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Ellie DobsonCAT Physics meeting 05-09-08

In collaboration with Matthias Schott & Troels Petersen (CERN)

Status of W/Z cross section measurements(electrons)

•Introduction to the theory and experimental procedure

•Data driven determination of efficiencies

•Data driven estimation of resolution impact on acceptance

•Background determination

•Fitting and cross section determination

•FDR experience

•Differential cross sections

•Unfolding techniques

•Beyond ZPt….

For more details see my recent talksATLAS CAT SM meeting 21-08-08SM meeting in physics + performance week 28-08-08

W/Z cross sections at the LHC

iit

ir

i

iB

iWZ

eWZLdtA

NNB

Probability that the event will trigger (in the electron channel)

Probability that the boson will be reconstructed

Probability that the constituents of the event (electrons, MET) will fall within the acceptance

Number of events (signal-background) counted in the detector

Data driven measurement of R (W/Z cross section ratio) May extract electroweak parameters (W branching ratios, width, VCS….)

Reduces theoretical and experimental uncertainties (ie resummation, luminosity)

Aim for MC experimental note (September 08), theory note (December 08) and data note (09?)

Very do-able at 10TeV (requires little data in comparison to, eg, W mass)

Differential cross section measurement Primary aim: to measure the differential XS in BosonPt (test of resummation)

Secondary aim: to measure the differential Z XS in Boson η (constrains knowledge on PDFs)

Require a data→truth unfolding method

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Measuring efficienciesTrigger (e20i) and reconstruction efficiencies determined using a ‘tag and probe’ data driven method in Z → ee events, which also may be applied W → eν events

Sample εT % (counting)

εT % (fit) εR(counting) εR (fit)

Zee 97.8 (98.8) 97.9 (98.9) 80.1 (67.5) 80.2 (67.9)

FDR m.aligned (fakes) 97.6 (98.8) 97.6 (98.4) 77.3 (61.8) 80.2 (64.1)

FDR m.aligned (no fakes) 96.5 (97.9) 97.9 (98.1) 78.6 (66.6) 82.7 (68.7)

Medium (Tight)

Statistics too limited in FDR to do anything other than a global efficiency

Method ‘a la’ Maria Fiascaris and Guillaume Kirsch (Oxford)

60-130GeV80-100GeV

•Trig (reco) efficiencies calculated within ~0.5 (2)% of the ‘MC efficiency’ in the FDR

•Aligned sample and ‘no fake’ sample have higher reco efficiencies

Tag condition (N1) Probe condition (N2)

Trigger e1: OL+L1+L2+EF

e2: OL

e2: L1+L2+EF

Reco e1: OL+L1+L2+EF

e2: Cluster (opposite hemisphere)

e2: OL

Unable to study separate levels of the trigger due to limited information available in FDR2- overall trigger efficiency stated

Statistical error (10pb-1) of the order 0.2% (trigger), 0.5% (reco) Reco-Truth agreement ~ 0.1% (trigger), 0.1% (reco) Source of systematics (need others…)

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…but good enough for FDR purposes

Signal/Background ratio worse for the reconstruction efficiencies than for the trigger(where limited background statistics lead to unreliable fitting)

Fitting εBW sigmaBW meanCB sigmaCB mean#BW#CB#BG

Some crystal ball parameters (controlling the asymmetric tail) have been fixed

Overall fit in N1 and N2 used for the background subtraction. Crystal ball convoluted with Breit Wigner used. Exponential function (parton luminosity term) to be convoluted in also.

FDR recoResults

Signal trigger results

Systematic on the fitting shape determined by comparing measured efficiency when using fit to measured efficiency when counting events in the signal peak. Found to be <0.1% (previous slide)

Signal fit still not great…

Differential ε

Difference between three results – systematic error on the method

Determined by counting how many truth electrons are matched to trigger objects

Trigger efficiencies are not flat in all phase space and for an accurate cross section differential efficiencies must be used.

•Have studied variables of projection (η, Pt, dR (electron-nearest jet), hadronic activity, Njets, ZPt….)

•‘Jet variables’ difficult as they are too correlated with the electron variables (for instance, a binning in dR (electron-nearest jet) picked up the v12 L2 tracking bug in η)

• For the purposes of XS, efficiencies are binned in coarse bins of η and Pt• Maximise statistics and accuracy• 8 bins chosen (4 in |η| and 2 in Pt(e))

Determined by counting how many truth electrons are matched to offline objects

Reco results

Trigger results

•εR determined separately for loose, medium and tight IsEM cuts.

•εT determined with respect to the same offline criteria

Smear Met vector with x, σ of Gaussian distribution of EtMiss resolved along/perpendicular to the axis directionCombine two smeared values

Truth Smeared

•EtMiss scale/smearing creates a systematic error on the acceptance in the W analysis •May estimate this by smearing truth particles with the smearing/scale and then running through the

acceptance cuts to get a modified acceptance calculation•Must estimate EtMiss resolution and scale from data (Z analysis as previously described)→ STRATEGY: to do this from Z events….

EtMiss systematic strategy

Overall smearing Component smearing

PerpendicularParallel

TruthSmeared

Smear Met Pt with x, σ of Gaussian fit of Pt resolution functionResolution function dependent on SumPt

See my talk in JetEtMiss performance meeting from the last Physics and Performance week

MC study of acceptances in the W channel:ΔA (Met smearing) ≈ 1.89%ΔA (electron smearing) ≈ 0.74%

MEt will be the largest correction (worse resolution) but similar game played with lepton scale & resolution→ determined from data from the ZMass peak

EtMiss Scales and resolutions

Hadronic recoil

EtMiss

e+

e-

•Need to measure EtMiss scales and resolutions from data alone….•Define an axis in the transverse plane from the event topology along which to

resolve quantities. •Find axis sensitive to lepton-jet balance:

vPerpendicular

et

et

et

et

p

p

p

pvPeaks in same direction as ZPt

direction…Axis defined from electron angles alone (very well defined in atlas)

Axis of resolution optimally defined

vParallel

Global analysis

Difference in W and Z resolutions- due to differing hadronic recoil distributions as the hadronic recoil is what drives the Met resolution

MC and data results agree globally

Mean

σ

For smearing, mean and σ taken from a Gaussian fit of the distributionsshown

Insitu determined by RefFinal.AMC determined by (RefFinal-Truth).A

Resolution better along the perpendicular than along the parallel- optimal resolution axis

Study distributions of Met resolved along the axes

EtMiss resolution

When binning in HR the W and Z distributions now agree along perpendicular

The Z insitu-ZMC discrepancy is due to the difference between RefFinal and RefFinal-Truth. Need to assume Met (truth) =0.

Y =σ of Gaussian fit of MEt resolved along parallel or perpendicular axis

W-Z hadronic recoil distributions are different. Hence the need to compare Met resolution functions in bins of hadronic recoil =SumPt-Pt(electrons)If the simple ‘out of the box’ sumet used the results do not work so well…

See again the improved resolution along the perpendicular

Sigma of Gaussian fit of EtMiss projected along resolution axis

FDR2

Can measure resolution even in FDR2 (0.36pb-1)

ZeeFDR (fakes)FDR (no fakes)

EtMiss scale

Mea

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gau

ss f

it o

f E

tMis

s re

solv

ed a

long

axi

s

No mechanism for bias along the parallel

Bias along perpendicular – performance issue….

•For a long time this technique has highlighted a scale bias in the Met calculation when resolved along the perpendicular axis.

•Topology of the event suggests the hadronic recoil magnitude is being underestimated.

•Important issue for XS calculations as a large bias in Met as seen in Z events will affect the acceptance….

ZeeFDR (fakes)FDR (no fakes)

Able to detect bias even in FDR2 (0.36pb-1)

FDR2

May obtain Met and Boson resolution functions for a W event by ‘neutrinofying’ a Z event

Neutrinofication from Zee

Broadened distribution in Z events due to higher hadronic activity – can be corrected by binning in SumPt

FDR results compatible with those from the Zee sample→ May obtain data driven resolution functions for Wenu in very early data!

‘truth’ MEt (Φ) =e1

‘reco’ MEt (Φ) = -e2 - HRHR= -e1 – e2 - RF

‘truth’ Pt (Φ) =e1 + e2

‘reco’ Pt (Φ) = e2 + (-e2 - HR)HR=-e1 – e2 - RF

e+

e-

ν

HR

EtMiss

Impact on acceptances

Variable used in calculation

Acc/%

EtMiss 51.34

EtMiss

(MC smearing)

49.44

EtMiss (neutrinofication smearing)

49.40

EtMiss

(axis smearing)

49.65

Impact on acceptance calculation evaluated by smearing truth EtMiss using the resolution functions obtained and running through the acceptance calculation

Smearing in MET has ~2% impact on the acceptanceData driven methods (using Z events) yield a value within 0.2% of MC smeared acceptances

EtMiss truth distributions

Backgroundsttbar background estimation has been scaled by trigger efficiency (as determined by tag and probe) as no trigger information in the sample

A Zee XS may be determined using a global fit Signal+Exponential BG; no precise BG determination really necessary→ Fitting method in Zee yields a XS in the FDR exercise to within 20% of the sample measured XS - see full analysis results in my presentation in the FDR2 for users meeting….

QCD background by brute force clearly unsatisfactory→Methods of QCD BG estimation from data

- Matrix methods? - Isolation studies? - Photon trigger? Medium IsEM

QCD BG Technique as developed by Alessandro Tricoli during the CSC exercise

1) Select sample with (g20i) photon trigger

2) Sample selected largely composed of jets faking photons

3) Sample is kinematically (MEt dist) similar to jets faking electrons

4) Normalise photon fit to (lower statistics) QCD sample passing electron (e20i) trigger in tails to estimate BG

NOTES / DISCLAIMERS:• Running on *very* low stats dijet sample → 200, 000 events: if only I had a million….• Thus feasibility study shown on using just the trigger (not OL selection cuts). Will extend with higher statistics• Fit from dijets+Wenu (data method) as opposed to dijets alone (ideal) leads to a very small (0.1%) variation in fit parameter• Final BG estimation has 0.3% contamination from W events

Normalisation region

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XS Results and uncertaintiesQuantity Measured

valueStat unc /%

(10pb-1)

Sys unc/% Sys eval method

Lumi 9.82pb-1 10 10 Lumi perf.group

74.72pb-1 10 10

NEvents 42185 0.5 Need QCD BG estimation…

23302 0.09 Need QCD

Acceptance 0.32 0.83 5.08 Smearing

0.28 0.47 6.74

Efficiency 0.78 0.70 0.14 Data-MC

0.64 0.95 0.28

Measured XS 20697pb-1 1.2 (247 abs) 5.09 (1053 abs) Excluding lumi

2138pb-1 1.1 (23 abs) 6.75 (144 abs)

Measured XS 21690pb-1 1.1 (247 abs) Excluding lumi

2139pb-1 0.5 (11 abs)

MediumIsEM

Unbinned effs

W values

Z values

Binned effs

MediumIsEM

W XS low using global ε as this is determined from Z events (different Pt distributions….)Z XS ports well from global → binned ε

Yields R value of 10.14 compared with input MC value of 10.39→ correct to 2.5%

Acceptance smearing correction very large….

Differential XS Differential Wenu XS with WPt

Binning doesn’t improve the reco-truth

offset because efficiencies

are flat with ZPt.

Truth corrected for acceptance

Reco corrected for efficiencies

Binned efficiencies clearly improve measurement bias

Truth-Reco matching is not as close as for the BosonPt case….

• Truth distributions weighted for acceptance, reco distributions weighted for efficiencies. The two should agree. • Integral of the curve yields the global XS• Integrals yield an accuracy truth-reco of Unbinned (binned) Wenu: 0.1 (4%)Unbinned (binned) Zee: 4 (3)%• The residual difference between truth and reco distributions may be reduced using unfolding techniques from data alone

Agreement worse than in Zee (MEt resolution is worse than electron resolution…)

Boson Pt unfolding

Impact of unfolding on measured-truth distributions

Aim: to measure a differential cross section with boson variablesProblem: to correct measured back to the truth cross section. unfolding – uses a response matrix mapping the true distribution with the measured oneUnfolding designed to have response matrix trained with (Truth, Reco) on event by event basisThe below is using (TruthBosonPt, RecoBosonPt) to train the response matrix.The reco BosonPt distribution is then unfolded….

Low statistics region. Need to implement variable binning…

Implemented package (RooUnfold) developed by Tim Adye & Kerstin Tackmann solve for μ iteratively, giving added weight to smoother solutions

- Bayes : use Bayes’ theorem to invert R and use an initial set of probabilities to converge onto new bin contents using a number of iterations

M

jjiji Rv

1

true distmeasured dist

Response matrix

e+

e-

νUse Zee events as before to predict W boson resolution (Pt, Phi). Use this in unfolding….

Pt unfolding from data

Alternate idea:Use Met and electron resolution functions determined from data to fit BosonPt resolved along x, y direction (Gaussian + exponential)

Would be nice to train the response matrix without relying on MCIf resolution functions are known can train the response matrix with (Truth, Smeared Truth)Have to obtain BosonPt resolution functions from data alone……

(Yes, this uses Monte Carlo. However unfolding relies on mapping and not absolute values so the input distribution is not so important)

Differential XS→ beyond standard variables….

• Don’t have to directly measure VPt differential cross section wrt VPt!• May use a differential measurement wrt a variable sensitive to the bosonPt then transform back to VPt later• Exploit the excellent lepton angular resolution in ATLAS for a huge improvement in resolution• If the variable is chosen carefully may massively beat down the resolution systematics…..

Axis as devised (M.Vesterinen, T. Wyatt)

DeltaPhi has by far the best resolution – may transform back to ZPt using the Mz lineshape as measured by LEP (best existing measurement to date….)

Perpendicular axis (as defined in the MEt study)

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Conclusions

To do.….• Refinement of fitting• QCD ‘photon’ background estimation on higher statistics• Further investigation into unfolding techniques

•Trigger and reconstruction efficiency measurements successfully run. FDR2 experience with the efficiencies successful- good news for a *very* early data measurement of efficiencies using tag and probe

•Cross section measurements made in signal analysis. FDR cross section measurements rather unreliable (fitting problems)

•Resolution studies (for the EtMiss systematic and performance group) work well in signal and are transportable to early data measurements

•In later data differential cross sections and unfolding techniques from data are promising….

•Starting to investigate exploiting angular resolutions in ATLAS to beat down the systematics in a differential XS measurement

Backup

Cut flow table: W selection

fraction remaining

Zee Wenu Ztautau dijets ttbar FDR

(no fakes)

FDR (fakes)

NEvents 107000 107000 48000 1.91x108 34900 41356 89779

1xe20i 0.78 0.66 0.22 0.001 0.98 (0.99) 0.36 0.50

1xPt(e)>25 0.34 0.54 0.13 0.0005 0.31 (0.32) 0.22 0.28

1xEta cuts 0.36 0.52 0.13 0.0005 0.31 (0.31) 0.21 0.26

1xIsEM 0.39 (0.40) 0.47 (0.41) 0.12 (0.10) 2x10-4

(5.6x10-5)

0.23 (0.18) 0.16 (0.08) 0.16 (0.05)

DiffObj+3elec

0.39 (0.40) 0.48 (0.41) 0.12 (0.11) 2x10-4 (6.1x10-5)

0.23 (0.18) 0.16 (0.08) 0.16 (0.05)

MEt>25 0.009 (0.01)

0.39 (0.33)

0.04 (0.03) 3.0x10-5 (2.6x10-5)

0.20 (0.16) 0.06 (0.04) 0.03 (0.02)

NEvents (Lsig)

130 (134) 42185

(35815)

28 (23) 56816 (48700)

896 (707) 67161 (51073)

76732

(59744)

No Wtaunu (available in v12 only; ttbar scaled with trigger efficiency)

medium (tight) Large systematic on this method due to the dijet sample

Cut flow bingo!Where does the W BG go?

Cut flow table: Z selectionZee Wenu Ztautau dijets ttbar FDR (no

fakes)FDR (fakes)

NEvents 107000 107000 48000 1.91x108 34900 41356 89779

2xe20i 0.78 0.66 0.22 0.001 1.0

(1.0)

0.36 0.50

2xPt(e)>25 0.35 0.02 0.016 2.6x10-5 0.18 (0.18) 0.05 0.04

2xEta cuts 0.31 0.02 0.015 1.7x10-5 0.17 (0.17) 0.04 0.03

2xIsEM 0.24 (0.17) 0.005 (0.004)

0.007 (0.005)

8.7x10-6 0.02 (0.01) 0.01 (0.007)

0.008 (0.004)

DiffObj+3elec

0.24 (0.17) 0.0001 (~0)

0.006 (0.003)

4.3x10-6 0.01 (0.01) 0.01 (0.007)

0.008 (0.004)

Mass cuts 80-100

0.22 (0.15) 0.0001 (0) 0.0004 (0.0002)

4.3x10-6 0.002 (0.0009)

0.008 (0.006)

0.005 (0.003)

NEvents (Lsig)

23302

(16417)

106 (0) 3 (2) 61782 (61782)

83 (33) 67456

(47531)

83853

(54795)

Simulation tells us ~85276 (78234) events pass selection, cf FDR values of 83853 (54795)

Cut flow bingo! Where does the Z BG go?