W/Z inclusive measurements in ATLAS - Standard Model @ LHC ... · W/Zcross-section:In˝ lepton W!...

20
W/Z inclusive measurements in ATLAS J-B. Blanchard On behalf of the Atlas collaboration Standard Model @ LHC 2012 - 12/04/2012

Transcript of W/Z inclusive measurements in ATLAS - Standard Model @ LHC ... · W/Zcross-section:In˝ lepton W!...

Page 1: W/Z inclusive measurements in ATLAS - Standard Model @ LHC ... · W/Zcross-section:In˝ lepton W! ˝ andZ! ˝˝ crosssections W! ˝ using2010data(˘35pb 1) Z! ˝˝ using1.32-1.55fb

W/Z inclusive measurements in ATLAS

J-B. Blanchard

On behalf of the Atlas collaboration

Standard Model @ LHC 2012 - 12/04/2012

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Introduction

W/Z physics at the LHC

LHC: a W/Z factory...I Theoretically well understood bosons, produced at high ratesI Unique signature in the lepton decay

... in a QCD environmentI Cross sections factorise at scale µ on PDF:

σpp =∑(a,b)

∫dxa dxb fa(xa, µ) fb(xb, µ) × σab (s)

I Explore phase space uncovered so far:

Q2 = M2W/Z and x1/2 = e±y MW/Z√

sMotivations

I Test pQCD predictions up to NNLOI Test phenomenological models: ME+PS, soft

gluon resummations. . .I Provide precision measurements: lepton

universality, polarisation, mW . . .

x

Q2 /

GeV

2

Atlas and CMS (7 TeV)

Atlas and CMS rapidity plateau

D0 Central+Fwd. Jets

CDF/D0 Central Jets

H1

ZEUS

NMC

BCDMS

E665

SLAC

10-1

1

10

10 2

10 3

10 4

10 5

10 6

10 7

10 8

10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 1

W/Z@LHC

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W/Z cross-section : In τ lepton

Outline

Introduction

W/Z cross-sectionIn τ leptonIn light flavour leptonsDifferential measurement in e/µ

Analysis of these cross-sections

Polarisation measurements

Conclusion

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W/Z cross-section : In τ lepton

W → τν and Z → ττ cross sections

W → τν using 2010 data (∼ 35 pb−1 )Z → ττ using 1.32 - 1.55 fb−1 in three channels:

I µ + hadrons + 3ν (τµτh)I e + hadrons + 3ν (τeτh)I e + µ + 4ν (τeτµ)

=⇒∼ 10% systematic uncertainties) [GeV]

hτ, µ(vism

0 20 40 60 80 100 120 140

Events

/2.5

GeV

0

100

200

300

400

500

600 Data 2011τ τ →*/Z γ

Multijetν µ →W ν τ →W

µ µ →*/Z γtt

Diboson

= 7 TeVs, ­1

Ldt = 1.55 fb∫ATLAS Preliminary

Validation of τ reconstruction performances critical for searches

Measurement in agreement with other leptonic decay channels

) [nb]lν l →(W σ

6 7 8 9 10 11 12 13 14 15 16

τν τ →W ATLAS

eν e →W ATLAS

µν µ →W ATLAS

= 7 TeV)sData 2010 (

Stat uncertainty

Stat ⊕Sys

Lumi⊕ Stat ⊕Sys

Prediction (NNLO)

Theory uncertainty

= 7 TeV)sData 2010 (

Stat uncertainty

Stat ⊕Sys

Lumi⊕ Stat ⊕Sys

Prediction (NNLO)

Theory uncertainty

ATLAS

) [nb]lν l →(W σ

6 7 8 9 10 11 12 13 14 15 16

τν τ →W ATLAS

eν e →W ATLAS

µν µ →W ATLAS

<116 [GeV]) [nb]inv

, 66<mττ →(Z σ0.7 0.8 0.9 1 1.1 1.2

­11.55fb

hτ µτ →Z

­11.34fb

hτ eτ →Z

­11.55fb

µτ eτ →Z

­133­36pb

combinedµµ ee/→Z

­11.34­1.55fb

combinedττ →Z

Stat

Stat ⊕Syst

Lumi⊕ Stat ⊕Syst

Theory (NNLO)

Stat

Stat ⊕Syst

Lumi⊕ Stat ⊕Syst

Theory (NNLO)

ATLAS

Preliminary

­11.55fb

hτ µτ →Z

­11.34fb

hτ eτ →Z

­11.55fb

µτ eτ →Z

­133­36pb

combinedµµ ee/→Z

­11.34­1.55fb

combinedττ →Z

12/04/2012 Standard Model @ LHC 2012 - J-B. Blanchard 4 / 18

ReferencesPhys. Lett. B706 (276-294), ATLAS-CONF-2012-006

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W/Z cross-section : In light flavour leptons

Lepton universality

W → `ν and Z0 → `+`− for ` = e, µI Inclusive measurements done with 2010 data (∼ 35 pb−1 )

=⇒ experimental accuracy of few %.I Ratio of e and µ cross sections in common fiducial region

=⇒ RW=1.006±0.024, to compare with world average 1.017±0.019=⇒ RZ=1.018±0.031, when world average is 0.9991±0.0024 (LEP)

Precise measurements guarantee lepton flavours combination

)­µ+µ → BR(Z⋅ Z

σ) / ­e+

e→ BR(Z⋅ Z

σ = ZR

0.8 0.9 1 1.1

)νµ

→± B

R(W

⋅ ±W

σ)

/ ν

e→±

BR

(W⋅ ±

=

WR

0.9

1

1.1

= 7 TeV)sData 2010 (

PDG world averageWR

PDG world averageZR

Standard Model

­1 L dt = 33­36 pb∫

68.3% CL ellipse area

ATLAS

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ReferencearXiv:1109.5141 sub. PRD

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W/Z cross-section : In light flavour leptons

Flavour combined cross sections

Combination of lepton flavour

I Cross sections provided with correlations between channels (Z0 → `+`− ,W+ → `+ν , W− → `−ν )

I Ratios of fiducial cross sections avoid phase space extrapolation (largertheoretical uncertainty), and cancel luminosity terms

I Broad agreement with NNLO predictions, different PDF dependences⇒ σfid

W+/ σfidW− sensitive to up-down PDF differences

⇒ σfidW±/ σfid

Z rather PDF insensitive (provided sea is flavour symmetric)

­W

fidσ / +W

fidσ1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6

= 7 TeV)sData 2010 (

total uncertainty

exp. uncertainty

ABKM09JR09HERAPDF1.5MSTW08

­1 L dt = 33­36 pb∫

ATLAS

*γZ/fidσ / ±W

fidσ9 9.5 10 10.5 11

= 7 TeV)sData 2010 (

total uncertainty

exp. uncertainty

ABKM09JR09HERAPDF1.5MSTW08

­1 L dt = 33­36 pb∫

ATLAS

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ReferencearXiv:1109.5141 sub. PRD

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W/Z cross-section : Differential measurement in e/µ

W/Z transverse momentum

Test multiple models of QCD predictions

Low pT soft/collinear partons.⇒ Logarithmic resummations up to NNLL in resbos⇒ PS (pythia, herwig) iterative splitting and radiation of parton⇒ME+PS (mc@nlo, powheg), with ME O(αs)

High pT hard partons.⇒ fewz, dynnlo available to O(α2

s )⇒ME+PS (sherpa, alpgen). High order ME but tree-level production hardparton

[GeV]W

Tp

0 50 100 150 200 250 300

(Data

,Pre

dic

tion)

/ R

ES

BO

S

0.6

0.8

1

1.2

1.4

1.6

1.8

2

= 7 TeVs

ATLAS

­1 31 pb≈Ldt ∫

Combined Data 2010

Stat. Uncert.)

sαDYNNLO O(

)2sαDYNNLO O(

)s

αMCFM O(

)2sαMCFM O(

RESBOS

[GeV]W

Tp

0 50 100 150 200 250 300

(Data

,Pre

dic

tion)

/ R

ES

BO

S

0.6

0.8

1

1.2

1.4

1.6

1.8

2

= 7 TeVs

ATLAS

­1 31 pb≈Ldt ∫

Combined Data 2010

Stat. Uncert.

ALPGEN+HERWIG

MC@NLO

POWHEG+PYTHIA

PYTHIA

RESBOS

SHERPA

Overall pWT range

Agreement within 20 % ofI resbosI alpgenI pythiaI sherpa

12/04/2012 Standard Model @ LHC 2012 - J-B. Blanchard 7 / 18

ReferencesPhys. Rev. D85 (012005), Phys. Lett. B705 (415-434)

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W/Z cross-section : Differential measurement in e/µ

W/Z rapidity

I Boson rapidity linked to parton momentum fraction

x1/2 = e±y MW/Z√s

I In the W boson case, lepton pseudo-rapidity η` is used.I Comparison to NNLO models shows broad agreement⇒ shows PDF sensitivity (even tension with few sets)

|l

η|0 0.5 1 1.5 2 2.5

Theory

/Data

0.9

1

1.10 0.5 1 1.5 2 2.5

| [p

b]

lη/d

d

300

400

500

600

700

800

= 7 TeV)sData 2010 (

MSTW08

HERAPDF1.5

ABKM09

JR09

­1 L dt = 33­36 pb∫ lν+

l→+W

Uncorr. uncertainty

Total uncertainty

ATLAS

|l

η|0 0.5 1 1.5 2 2.5

Theory

/Data

0.9

1

1.10 0.5 1 1.5 2 2.5

| [p

b]

lη/d

d

100

200

300

400

500

600

= 7 TeV)sData 2010 (

MSTW08

HERAPDF1.5

ABKM09

JR09

­1 L dt = 33­36 pb∫ lν

­ l→

­W

Uncorr. uncertainty

Total uncertainty

ATLAS

|Z

|y0 0.5 1 1.5 2 2.5 3 3.5

Theory

/Data

0.91

1.10 0.5 1 1.5 2 2.5 3 3.5

| [p

b]

Z/d

|yσ

d

20

40

60

80

100

120

140

160

= 7 TeV)sData 2010 (

MSTW08

HERAPDF1.5

ABKM09

JR09

­1 L dt = 33­36 pb∫

­l

+ l→Z

Uncorr. uncertainty

Total uncertainty

ATLAS

12/04/2012 Standard Model @ LHC 2012 - J-B. Blanchard 8 / 18

ReferencearXiv:1109.5141 sub. PRD

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Analysis of these cross-sections : W charge asymmetry

Outline

Introduction

W/Z cross-section

Analysis of these cross-sectionsW charge asymmetryStrange quark density

Polarisation measurements

Conclusion

12/04/2012 Standard Model @ LHC 2012 - J-B. Blanchard 9 / 18

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Analysis of these cross-sections : W charge asymmetry

W charge asymmetry

Definiton

A(η`) =dσW+(η`)− dσW−(η`)

dσW+(η`) + dσW−(η`)

I Sensitive to valence quark (ud→ W+/du→ W−)I Usable to constrain uv / dv at low x

|l

η|

0 0.5 1 1.5 2 2.5

lA

0.1

0.15

0.2

0.25

0.3

0.35 = 7 TeV)sData 2010 (

MSTW08

HERAPDF1.5

ABKM09

JR09

­1 L dt = 33­36 pb∫

Stat. uncertainty

Total uncertainty

ATLAS

η

0 0.5 1 1.5 2 2.5 3 3.5 4

Le

pto

n c

ha

rge

asym

me

try

­0.3

­0.2

­0.1

0

0.1

0.2

0.3

­1) 35 pbν l→ATLAS (extrapolated data, W­1) 36 pbνµ →CMS (W­1) 36 pbνµ →LHCb (W

MSTW08 prediction (MC@NLO, 90% C.L.)

CTEQ66 prediction (MC@NLO, 90% C.L.)

HERA1.0 prediction (MC@NLO, 90% C.L.)

ATLAS+CMS+LHCb

Preliminary=7 TeVs

> 20 GeVl

Tp Combined results

I More constrained in central region(CMS+ATLAS)

I Extended up to η ∼3.7 (LHCb)

12/04/2012 Standard Model @ LHC 2012 - J-B. Blanchard 10 / 18

ReferencesATLAS-CONF-2011-129, arXiv:1109.5141 sub. PRD

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Analysis of these cross-sections : Strange quark density

Strange density: state of the art

x-310 -210 -110

)2 =

1.9

GeV

2)(

x, Q

sx(

s+

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2 = 1.9 GeV2 distribution at Qss+

NLO PDF (68% C.L.)MSTW08CT10NNPDF2.1ABKM09HERAPDF1.0

x-310 -210 -110

)2 =

1.9

GeV

2)(

x, Q

sx(

s+

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Little is known about strange densityI Flavour SU(3) suggests equal proportion

in sea (u, d and s)

I rs =12

(s(x) + s(x))

d(x)

I s suppression assumed in many PDFsbecause of s mass (rs ∼ 0.5)

MotivationsI Higher relevance than at Tevatron⇒central W+ cs 30%(pp) / 10%(pp)

I Better accuracy needed for precision measurement as mW (c and balready measured by HERA with 5% and 20% accuracy)

I Might be constrained by Z rapidity and W+charm

G. Watt

(NuTeV, CCFR)

12/04/2012 Standard Model @ LHC 2012 - J-B. Blanchard 11 / 18

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Analysis of these cross-sections : Strange quark density

Measurement principle

Perform NNLO fits onI HERA ep DIS data (sensitive to linear combination of q + q)⇒ cover 10−4 . x . 0.6 for 1 . Q2 . 104 GeV2

I ATLAS W+, W− and Z0 data (sensitive to bilinear combination of q + q)⇒ cover 0.001 . x . 0.1 for Q2 = M2

W/Z GeV2

Results extrapolated to low Q2 with pQCD (chosen scale Q20 = 1.9 GeV2)

2 fits procedure

Fixed s/d Free s/d

χ2/NDF All data 546.1/567 538.4/565ATLAS data 45.0/30 33.9/30

⇒ Free s/d fit determines value of rsrs = 1.00± 0.20exp ± 0.07mod

+0.10−0.15par

+0.06−0.07αs ± 0.08th

|Z

|y0 0.5 1 1.5 2 2.5 3 3.5

sfr

ee/fix

ed

0.981

1.020 0.5 1 1.5 2 2.5 3 3.5

| [p

b]

Z/d

|yσ

d

60

80

100

120

140

­1 L dt = 33­36 pb∫

­l

+ l→Z

= 7 TeV)sData 2010 (

stat. uncertainty)⊕(uncorr. sys.

sepWZ fixed

sepWZ free

ATLAS

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ReferencearXiv:1203.4051 sub. PRL

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Analysis of these cross-sections : Strange quark density

Results and interpretations

Results in two kinematical zonesI (Q2,x)=(1.9,0.023) and (M2

W/Z,0.013)I Uncertainties are smaller at Q2 = M2

W/Zgluon splitting into qq flavour independant=⇒ Same tension with predictions

sr­0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

ABKM09

NNPDF2.1

MSTW08CT10 (NLO)

total uncertainty

experimental uncertainty

ATLAS, x=0.0232 = 1.9 GeV2QsepWZ free

sr­0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

ABKM09

NNPDF2.1

MSTW08CT10 (NLO)

total uncertainty

experimental uncertainty

ATLAS, x=0.0132Z = M2Q

sepWZ free

x

­310 ­210 ­110

sx

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45 2 = 1.9 GeV

2Q

sepWZ fixed

s epWZ free

ATLAS

Effect of s increasing

I u, d decrease by 10%I total sea is enhanced by 8%I better agreement found in

ratio σfidW±/σfid

Z*γZ/

fidσ / ±W

fidσ9 9.5 10 10.5 11

ATLAS

­1 L dt = 33­36 pb∫

= 7 TeV)sData 2010 (

total uncertainty

exp. uncertainty

ABKM09

JR09

HERAPDF1.5MSTW08

sepWZ free

s

12/04/2012 Standard Model @ LHC 2012 - J-B. Blanchard 13 / 18

ReferencearXiv:1203.4051 sub. PRL

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Polarisation measurements

Outline

Introduction

W/Z cross-section

Analysis of these cross-sections

Polarisation measurementsW boson polarisationτ polarisation from W → τν

Conclusion

12/04/2012 Standard Model @ LHC 2012 - J-B. Blanchard 14 / 18

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Polarisation measurements : W boson polarisation

W boson polarisation

MotivationsI W in three states: fL, f0 and fR:⇒ LO: predominantly left-handed⇒ NLO: all states possibles.

I Compare to LO and NLO predictionsI Good understanding needed for

precision measurement

PrincipleI No pνz ⇒ use reduction of cosθ∗

cos θ2D = (−→p `∗T · −→p W

T )/(|−→p `∗T | |−→p W

T |)I 35 < pW

T < 50 and pWT > 50 GeV

I Template fits give access to f0 and fL − fR

)2Dθcos(

­1 ­0.5 0 0.5 1

Entr

ies/0

.1

0

50

100

150

200

250

300

350

400

­1 L dt = 37 pb∫ATLAS

ν+ e→+

W

> 50 GeVW

Tp

=7 TeV)sData (Fit result

Left

Longitudinal

Right

)2Dθcos(

­1 ­0.5 0 0.5 1

Entr

ies/0

.1

0

50

100

150

200

250

­1 L dt = 37 pb∫ATLAS

ν­ e→­

W

> 50 GeVW

Tp

=7 TeV)sData (Fit result

Left

Longitudinal

Right

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ReferencearXiv:1203.2165 sub. EPJC

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Polarisation measurements : W boson polarisation

W boson polarisation

Measurement and resultsI Measurement done with 2 Monte-Carlo

generators: mc@nlo, powheg⇒ get uncertainty for unfolding procedure

I High sensitivity to energy scale (lepton, /ET)I Scale uncertainty on fL − fR drastically

reduced when averaged over chargeI Agreement with predictions within

uncertainties (fL − fR∼ 25%)

|W

|y0 0.5 1 1.5 2 2.5 3

[%

]0

f

10

15

20

25

30

35

40 ν l → +

W

MC@NLO

POWHEG

Blackhat

ATLASSimulation

<50 GeVW

T35<p

|W

|y0 0.5 1 1.5 2 2.5 3

[%

]0

f

10

15

20

25

30

35

40 ν l → +

W

MC@NLO

POWHEG

Blackhat

ATLASSimulation

<70 GeVW

T50<p

|W

|y0 0.5 1 1.5 2 2.5 3

[%

]0

f

10

15

20

25

30

35

40 ν l → ­

W

MC@NLO

POWHEG

Blackhat

ATLASSimulation

<50 GeVW

T35<p

|W

|y0 0.5 1 1.5 2 2.5 3

[%

]0

f

10

15

20

25

30

35

40 ν l → ­

W

MC@NLO

POWHEG

Blackhat

ATLASSimulation

<70 GeVW

T50<p

R ­ fLf

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0f

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

< 50 GeVW

T35 < p

> 25 GeV,ν

Tp

> 20 GeV, l

T| > 2.4, plη|

< 110 GeV,WT

50 < m

= 7 TeVsData

uncertaintyσ1

MC@NLO

POWHEG

Unphysical area

ATLAS

R ­ fLf

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0f

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

> 50 GeVW

Tp

> 25 GeV,ν

Tp

> 20 GeV, l

T| > 2.4, plη|

< 110 GeV,WT

50 < m

= 7 TeVsData

uncertaintyσ1

MC@NLO

POWHEG

Unphysical area

ATLAS

FutureI Would like to have

access to the 9polarisation matrixelements in MC

12/04/2012 Standard Model @ LHC 2012 - J-B. Blanchard 16 / 18

ReferencearXiv:1203.2165 sub. EPJC

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Polarisation measurements : τ polarisation from W → τν

τ polarisation from W → τν decay

τ polarisation Pτ=(σR − σL)/(σR + σL) can be measured at LHCW→ τhν Z→ ττ H→ ττ H− → τν

Expected Pτ -1 ∼ 0.15 0 +1

First τ polarisation measurement at LHCI Use charged asymmetry variable in one prong decay

Υ = (Eπ−

T − Eπ0

T )/|−→p π−T +−→p π0

T |I Produce left- and right-handed templatesI Fit 24 pb−1 with these templates⇒ Pτ = −1.06± 0.04stat+0.05

−0.07syst

ϒ

­1 ­0.5 0 0.5 1 1.5 2 2.5 3

Entr

ies/0

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80

100

Data 2010 ν

Lτ →W

Multijets

EW

ATLAS Preliminary

= 7 TeVs

­1 L dt = 24 pb∫

ϒ

­1 ­0.5 0 0.5 1 1.5 2 2.5 3

Entr

ies/0

.1

0

20

40

60

80

100

120

140

Data 2010 ν

Rτ →W

Multijets

EW

ATLAS Preliminary

= 7 TeVs

­1 L dt = 24 pb∫

Ù Results in agreement with SM predictions

ϒ

­1 ­0.5 0 0.5 1 1.5 2 2.5 3

Entr

ies/0

.1

0

20

40

60

80

100

Data 2010

Fit

Left­handed

Right­handed

ATLAS Preliminary

= 7 TeVs

­1 L dt = 24 pb∫

τ L

τR

12/04/2012 Standard Model @ LHC 2012 - J-B. Blanchard 17 / 18

ReferenceATLAS-CONF-2012-009

Page 18: W/Z inclusive measurements in ATLAS - Standard Model @ LHC ... · W/Zcross-section:In˝ lepton W! ˝ andZ! ˝˝ crosssections W! ˝ using2010data(˘35pb 1) Z! ˝˝ using1.32-1.55fb

Conclusion

Conclusion

W/Z cross sectionI Inclusive measurement done with every lepton channelI Differential measurement as function of pT , η or y⇒ very accurate measurement in e/µ (RW comparable to world average)

I Can already be used to constrain PDFs models⇒W charge asymmetry for u/d⇒ strange quark density (underestimated in most PDF sets)

Particles propertiesI τ polarisation from W → τν decayI W boson polarisation

To be pursuedI Exploit much larger dataset available to explore more differential

distributionsI Increase the menu of measurements

12/04/2012 Standard Model @ LHC 2012 - J-B. Blanchard 18 / 18

Page 19: W/Z inclusive measurements in ATLAS - Standard Model @ LHC ... · W/Zcross-section:In˝ lepton W! ˝ andZ! ˝˝ crosssections W! ˝ using2010data(˘35pb 1) Z! ˝˝ using1.32-1.55fb

Back-up

Page 20: W/Z inclusive measurements in ATLAS - Standard Model @ LHC ... · W/Zcross-section:In˝ lepton W! ˝ andZ! ˝˝ crosssections W! ˝ using2010data(˘35pb 1) Z! ˝˝ using1.32-1.55fb

Back-up

Effect of rs on PDFs

x

­310 ­210 ­110

vxu

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.82

= 1.9 GeV2

Q

sepWZ fixed

s epWZ free

ATLAS

x

­310 ­210 ­110v

xd

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.42

= 1.9 GeV2

Q

sepWZ fixed

s epWZ free

ATLAS

x

­310 ­210 ­110

xg

0

0.5

1

1.5

2

2.5

2 = 1.9 GeV

2Q

sepWZ fixed

s epWZ free

ATLAS

x

­310 ­210 ­110

ux

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.452

= 1.9 GeV2

Q

sepWZ fixed

s epWZ free

ATLAS

x

­310 ­210 ­110

dx

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.452

= 1.9 GeV2

Q

sepWZ fixed

s epWZ free

ATLAS

x

­310 ­210 ­110)s

+d

+u

= 2

x(

Σx

0

0.5

1

1.5

2

2.52

= 1.9 GeV2

Q

sepWZ fixed

s epWZ free

ATLAS

uv dv g

u d 2(u+d+s)

12/04/2012 Standard Model @ LHC 2012 - J-B. Blanchard 20 / 18