for W andZ production is between 1.5% and 2.0%, as mentionedabove.

The cross sections measured as a function of the W

electron pseudorapidity, for separated charges, and of theZ rapidity are presented in Tabs. XVI, XVII, XVIII andXIX. The statistical, bin-correlated and uncorrelatedsystematic and total uncertainties are provided. Theoverall luminosity uncertainty is not included. The sta-tistical uncertainty in each bin is about 1-2% for the Wdifferential measurements, while the total uncertainty isat the 2.5-3% level. For the Z rapidity measurement thestatistical uncertainty is about 2% for |yZ | < 1.6 andgrows to 3-5% in the more forward bins. The total un-certainty on the Z cross sections is 3-4% in the centralregion and up to 10% in the most forward bins. It ismainly driven by the uncertainties on the electron recon-

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FIG. 8. Transverse mass distribution of candidate W+ (top)and W− (bottom) events. The simulation is normalised to thedata. The QCD background shape is taken from simulationand normalised to the number of QCD events measured fromdata.

uncertainty on the momentum scale correction.The Z → µµ cross section is measured, apart from the

luminosity contribution, with an experimental precisionof 0.9%. This is dominated by the uncertainty in themuon reconstruction efficiency (0.6%), with about equalsystematic and statistical components due to the limitedsample of Z → µµ events. The uncertainty of the mo-mentum scale correction has an effect of 0.2% while theuncertainty from momentum resolution is again found tobe negligible. The impact of the QCD background un-certainty is at the level of 3 per mille.The theoretical uncertainties on CW/Z are evaluated

as in the electron channels and found to be 0.7-0.8% forCW and 0.3% for CZ .The uncertainty on the theoretical extrapolation from

the fiducial region to the total phase space for W and Z

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production is between 1.5% and 2.1%.

The cross sections measured as a function of the Wmuon pseudorapidity, for separated charges, and of theZ rapidity are shown in Tabs. XX, XXI and XXII. Thestatistical, bin correlated and uncorrelated systematicand total uncertainties are provided. The uncertaintieson the extrapolation to the common fiducial volume, onelectroweak and multijet backgrounds, on the momen-tum scale and resolution are treated as fully correlatedbetween bins for both W and Z measurements. Otheruncertainties are considered as uncorrelated.

The statistical uncertainties on the W differential crosssections are in the range 1-2%, and the total uncertaintiesare in the range of 2-3%.

The differential Z cross section is measured with a sta-tistical uncertainty of about 2% up to |yZ | < 1.6, 2.6%

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MT =�

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W→lν解析での小ネタ

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correct pT distribution, and the shaded area includes the effects of detector resolution [4].

measured in the calorimeter and p is the momentum of the electron track. The width of the distribution near thepeak is used to measure the energy resolution. The energy scale and resolution is also measured using a Z → e+e−

sample, which was the method used by CDF and D0 for the Run 1 measurements.

2.3. Backgrounds

The W sample has a background contamination from several sources. For W → µν, the largest background isZ → µµ events where one of the muons is not reconstructed. The missing track also gives a momentum imbalance,allowing the event to pass the selection requirement for missing transverse momentum. This background is estimatedusing a MC sample to determine the fraction of Z events which pass the W selection cuts and normalized to theknown ratio of W to Z production. These events are about 4% of the sample and MC events are used to model theshape of this background. For the W → eν sample, Z → ee contamination is estimated in the same way and is lessthan half a percent.

Another background comes from W → τν events with the subsequent decay of the tau to an electron or muon.These events are indistinguishable from signal events, but have a softer lepton momentum spectrum. Again a MCsample is used to measure the efficiency and shape for reconstructing these events and the background is normalizedto the known W cross section and leptonic branching fractions. The W → τν events are 1-2% of the sample.

QCD background events are from jets which fake a lepton and also have a transverse momentum imbalance dueto mismeasured jet energies. For most events with fake leptons, the lepton is not isolated from a jet and containssignificant energy in a cone around the lepton. In addition, most of these events do not have a momentum imbalance.This background is estimated using events with either low momentum imbalance or non-isolated leptons to extrapolateinto the signal region. The sideband events also give the kinematic shape of the background. The QCD backgroundis about 1% of the sample.

SLAC Summer Institute on Particle Physics (SSI04), Aug. 2-13, 2004

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Figure 2: The W transverse mass distribution from simulation. The solid line is generated with the W pT = 0, the points use

the correct pT distribution, and the shaded area includes the effects of detector resolution [4].

W mass. This has the advantage of just using the charged lepton momentum which is the best measured quantity inthe event, and avoiding the uncertainty associated with reconstructing the neutrino. However, relating the chargedlepton momentum to the W mass requires an understanding of the transverse momentum distribution of the W. Thisintroduces an uncertainty based on the theoretical modeling of the W pT distribution. In contrast, the transversemass distribution is to first order insensitive to the transverse momentum of the W. Figures 3 and 2 illustrate thetradeoffs in the understanding of the W pT spectrum and the neutrino measurement resolution.

2.2. Energy Scale Calibration

Measuring the W mass requires an absolute calibration of the energy and momentum scale of the detector. Under-standing this scale has been the dominant systematic error for the W mass measurement and is ultimately limitedby the size of the control samples used to set the scale.

A sample of J/ψ → µ+µ−, Υ(1S) → µ+µ−, and Z → µ+µ− events are used to set the momentum scale for chargedparticle tracking. The large statistics J/ψ → µ+µ− sample sets the momentum scale. Studying the momentumscale dependence on the polar angle of the track gives the track curvature correction as a function of polar angle.The momentum scale dependence on the track momentum is sensitive to the ionization energy loss and is used forcalibration of the MC for material in the detector. The Υ(1S) → µ+µ− sample provides a check of the momentumscale at 10 GeV/c2 which is intermediate to the mass scale of the W and Z at 80 and 90 GeV/c2, and the 3 GeV/c2

mass of the J/ψ. The Z → µ+µ− sample provides a check of the momentum scale at the high mass scale. The fit tothe width of the Z provides a measurement of the track resolution at that momentum which is used to tune the MCsimulation. Figure 4 shows the CDF Z → µ+µ− sample used for the Run 2 W mass analysis.

With the track momentum scale set using J/ψ decays, the electromagnetic calorimeter energy scale can be setusing the peak of the E/p distribution for W → eν decays, where E is the electromagnetic energy of the electron

SLAC Summer Institute on Particle Physics (SSI04), Aug. 2-13, 2004

THT001 3

WのpT=0

WのpT≠0

検出器の分解能

W/Z + jets

9

ATLAS Collaboration / Physics Letters B 698 (2011) 325–345 331

Table 5The measured cross section ratio for W + jets in the electron and muon channels as a function of corrected jet multiplicity with (in order) statistical and systematicuncertainties. The cross section ratios are quoted in a limited and well-defined kinematic region, described in the text. The measurement was not performed in the inclusive4-jet bin in the electron channel because of the poor signal-to-background ratio. Theoretical predictions from MCFM are also shown, with all uncertainties combined. MCFMprovides NLO predictions for Njet ! 2 and a LO prediction for Njet = 3.Jet multiplicity W → eν MCFM W → eν W → µν MCFM W → µν" 1/ " 0 0.185± 0.007+0.025−0.019 0.159+0.006−0.005 0.183± 0.007+0.023−0.020 0.160+0.006−0.005" 2/ " 1 0.250 ± 0.019+0.019−0.010 0.255+0.017−0.022 0.274± 0.020+0.018−0.011 0.255+0.017−0.021" 3/ " 2 0.224± 0.037± 0.022 0.241+0.108−0.061 0.278± 0.041+0.024−0.020 0.242+0.104−0.061" 4/ " 3 – – 0.297± 0.088+0.037−0.026 –

Fig. 3. W + jets cross section results as a function of corrected jet multiplicity. Left: electron channel. Right: muon channel. The cross sections are quoted in a limited andwell-defined kinematic region, described in the text. For the data, the statistical uncertainties are shown by the vertical bars, and the combined statistical and systematicuncertainties are shown by the hashed regions. Note that the uncertainties are correlated from bin to bin. Also shown are predictions from PYTHIA, ALPGEN, SHERPA andMCFM, and the ratio of theoretical predictions to data (PYTHIA is not shown in the ratio). The theoretical uncertainties are shown only for MCFM, which provides NLOpredictions for Njet ! 2 and a LO prediction for Njet = 3.

Fig. 4. W + jets cross section ratio results as a function of corrected jet multiplicity. Left: electron channel. Right: muon channel. The cross sections are quoted in a limitedand well-defined kinematic region, described in the text. For the data, the statistical uncertainties are shown by the vertical bars, and the combined statistical and systematicuncertainties are shown by the hashed regions. Also shown are theoretical predictions from PYTHIA, ALPGEN, SHERPA, and MCFM. The theoretical uncertainties are shownonly for MCFM, which provides NLO predictions for Njet ! 2 and a LO prediction for Njet = 3.

sation scale uncertainties were estimated by varying the scales, inall combinations, up and down, by factors of two. PDF uncertain-ties were computed by summing in quadrature the dependence oneach of the 22 eigenvectors characterising the CTEQ6.6 PDF set;the uncertainty in αs was also taken into account. An alternativePDF set, MSTW2008 [13], with its set of 68% C.L. eigenvectors was

also examined, and the envelope of the uncertainties from CTEQ6.6and MSTW2008 was taken as the final PDF uncertainty. The totalresulting uncertainties are given in Tables 4 and 5.

In conclusion, this Letter presents a measurement of the W +jets cross section as a function of jet multiplicity in pp collisionsat

√s = 7 TeV in both electron and muon decay modes of the

14

1 2 3 4

) [pb

]je

t N!

)+- e+ e

"*(#(Z

/$

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410 ATLAS-1 L dt = 36 pb%

jets, R = 0.4,tanti-k| < 4.4jet > 30 GeV, |yjet

Tp

) + jets-e+ e"*(#Z/ = 7 TeV)sData 2010 (

ALPGEN + HERWIGSherpaPYTHIA (normalized to data)BlackHat

1 2 3 4

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/ NL

O

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11.21.41.6 Data 2010 / BlackHat

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) [pb

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t N!

)+-µ+

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410 = 7 TeV)sData 2010 (

ALPGEN + HERWIG Sherpa PYTHIA (normalized to data)BlackHat

ATLAS )+jets-µ+µ "*(#Z/

-1 L dt = 35 pb% jets, R = 0.4,tanti-k

| < 4.4jet > 30 GeV, |yjetTp

Data

/ NL

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11.21.41.6 Data 2010 / BlackHat

theoretical uncertainties

Data

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jet N1! 2! 3! 4!

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Data 2010 / Sherpa

FIG. 3: Measured cross section σNjet (black dots) for (left) Z/γ∗(→ e+e−)+jets and (right) Z/γ∗(→ µ+µ−)+jets production

as a function of the inclusive jet multiplicity, for events with at least one jet with pT > 30 GeV and |y| < 4.4 in the final state.In this and subsequent figures 4 - 14 the error bars indicate the statistical uncertainty and the dashed areas the statistical andsystematic uncertainties added in quadrature. The measurements are compared to NLO pQCD predictions from BlackHat,as well as the predictions from ALPGEN and Sherpa (both normalized to the FEWZ value for the total cross section), andPYTHIA (normalized to the data as discussed in Section XII).

まあまあの理解度誤差の要因はjet energy scale

QCDの理解探索における重要なバックグラウンド

t-tbar 生成断面積 (1)

QCDの総合テスト探索における最重要バックグラウンド

10

85% vs 15%(Tevatronとの違い)

BR(t→bW)~100%


Lepton + jets‣ 孤立レプトン＋missing ET ← W๏ W＋jets が主な背景事象✓ジェットの数の違い✓b-jetがあるかないか

11

jetsN1 2 3 4 5≥

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tt

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jetsN1 2 3 4 5≥

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= 7 TeVsData 2011,

tt

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+ Jetsµ

ATLAS Preliminary

(b) µ + jets channel

Figure 1: Event yields in the control and signal region for the (a) e + jets and (b) µ + jets channels. TheW+jets and QCD multijet contributions are extracted from data as explained in the text. All other physicsprocesses are normalized to the predictions from MC simulation.

The distributions of input variables are shown in Fig. 2 and Fig. 3 for the µ+jets channel and in Fig. 4 andFig. 5 for the e + jets channel before applying the fitting procedure. The shape and normalization of theQCD multijet events is obtained from data, the normalization for W+jets events is measured exploitingthe W boson production charge asymmetry as discussed above, while the shape comes from MC. Allother contributions are taken from MC prediction for both normalization and shape.

A likelihood discriminant is built from these input variables using the projective likelihood optionin the TMVA package [22]. The likelihood discriminant Di for an event i is defined as the ratio of thesignal to the sum of signal and background likelihoods, where the individual likelihoods are products ofthe corresponding probability densities of the discriminating input variables. This approach assumes thatthe latter are uncorrelated.

The discriminant function is evaluated for each physics process considered in this analysis and thecorresponding template is created. For tt̄, Z+jets, single top and diboson production templates are ob-tained from simulation and normalized to the luminosity of the data sample. For W+jets, templates arealso obtained from MC but normalized to the data-driven yield estimate. A template for the QCD mul-tijet background is obtained from data using loose and tight events weighted according to the matrixmethod. Templates containing 20 bins each are created for each of six analysis channels correspondingto different lepton flavor (e or µ) and jet multiplicity (3, 4 and ≥ 5 jets) and combined into one, 120 bin,histogram as shown in Fig. 6.

The tt̄ cross section is extracted by performing a maximum-likelihood fit to the discriminant dis-tribution observed in data using templates for signal and all backgrounds. The likelihood is defined asfollows:

L(�β,�δ) =120�

k=1

P(µk, nk) ×�

j

G(β j,∆ j) ×�

i

G(δi, 1) (3)

where the first term represents the Poisson probability density of observing nk events in bin k given thatµk is expected from the sum of all templates. The second term implements a number of free parameters

6

t-tbar 生成断面積（３）

dilepton : 高いS/N‣ 2つの孤立レプトン + missing ET‣ Mll ~ MZ はveto๏ Z+jets, WW, WZ, single top が背景事象✓ジェットの数とb-jetのあるなし

12

Number of jets0 1 2 3 4!

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*+jets#Z/Fake leptonsOther EW

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All channelsATLAS Preliminary

0 1 2 3 4!

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(b)

Figure 1: (a) Jet multiplicity distribution for ee+µµ+eµ events without b-tag. (b) Multiplicity distribu-tion of b-tagged jets in ee+µµ+eµ events. Contributions from diboson and single top-quark events aresummarized as ‘Other EW’. Note that the events in (b) are not a simple subset of those in (a) because the

event selections for the b-tag and non-b-tag analyses differ.

[GeV]TH0 100 200 300 400 500 600 !700

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Figure 2: The HT distribution in the signal region for (a) the non-b-tag eµ channel, (b) the b-tagged eµchannel. Contributions from diboson and single top-quark events are summarized as ‘Other EW’.

9


13

[TeV]s1 2 3 4 5 6 7 8

[pb]

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NLO QCD (pp)Approx. NNLO (pp)

)pNLO QCD (p

) pApprox. NNLO (p

CDF

D0

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pb-14+17Dilepton 173

81 pb±All-hadronic 167 pb-10

+11Combined 177

7 8

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WW, ZZ 生成断面積

WW‣ dilepton, large missing ET, and jet veto to reject topZZ‣ 4 leptons

14

2

calorimeter is finely segmented and plays an important

role in electron identification. The muon spectrometer

has separate trigger and high-precision tracking cham-

bers which provide muon identification and measurement

in |η| < 2.7.A three-level trigger system selects events to be

recorded for offline analysis. The events used in thisanalysis were selected with single-lepton triggers with

nominal transverse momentum thresholds of 20 GeV for

electrons and 18 GeV for muons. The efficiencies of thesingle-lepton triggers have been determined as a function

of lepton pT using large samples of Z → �+�− events.The trigger efficiency for events passing the offline se-lection described below is 99.9% with an uncertainty of

0.1%.

This measurement uses a data sample of proton-proton

collisions at√s = 7 TeV recorded between February and

June 2011. After data quality requirements, the total

integrated luminosity used in the analysis is 1.02 fb−1.The integrated luminosity uncertainty is 3.7% [12].

Events are required to contain a primary vertex formed

from at least three associated tracks. The vertex with

the largest sum of the p2T computed from the associatedtracks is selected as the primary vertex.

Signal events are characterized by four high-pT, iso-lated electrons or muons, in three channels: e+e−e+e−,µ+µ−µ+µ− and e+e−µ+µ−. Lepton candidates are re-quired to be consistent with originating from the primary

vertex. Muons are identified by matching tracks (or track

segments) reconstructed in the muon spectrometer to

tracks reconstructed in the inner detector [13]. Their mo-

mentum is calculated by combining the information from

the two systems and correcting for the energy deposited

in the calorimeters. Only muons with pT > 15 GeV and|η| < 2.5 are considered. In order to reject muons fromthe decay of heavy quarks, isolated muons are selected

by requiring the scalar sum of the transverse momenta

(ΣpT) of other tracks with pT > 1 GeV inside a cone ofsize ∆R = 0.2 around the muon to be no more than 15%of the muon pT. The overall reconstruction, identifica-tion and isolation efficiency, measured in data using alarge sample of Z → µ+µ− events, varies as a functionof pT from 92% at 15 GeV to 95% at 45 GeV.

Electrons are reconstructed from a cluster in the elec-

tromagnetic calorimeter matched to a track in the in-

ner detector [13]. Electron candidates are required to

pass the ‘medium’ identification criteria described in

Ref. [13], to have a transverse momentum (measured in

the calorimeter) of at least 15 GeV and a pseudorapidity

of |η| < 2.47. They must be isolated, using the samecriterion as for muons, calculating the ΣpT around theelectron track. Electron candidates within ∆R = 0.1 ofany selected muon are rejected, and if two electron candi-

dates are within ∆R = 0.1 of each other the one with thelower pT is rejected. The overall reconstruction, identifi-cation and isolation efficiency varies as a function of pTfrom 63% at 15 GeV to 81% at 45 GeV.

Selected events are required to have exactly four lep-

tons, and to have passed a single-muon or single-electron

trigger. To ensure high trigger efficiency, at least oneof these leptons must have pT > 20 GeV (25 GeV) for amuon (electron) and match to a muon (electron) recon-

structed online by the trigger system within ∆R < 0.1(0.15).

Same-flavour, oppositely-charged lepton pairs are com-

bined to form Z candidates. An event must containtwo such pairs. In the e+e−e+e− and µ+µ−µ+µ− chan-nels, ambiguities are resolved by choosing the pairing

which results in the smaller value of the sum of the two

|m�+�− −mZ | values. Figure 1 shows the correlation be-tween the invariant mass of the leading (higher pT) andthe subleading (lower pT) lepton pair. The events clusterin the region where both masses are around mZ . Eventsare required to contain two Z candidates with invariantmasses satisfying 66 GeV < m�+�− < 116 GeV.

Subleading lepton pair mass [GeV]40 60 80 100 120 140 160 180 200

Lead

ing

lept

on p

air m

ass

[GeV

]

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Signal Region

-1 L dt = 1.02 fb!= 7 TeVs

Expected backgroundin signal region:

(syst)0.3"0.4+ 0.3 (stat) ±0.3

ATLAS

FIG. 1. The mass of the leading lepton pair versus the massof the subleading lepton pair. The events observed in thedata are shown as solid circles and the ZZ signal predictionfrom simulation as boxes. The large dashed box indicates thesignal region defined by the requirements on the lepton-pairmasses.

The reconstruction efficiency for ZZ events is deter-mined from a detailed Monte Carlo simulation. The LO

generator Pythia [14] with the MRST modified LO par-ton density function (PDF) set [15] is used to model

pp → ZZ → �+�−�+�− events, where � includes elec-trons, muons and τ leptons. The Pythia simulationincludes the interference terms between the Z and γ∗

diagrams; the mass threshold for the Z/γ boson is set to12 GeV. The detector response is simulated [16] with a

program based on GEANT4 [17]. Additional inelastic ppevents are included in the simulation, distributed so as

requirement. In all three distributions, the data in thebackground regions are in agreement with the standardmodel expectation and the signal is clearly visible.

The acceptance, which converts the observed yield inthe kinematically restricted signal region to the inclusiveWþW" cross section, is derived from simulation and iscorrected with scale factors based on measurements inindependent data samples. The scale factors correct forthe difference in trigger, lepton reconstruction and identi-fication, and jet-veto efficiencies between data and simu-lation. The efficiency to pass the trigger criteria is close tounity and has small statistical and systematic uncertainties.For the lepton reconstruction and identification, the scalefactors differ from unity by at most a few percent, indicat-ing the accuracy of the simulation, and have systematicuncertainties derived from the efficiency measurementsdescribed above. A small smearing is added to the muonpT in simulation, so that it replicates the Z ! !! invariantmass distribution in data. The acceptance uncertainty dueto the PDF uncertainties is 1.2%.

There are two major sources of systematic uncertainty inthe jet-veto efficiency. The first is the modeling of jetproduction in association with WþW" due to initial stateradiation, radiation from the internal line in the t-channeldiagram, and additional parton collisions in the same ppcollision. The second is the jet-energy scale, which is thecorrespondence between the true particle jet pT and thereconstructed jet pT . To minimize the systematic uncer-tainty due to these two effects, control samples of Z ! ‘‘are used. These are sufficiently large and pure that the jet-veto efficiency can be directly measured and compared tosimulation using the same QCD modeling as the WþW"

signal. The ratio of the observed to the simulated zero-jetfraction in the Z ! ‘‘ sample to simulation is used todefine a jet-veto scale factor of 0:97# 0:06. The uncer-tainty is due to differences between the jet-veto efficiencyin Z andWþW" events which is assessed including effectsfrom the choice of renormalization and fragmentationscales [19].

The overall selection acceptances for signal events are4:1# 0:1% for e"e", 8:6# 0:1% for !"!", and 11:5#0:6% for e"!". The relative acceptance in event selectionare lepton acceptance and identification (18%, 41%, 27%)and the mll (85%, 84%, 100%), E

missT;rel (41%, 43%, 69%),

and jet-veto (64%, 59%, 61%) requirements, where thethree percentages indicate the ee, !!, and e! channels,respectively, and each factor is relative to the previousrequirement. The contributions from WþW" productionwhere one or both W bosons decays to a # which subse-quently decays to an e or ! are less than 10% of the finalselected WþW" signal events in all three channels.With the exception of W þ jets, the backgrounds are

derived from simulations, corrected with the same scalefactors as applied to the modeling of the signal acceptance.The backgrounds are scaled to the data sample based on theintegrated luminosity and predicted cross sections. The topand WZ processes are simulated with MC@NLO, the ZZprocess is simulated with HERWIG, the W$ is simulatedwith madgraphþ pythia [20,21], and the Drell-Yan process issimulated with ALPGEN [22] and PYTHIA [20]. The QCD jetcontribution, which is not significant after the EmissT;rel cut, ismodeled with PYTHIA in Fig. 1, which includes data belowthe EmissT;rel requirement.Like the signal acceptance, the background estimates

have uncertainties due to the trigger, lepton reconstructionand identification, and jet-veto efficiencies, in addition tothe uncertainties on the integrated luminosity and theoreti-cal cross sections. The Drell-Yan and top backgroundestimates have additional uncertainties described below.Most of the Drell-Yan events are removed by the dileptoninvariant mass and EmissT;rel requirements, but because of thelarge cross section some remain as background. The un-certainty on this background due to the simulation of EmissT;relis assessed using a control sample of Z=$$ ! ee andZ=$$ ! !! events in the Z mass peak region, jm‘‘ "mZj< 10 GeV, passing a relaxed requirement of EmissT;rel >30 GeV. Despite the EmissT;rel requirement, this sample is still

0 20 40 60 80 100 120 140-110

1

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310 -1Ldt = 34 pb∫ATLAS=7TeVs Data

Drell-YanQCD jetDibosonW+jetstop

νeνe→WWνµνµ+

0 20 40 60 80 100 120 140E

vent

s / 1

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-1Ldt = 34 pb∫ATLAS=7TeVs Data


νµνe→WW

0 1 2 3 4 5 6 7 8 9 10

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-1Ldt = 34 pb∫ATLAS=7TeVs Data


νlνl→WWEve

nts

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[GeV]missT, relE [GeV]missT, relE Jet Multiplicity

FIG. 1 (color online). EmissT;rel distributions for the selected ee and!! (left) and e! (center) events and the multiplicity distribution forjets with pT > 20 GeV and j%j< 3:0 for all three dilepton channels combined (right). The distributions show events with all selectioncriteria applied except for EmissT;rel in the E

missT;rel distribution and the jet-veto in the jet multiplicity distribution. Simulation is used for the

QCD jet and W þ jets background contributions in these plots as opposed to the data-driven method used for W þ jets in the signalregion described in the text. The QCD jet contribution is negligible in the signal region.

PRL 107, 041802 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending22 JULY 2011

041802-3

CERN-PH-EP-2011-166

Submitted to Physical Review Letters

Measurement of the ZZ production cross section and limits on anomalous neutraltriple gauge couplings in proton-proton collisions at

√s = 7 TeV with the ATLAS

detector(The ATLAS Collaboration)(Dated: November 25, 2011)

A measurement of the ZZ production cross section in proton-proton collisions at√s = 7 TeV

using data recorded by the ATLAS experiment at the LHC is presented. In a data sample cor-

responding to an integrated luminosity of 1.02 fb−1 collected in 2011, 12 events containing twoZ boson candidates decaying to electrons and/or muons are observed. The expected backgroundcontribution is 0.3 ± 0.3(stat.)+0.4−0.3(syst.) events. The cross section measured in a phase-space re-gion with good detector acceptance and for dilepton masses within the range 66 GeV to 116 GeV is

σfidZZ→�+�−�+�− = 19.4+6.3−5.2(stat.)

+0.9−0.7(syst.)± 0.7(lumi.) fb. This result is then used to derive the to-

tal cross section for on-shell ZZ production, σtotZZ = 8.5+2.7−2.3(stat.)

+0.4−0.3(syst.)±0.3 (lumi.) pb, which

is consistent with the Standard Model expectation of 6.5+0.3−0.2 pb calculated at the next-to-leadingorder in QCD. Limits on anomalous neutral triple gauge boson couplings are derived.

PACS numbers: 14.70.Hp, 12.15.Ji, 12.60.Cn, 13.85.Qk

The production of pairs of Z bosons at the LHC is ofgreat interest since it provides an excellent opportunityto test the predictions of the electroweak sector of theStandard Model at the TeV energy scale; moreover it isthe irreducible background to the search for the Higgsboson in the H → ZZ decay channel. In the StandardModel, ZZ production proceeds at leading order (LO)via t-channel quark-antiquark interactions; the ZZZ andZZγ neutral triple gauge boson couplings (nTGCs) areabsent, hence there is no contribution from s-channel qq̄annihilation at tree level. At the one-loop level, fermiontriangles generate nTGCs of O(10−4) [1]. Many mod-els of physics beyond the Standard Model predict valuesof nTGCs at the level of 10−4 to 10−3 [2]. The signa-ture of non-zero nTGCs is an increase of the ZZ crosssection at high ZZ invariant mass and high transversemomentum of the Z bosons [3]. ZZ production has beenstudied in e+e− collisions at LEP [4, 5] and in pp col-lisions at the Tevatron [6, 7]. No deviation of the mea-sured cross section from the Standard Model expectationhas been observed, and limits on anomalous nTGCs havebeen set [5, 6].

This letter presents the first measurement of ZZ [8]production in proton-proton collisions at a centre-of-massenergy

√s of 7 TeV, and limits on the anomalous nTGCs.

The cross section for on-shell ZZ production (i.e. inthe zero-width approximation) is predicted at next-to-leading order (NLO) in QCD to be 6.5+0.3−0.2 pb [9]; thisincludes a ∼6% contribution from gluon fusion. Candi-date ZZ events are reconstructed in the ZZ → �+�−�+�−decay channel, where � can be an electron or muon. Al-though this channel constitutes only ∼0.5% of the totalZZ cross section, its final state with four high transverse-momentum, isolated leptons has a very high expectedsignal to background ratio of ∼30.

To reduce systematic uncertainties, the cross section ismeasured within a phase-space that corresponds closelyto the experimental acceptance; this is termed the ‘fidu-cial’ cross section. The fiducial phase-space definition

requires the invariant mass of both lepton pairs to be be-tween 66 GeV and 116 GeV and all four leptons to bewithin the pseudorapidity [10] range |η| < 2.5 and havetransverse momentum pT > 15 GeV. The four-momentaof all photons present after the simulation of the partonshower which are within ∆R ≡

�∆φ2 +∆η2 < 0.1 of a

lepton are summed into the four momentum of that lep-ton. The total ZZ cross section in the on-shell approx-imation is obtained from the fiducial cross section usingthe known Z → �+�− branching ratio and a correctionfactor for the kinematic and geometrical acceptance.

Anomalous nTGCs for on-shell ZZ production can beparameterized by two CP-violating (fV4 ) and two CP-conserving (fV5 ) complex parameters (V = Z, γ) whichare zero in the Standard Model [3]. To ensure partial-wave unitarity, a form-factor parameterization is intro-duced to cause the couplings to vanish at high partoncentre-of-mass energy

√ŝ: fVi = f

Vi0/(1+ŝ/Λ

2)n. Here, Λis the energy scale at which physics beyond the StandardModel will be directly observable, fVi0 are the low-energyapproximations of the couplings, and n is the form-factorpower. Following Ref. [3], n = 3 and Λ = 2 TeV arechosen, so that expected limits are within the values pro-vided by unitarity at LHC energies. The results withenergy cutoff Λ = ∞ are also presented as a comparisonin the unitarity violation scheme.

The ATLAS detector [11] consists of inner tracking de-vices surrounded by a superconducting solenoid, electro-magnetic and hadronic calorimeters and a muon spec-trometer with a toroidal magnetic field. The inner detec-tor, in combination with the 2T field from the solenoid,provides precision tracking of charged particles for |η| <2.5. It consists of a silicon pixel detector, a silicon stripdetector and a straw tube tracker that also provides tran-sition radiation measurements for electron identification.The calorimeter system covers the pseudorapidity range|η| < 4.9. It is composed of sampling calorimeters witheither liquid argon (LAr) or scintillating tiles as the activemedia. In the region |η| < 2.5 the electromagnetic LAr

arX

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ov 2

011

σWW = 41+20−16(stat.)± 5(syst.)± 1(lumi.) pb

PDFジェット生成Wの電荷非対称度‣ uとdの違いZ+b‣ bに対する感度

15

0

0.2

0.4

0.6

0.8

1

-410 -310 -210 -110 1

0

0.2

0.4

0.6

0.8

1

ZEUS-JETS PDF

)=0.1180Z(Ms!

uncorr. uncert.

total exp. uncert.

2 = 10 GeV2

Q

vxu

vxd

0.05)"xS (

0.05)"xg (

0

0.2

0.4

0.6

0.8

1

-410 -310 -210 -110 1

0

0.2

0.4

0.6

0.8

1

ZEUS-S PDF

0

0.2

0.4

0.6

0.8

1

-410 -310 -210 -110 1

0

0.2

0.4

0.6

0.8

1

MRST2001

0

0.2

0.4

0.6

0.8

1

-410 -310 -210 -110 1

0

0.2

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0.6

0.8

1

CTEQ6.1M

0

0.2

0.4

0.6

0.8

1

ZEUS

x

xf

図 6: Q2 = 10 GeV2 における PDF分布をビヨルケン xの関数として示す。xuv は価 uクォーク PDF、xdv は価dクォーク PDF、xgはグルーオン PDF、xSは海クォーク PDFである。同一図に収めるため、グルーオンと海クォークは 1/20にして表示してある。

• PDFの包括的な理解

– グルーオン分布と重いクォークの生成断面積– 高い x領域– フレーバー分解

• 前方ジェット生成、多ジェット終状態

以下の章では各々の課題についてその物理的意義や現状・最新結果などを述べる。

6.2 高いQ2での新相互作用の探索と陽子・縦偏極電子衝突による電弱相互作用の検証

高い Q2 では超短距離で電子とクォークが相互作用することになり、標準模型を越える物理が観測される可能性がある。また、観測されない場合でも、高い Q2 において摂動論的 QCD 、特に DGLAP 発展を詳細に検証することが非常に大切である。というのも、HERAで測定されたパートン分布関数を LHCで到達する超高 Q2 領域までDGLAP方程式で外挿する正当性を精密に検証する必要があるからである。図 7に、HERAおよび従来の固定標的型DIS実験、そして TEVATRONと LHCの運動学領域を (x,Q2)平面で示した。LHCの主な運動学的領域は、xでは 10−4 ! x ! 10−1 と HERAとほぼ同じ

x

Q2 /

GeV

2

Atlas and CMS

Atlas and CMS rapidity plateau

D0 Central+Fwd. Jets

CDF/D0 Central Jets

H1

ZEUS

NMC

BCDMS

E665

SLAC

10-1

1

10

102

103

104

105

106

107

108

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

図 7: HERAおよび固定標的型DIS実験とTEVATRON、LHCの運動学的領域。横軸はビヨルケン x、縦軸は Q2である。LHC運動学的領域は、質量M の粒子がラピディティy に生成される際の素過程パートンの運動学領域として示してある。

であり、Q2では 104 ! Q2 ! 108 GeV2とHERAの最大Q2 領域と一部重なっている。HERA-Iでの DIS断面積測定では Q2 " 103 GeV2 でまだ統計誤差が系統誤差を上回っており (散乱断面積はプロパゲーター 1/Q4で落ちる)、LHC実験開始までに HERA-IIの高統計で最大 Q2まで詳細に検証しておくことが肝要である。

HERA-IIでは世界で初めて陽子と縦偏極電子の高エネルギー衝突が実現した。高い Q2 では電磁相互作用だけでなく電子と陽子の間にZ、W ボソンを交換する弱い相互作用の効果も入る。したがって、縦偏極電子ビームを用いることにより電弱相互作用の左右非対称性を直接に検証することが出来る。荷電流 DIS反応 ep → νX はニュートリノ散乱の逆反

応であり、W ボソンを交換する純粋な弱い相互作用である。標準模型では弱い相互作用は V −A型、パリティは最大に破れているので右巻き荷電流の寄与はゼロとなり、散乱断面積は電子の縦偏極度の一次関数として

σP (e±p → νX) = (1 ± P )σ0 (2)

と書ける。P は縦偏極度、σP は縦偏極度 P の時の荷電流 DIS断面積、 σ0 は無偏極の時の荷電流 DIS断面積である。荷電流DIS散乱の電子の縦偏極度依存性をみる解析は

HERA-IIの「目玉」であり運転開始以来、重点的に行わ

6

b

b

Z

g

(a)

b

b

Z

g

(b)

q

q

b

b

Z

(c)

q Z

b

bq

(d)

Figure 1: Main diagrams for associated production of a Z boson and one ormore b-jets.

of secondary decay vertices. The electromagnetic calorime-ter uses lead absorbers and liquid argon as the active materialand covers the rapidity range |η| < 3.2, with high longitudi-nal and transverse granularity for electromagnetic shower re-construction. For electron detection the transition region be-tween the barrel and end-cap calorimeters, 1.37 < |η| < 1.52,is not considered in this analysis. The hadronic tile calorime-ter is a steel/scintillating-tile detector that extends the instru-mented depth of the calorimeter to fully contain hadronic par-ticle showers. In the forward regions it is complemented bytwo end-cap calorimeters using liquid argon as the active ma-terial and copper or tungsten as the absorber material. Themuon spectrometer comprises three large air-core supercon-ducting toroidal magnets which provide a typical field integralof 3 Tm. Three stations of chambers provide precise trackinginformation in the range |η| < 2.7, and triggers for high mo-mentum muons in the range |η| < 2.4. The transverse energyET is defined to be Esinθ, where E is the energy associatedwith a calorimeter cell or energy cluster. Similarly, pT is themomentum component transverse to the beam line.

3. Collision data and simulated samples

3.1. Collision data

The analysis presented here is performed on data from ppcollisions at a centre-of-mass energy of 7 TeV recorded by AT-LAS in 2010 in stable beams periods and uses data selectedfor good detector performance. The events were selected on-line by requiring at least one electron or muon with high trans-verse momentum, pT. The trigger thresholds evolved withtime to keep up with the increasing instantaneous luminositydelivered by the LHC. The highest thresholds applied in thelast data taking period were ET > 15 GeV for electrons andpT > 13 GeV for muons. The integrated luminosity after beam,detector and data-quality requirements is 36.2 pb−1(35.5 pb−1)for events collected with the electron (muon) trigger, measuredwith a ±3.4% relative error [8, 9].

3.2. Simulated events

The measurements will be compared to theoretical predic-tions of the StandardModel, using fully simulatedMonte-Carlosamples of signal and backgrounds.Samples of signal events containing a Z boson decaying into

electrons or muons and at least one b-jet have been simulatedusing the ALPGEN, SHERPA, and MCFM generators, usingthe CTEQ6.6 PDF set [10]. The ALPGEN generator is in-terfaced to HERWIG [11] for parton shower and fragmenta-tion, and JIMMY for the underlying event simulation [12]. Forjets originating from the hadronisation of light quarks or glu-ons (hereafter referred to as light-jets), the LO generator ALP-GEN uses MLM matching [13] to remove any double countingof identical jets produced via the matrix element and partonshower, but this is not available for b-jets in the present version.Therefore events containing two b-quarks with ∆R < 0.4 (∆R >0.4) coming from the matrix element (parton shower) contribu-tion are removed. SHERPA uses the CKKW [14] matching forthe same purpose. The MCFM NLO generator lacks an inter-face to a parton shower and fragmentation package, hence tocompare with the data we apply correction factors describingthe parton-to-particle correspondence, obtained from particle-level LO simulations. For all Monte-Carlo events, the cross-section is normalised by rescaling the inclusive Z cross-sectionof the relevant generator to the NNLO cross-section [15].The dominant background comes from Z + jets events, with

the Z decaying into electrons, muons or tau leptons, where onejet is a light or c-jet which has been incorrectly tagged as a b-jet. These events are simulated using the same generators asthe signal. Other backgrounds considered include tt̄ pair pro-duction simulated by MC@NLO [16, 17],W(→ lν) + jets sim-ulated by PYTHIA [18], WW/WZ/ZZ simulated by ALPGEN,and single-top production simulated by MC@NLO. The cross-sections for these processes (except single-top) have been nor-malised to the most recent predictions of [19, 20] (approximateNNLO), [15] (NNLO), [16, 17] (NLO), and [3] (NLO) respec-tively. In addition, a PYTHIA multi-jet sample is used in thecalculation of the multi-jet background in the muon channel.Events have been generated with the number of collision ver-

tices drawn from a Poisson distribution with an average of 2.0vertices per event. Simulated events are then reweighted tomatch the observed vertex distribution in the data.

4. Reconstruction and selection of Z + b candidates

Events are required to contain one primary vertex with atleast three high-quality charged tracks. As the final state shouldcontain a Z boson, the selection of events closely follows theselection criteria used by ATLAS for the inclusive Z analysis[21]. In the e+e− channel, two opposite sign electron candi-dates are required with ET > 20 GeV and |η| < 2.47. Electroncandidates are reconstructed from a cluster of cells in the elec-tromagnetic calorimeter and a charged particle track in the innerdetector. Criteria are applied on the longitudinal and transverseshower shapes in the calorimeters and on the matching of thetrack with the cell cluster, requesting a Medium [21] electron

2

Experiment (7.6+1.8−1.6(stat)+1.5−1.2(syst)) × 10

−3

MCFM (8.8 ± 1.1) × 10−3

ALPGEN (6.2 ± 0.1 (stat only)) × 10−3SHERPA (9.3 ± 0.1 (stat only)) × 10−3

Table 5: Experimental measurement and predictions of the average number ofb-jets produced in association with a Z boson, with the same fiducial region asdefined in the text for σb.

boson (for the same fiducial restrictions on the Z decay), i.e. theaverage number of b-jets per Z event. To obtain the inclusiveZ sample, the analysis is repeated with the same selection asabove, except the jet requirements. The cross-section obtainedfor the inclusive Z production with the same fiducial region forthe leptons is 465 ± 3 pb (statistical error only), in agreementwith the ATLAS measurement [30]. The systematic uncertain-ties on the ratio are propagated coherently in the Z + b and Zselections. The uncertainties related to leptons cancel to a neg-ligible level, and those related to luminosity cancel completely.However as the main systematic uncertainties concern only theZ + b analysis (b-tagging, model dependence, jet energy scale),the overall systematic uncertainty is only marginally reduced.The MCFM prediction of this ratio is calculated with the

same method and assumptions as above. To estimate the sys-tematic uncertainty, the scale and PDF choices are varied co-herently between the Z + b and inclusive Z samples for eachsub-process simulated. Table 5 shows the experimentally mea-sured result for the average number of b-jets per Z event andcomparisons to the theoretical predictions. The MCFM NLOprediction is in agreement with the data. The ALPGEN andSHERPA predictions differ significantly, but are both compati-ble with the data within the experimental uncertainties.

7. Conclusions

A first measurement is made of the cross-section for the pro-duction of b-jets in association with a Z boson in proton-protoncollisions at

√s = 7 TeV, using 36 pb−1 of data collected in

2010 by the ATLAS experiment. In addition, the average num-ber of b-jets per Z event is extracted. Both measurements arecurrently statistics limited. The predictions from NLO pQCDcalculations agree well with both results. Leading order gen-erators are able to reproduce the measured average number ofb-jets per Z event within the uncertainties of the measurement,although their predictions differ significantly from each other.

Acknowledgements

We thank CERN for the very successful operation of theLHC, as well as the support staff from our institutions withoutwhom ATLAS could not be operated efficiently.

We acknowledge the support of ANPCyT, Argentina; Yer-PhI, Armenia; ARC, Australia; BMWF, Austria; ANAS, Azer-baijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC,NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOSTand NSFC, China; COLCIENCIAS, Colombia; MSMT CR,MPO CR and VSC CR, Czech Republic; DNRF, DNSRCand Lundbeck Foundation, Denmark; ARTEMIS, EuropeanUnion; IN2P3-CNRS, CEA-DSM/IRFU, France; GNAS, Geor-gia; BMBF, DFG, HGF, MPG and AvH Foundation, Germany;GSRT, Greece; ISF, MINERVA, GIF, DIP and Benoziyo Cen-ter, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Mo-rocco; FOM and NWO, Netherlands; RCN, Norway; MNiSW,Poland; GRICES and FCT, Portugal; MERYS (MECTS), Ro-mania; MES of Russia and ROSATOM, Russian Federation;JINR; MSTD, Serbia; MSSR, Slovakia; ARRS and MVZT,Slovenia; DST/NRF, South Africa; MICINN, Spain; SRC andWallenberg Foundation, Sweden; SER, SNSF and Cantons ofBern and Geneva, Switzerland; NSC, Taiwan; TAEK, Turkey;STFC, the Royal Society and Leverhulme Trust, United King-dom; DOE and NSF, United States of America.The crucial computing support from all WLCG partners is

acknowledged gratefully, in particular from CERN and theATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Den-mark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA(Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC(Spain), ASGC (Taiwan), RAL (UK) and BNL (USA) and inthe Tier-2 facilities worldwide.

References

[1] M. Mangano, et al., ALPGEN, a generator for hard multiparton processesin hadronic collisions, JHEP 07 (2003) 001. ALPGEN version 2.13 isused.

[2] T. Gleisberg, et al., Event generation with SHERPA 1.1, JHEP 02 (2009)007. SHERPA version 1.1.3 is used.

[3] J. M. Campbell, R. Ellis, MCFM for the Tevatron and the LHC,Nucl.Phys.Proc.Suppl. 205-206 (2010) 10–15. MCFM version 5.8 isused.

[4] CDF Collaboration, Measurement of cross sections for b jet productionin events with a Z boson in p− anti-p collisions at

√s=1.96 TeV, Phys.

Rev. D79 (2009) 052008.[5] D0 Collaboration, A measurement of the ratio of inclusive cross sectionsσ(pp̄ → Z + b jet)/σ(pp̄ → Z + jet) at

√s=1.96 TeV, Phys. Rev. D83

(2011) 031105.[6] ATLAS Collaboration, Measurement of the cross section for the produc-

tion of a W boson in association with b-jets in pp collisions at√s=7 TeV

with the ATLAS detector, submitted to Phys. Lett. B (2011).[7] ATLAS Collaboration, The ATLAS Experiment at the CERN Large

Hadron Collider, JINST 3 (2008) S08003.[8] ATLAS Collaboration, Luminosity Determination in pp Collisions at√

s=7 TeV Using the ATLAS Detector at the LHC, Eur.Phys.J. C71(2011) 1630.

[9] ATLAS Collaboration, Updated luminosity determination in pp colli-sions at

√s=7 TeV using the ATLAS detector, ATLAS-CONF-2011-011

(2011). http://cdsweb.cern.ch/record/1334563.[10] P. M. Nadolsky, et al., Implications of CTEQ global analysis for collider

observables, Phys. Rev. D78 (2008) 013004.[11] G. Corcella, et al., HERWIG 6.5: an event generator for Hadron Emission

Reactions With Interfering Gluons (including supersymmetric processes),JHEP 01 (2001) 010.

[12] J. M. Butterworth, J. R. Forshaw, M. Seymour, Multiparton interactionsin photoproduction at HERA, Z. Phys. C72 (1996) 637–646. HERWIGversion 6.510 is used.

7

標準模型まとめ

16

W Z WW Wt

[pb]

tota

l

1

10

210

310

410

510

-120 fb

-113 fb

-15.8 fb

-15.8 fb

-14.6 fb

-12.1 fb-14.6 fb

-14.6 fb-11.0 fb

-11.0 fb

-135 pb

-135 pb

tt t WZ ZZ

= 7 TeVsLHC pp Theory

)-1Data (L = 0.035 - 4.6 fb

= 8 TeVsLHC pp Theory

)-1Data (L = 5.8 - 20 fb

ATLAS PreliminaryATLAS PreliminaryATLAS Preliminary

測定精度（探索感度）を決めるもの

何が今の結果をリミットしているのか？‣ 統計 or 系統誤差๏ 系統誤差はMCなどの統計誤差を含む

17

ee µµ eµ CombinedUncertainty Source ∆σ/σ[%] ∆σ/σ[%] ∆σ/σ[%] ∆σ/σ[%]Data statistics -8.3 / 8.7 -5.8 / 6.1 -4.2 / 4.4 -3.2 / 3.3

Luminosity -3.8 / 4.5 -3.7 / 4.1 -4.3 / 4.7 -4.1 / 4.5

MC statistics -3.8 / 4.5 -2.6 / 2.9 -2.1 / 2.2 -1.5 / 1.6

Lepton energy scale -0.7 / 0.0 -0.5 / 0.0 -0.3 / 0.3 -0.3 / 0.3

Lepton energy resolution 0.0 / 0.4 -0.6 / 0.0 0.0 / 0.0 0.0 / 0.3

Lepton ident. scale factor -5.5 / 6.3 -2.3 / 2.4 -3.1 / 3.4 -2.4 / 2.6

Jet energy scale -9.7 / 4.8 -4.9 / 5.5 -4.9 / 5.1 -4.7 / 5.3

Jet energy resolution -1.9 / 2.0 -1.4 / 1.3 -1.4 / 1.4 -1.4 / 1.5

Jet reconstr. efficiency 0.0 / 0.0 -0.6 / 0.0 -0.3 / 0.3 -0.3 / 0.3

Drell-Yan prediction -0.6 / 0.6 -0.6 / 0.0 0.0 / 0.0 0.0 / 0.0

Fake leptons -1.9 / 1.8 -0.6 / 0.0 -1.9 / 1.8 -1.1 / 1.2

MC generator -5.7 / 7.0 -1.3 / 1.3 -2.7 / 2.9 -0.7 / 0.7

Parton shower -0.6 / 0.0 0.0 / 0.0 0.0 / 4.0 0.0 / 0.3

b-tag efficiency -3.2 / 4.5 -3.0 / 4.1 -3.5 / 4.7 -3.4 / 4.5Light quark tag eff. 0.0 / 0.0 -0.6 / 0.0 -0.5 / 0.0 -0.3 / 0.3

ISR -4.8 / 5.8 -1.5 / 1.5 -0.3 / 0.4 -0.4 / 0.4

FSR -8.7 / 11.2 -2.8 / 3.1 -0.9 / 0.8 -2.0 / 2.1

PDF -2.7 / 3.2 -2.3 / 2.5 -2.4 / 2.6 -2.5 / 2.7

EmissT

reconstruction -0.9 / 0.0 -1.0 / 0.0 0.0 / 0.0 -0.0 / 0.0

Pile-up -0.8 / 0.0 -0.3 / 0.0 0.0 / 0.0 -0.0 / 0.0

Detector modeling -0.7 / 1.4 -0.8 / 2.2 -1.1 / 1.6 -1.9 / 1.8

Theoretical cross-sections -0.4 / 0.4 -1.1 / 0.6 -0.7 / 0.7 -0.7 / 0.7

All systematics -16 / 20 -7.9 / 9.9 -8.2 / 11 -8.1 / 9.7

Stat. + Syst. -19/ 22 -10 / 12 -10 / 13 -9.0 / 11

Table 3: Overview of the tt̄ cross-section uncertainties for each channel, and for the combination, ob-tained from the likelihood minimization in the b-tag analysis.

8

例

ミューオンの運動量測定の分解能Jet Energy Scale の不定性

18

!"#$%!#&'$("&%)'*#+"(,#$

-../0102 345!"#$%&'()*

2/

Total

Energy

loss

Tube

Resol

Alignment

Multiple Scattering

!"#$%&'%())*+,-').)/01&)+%*',(2#%(3)45'6#$%)-2"+'7

! +,-./0123-456/789(:678+';)'*#+"(,#$8

Pcorr 8)94Prec,MC : ;E;!FG

! H(9(%:;2.%12NOE"F'%?'*#+"(,#$%

G+,D$&'$(%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

?'*#+"(,#$%@%;%2.B

Systematicshift

Smearing

effect

Page 8 of 59 Eur. Phys. J. C (2011) 71: 1512

Fig. 4 Fractional jet energyscale systematic uncertainty as afunction of pT for jets in thepseudorapidity region0.3 < |η| < 0.8 in the barrelcalorimeter. The total systematicuncertainty is shown as well asthe individual sources, withstatistical errors if applicable

Fig. 5 Fractional jet energyscale systematic uncertainty as afunction of pT for jets in thepseudorapidity region2.1 < |η| < 2.8. The JESuncertainty for the end-cap isextrapolated from the barreluncertainty using dijet balance,with the contributions from thedeviation from unity in the data(η relative intercalibration) andthe deviation between data andsimulation (η intercalibrationData/MC) shown separately.The other individual sources arealso shown, with statisticalerrors if applicable

9 Event selection

The jet algorithm is run on energy clusters assuming thatthe event vertex is at the origin. The jet momenta are thencorrected for the beamspot position. After calibration, allevents are required to have at least one jet within the kine-matic region pT > 60 GeV, |y| < 2.8. Additional quality cri-teria are also applied to ensure that jets are not produced bynoisy calorimeter cells or poorly-calibrated detector regions.Events are required to have at least one vertex with at leastfive reconstructed tracks connected, within 10 cm in z of thebeamspot. Simulated events are reweighted so that the z ver-tex distribution agrees with the data. Of the events passingthe kinematic selection, 2.6% have more than one vertex.The overall efficiency of these selection cuts, evaluated insimulation using triggered events with truth jets in the kine-matic region of the measurement, is above 99%, and has a

small dependence on the kinematic variables. Backgroundcontributions from non-pp-collision sources were evaluatedusing unpaired and empty bunches and found to be negligi-ble.

After this selection, 56 535 (77 716) events remain, forR = 0.4 (0.6), with at least one jet passing the inclusive jetselection. Of these, 45 621 (65 739) events also pass the dijetselection.

10 Data correction

The correction for trigger and detector efficiencies and res-olutions, other than the energy scale correction already ap-plied, is performed in a single step using a bin-by-bin un-folding method evaluated using the MC samples. For eachmeasured distribution, the corresponding MC cross section

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