1. T. Dai, J. Liu, L. Liu, Y. Wu, B. Zhou, J. Zhu
Update of WW ATGC
Haijun Yang
T. Dai, J. Liu, L. Liu, Y. Wu, B. Zhou, J. Zhu
ATLAS SM EW Meeting
October 7, 2011

2. H. Yang - Anomalous TGC Limits
What’s New
WW ATGC limits vs different binning (optimization)
1bin (total event, >20 GeV)
2bins ( GeV, >100 GeV)
5bins (20-40,40-60,60-80,80-100,>100 GeV)
6bins (20-40,40-60,60-80,80-100, ,>120 GeV)
8bins (20-40,40-50,50-60,60-70,70-80,80-100, ,>120 GeV)
10bins (20-30,30-40,40-50,50-60,60-70,70-80,80-90,90-100, ,>120 GeV)
Include leading lepton Pt bin-by-bin uncertainty (see Jianbei’s talk)
H. Yang - Anomalous TGC Limits

3. ATGC Limits(95%CL) with LEP Constraint
 Fit anomalous TGCs using leading lepton Pt with different binning  No systematic errors are considered for these limits  6-bin keeps the lepton Pt spectrum and yields good sensitivity
Fit PTl (LEP) - MC
DkZ
lg = lZ
Dg1Z
Infinity CTEQ6M (1-bin)
[-0.165, 0.149]
[-0.176, 0.158]
[-0.120, 0.176]
Infinity CTEQ6M (2-bin)
[-0.050,0.034]
[-0.054,0.036]
[-0.011,0.068]
Infinity CTEQ6M (5-bin)
[-0.052,0.037]
[-0.055,0.040]
[-0.012,0.071]
Infinity CTEQ6M (6-bin)
[-0.051,0.037]
[-0.054,0.040]
[-0.012,0.070]
Infinity CTEQ6M (8-bin)
[-0.055,0.042]
[-0.058,0.045]
[-0.017,0.074]
Infinity CTEQ6M (10-bin)
[-0.064,0.052]
[-0.067,0.056]
[-0.025,0.083]
H. Yang - Anomalous TGC Limits 3 3

4. ATGC Limits(95%CL) with LEP Constraint
 Fit anomalous TGCs using leading lepton Pt with different binning  Include systematic errors (3% for bin-by-bin shape uncertainty)  6-bin keeps the lepton Pt spectrum and yields good sensitivity
Fit PTl (LEP) - Data
DkZ
lg = lZ
Dg1Z
Infinity CTEQ6M (1-bin)
[-0.240, 0.224]
[-0.256, 0.238]
[-0.189, 0.245]
Infinity CTEQ6M (2-bin)
[-0.064,0.048]
[-0.069,0.051]
[-0.024,0.080]
Infinity CTEQ6M (5-bin)
[-0.065,0.050]
[-0.068,0.054]
[-0.024,0.083]
Infinity CTEQ6M (6-bin)
[-0.063,0.048]
[-0.066,0.052]
[-0.022,0.081]
Infinity CTEQ6M (8-bin)
[-0.067,0.054]
[-0.070,0.059]
[-0.028,0.085]
Infinity CTEQ6M (10-bin)
[-0.078,0.067]
[-0.081,0.072]
[-0.040,0.096]
H. Yang - Anomalous TGC Limits 4 4

5. ATGC Limits(95%CL) with LEP Constraint
 Fit anomalous TGCs using one bin
Assuming same systematic uncertainty for different Pt cuts.
MC expected limits at 95% C.L.
Fit PTl (LEP) – MC
DkZ
lg = lZ
Dg1Z
Infinity CTEQ6M (Pt>80GeV)
[-0.078, 0.063]
[-0.084, ]
[-0.037, 0.094]
Infinity CTEQ6M (Pt>90GeV)
[-0.073,0.058]
[-0.079,0.061]
[-0.032,0.089]
Infinity CTEQ6M (Pt>100GeV)
[-0.071,0.055]
[-0.076,0.058]
[-0.030,0.086]
Infinity CTEQ6M (Pt>110GeV)
[-0.069,0.053]
[-0.074,0.056]
[-0.028,0.085]
Infinity CTEQ6M (Pt>120GeV)
[-0.067,0.052]
[-0.072,0.054]
[-0.027,0.083]
H. Yang - Anomalous TGC Limits 5 5

6. Fit Kinematic Distribution (PTl)
We use MC truth PT(l+), PT(l-), MET_Rel spectra to determine the 3D reweighting coefficients in each bin (10GeV).
Then apply 3D reweighting ratio of a given anomalous couplings to modify event weight of each selected WW event based on MC truth PT(l+), PT(l-), MET_Rel.
The reconstructed PTl with modified event weights is used to determine limits of the anomalous couplings.
Sensitivity to anomalous couplings mainly comes from high Pt region
Last bin includes overflow events
H. Yang - Anomalous TGC Limits 6

7. Binned Likelihood Function
Assuming systematic uncertainties of luminosity (sc), signal (ss) and four backgrounds (sb1-b4) are Gaussian and uncorrelated, we convolve six Gaussian distributions with a Poisson distribution to form a binned likelihood function. Systematic uncertainties
- Luminosity (sc =3.7%) (correlated uncertainty for all MC)
- Signal (ss = 7.6%)
- Backgrounds: Wjets (sb1 = 27.8%, data-driven)
other diboson (sb2 = 13.1%, MC), Zjets (sb3 = 18.1%, data-driven)
Top (sb4 = 30.3%, data-driven), shape error (bin-by-bin ~7-11%)
Ns is expected signal events which depends on reweighting function R (as a function of anomalous couplings).
H. Yang - Anomalous TGC Limits 7

8. ATGC Limits with bin-by-bin uncertainty
Lepton Pt Bin-by-bin uncertainty (theoretical  Experiemental)
Details are described in Jianbei’s talk
Pt (GeV)
25-40
40-60
60-80
80-100
>120
Errors 
7.28%
7.68%
7.31%
7.77%
10.81%
8.52%
Fit PTl (LEP) MC
Dkg
DkZ
lg = lZ
Dg1Z
Infinity CTEQ6M
(6-bin with errors)
[-0.190,0.238]
[-0.071,0.057]
[-0.075,0.061]
[-0.030,0.089]
Fit PTl (LEP)
Data
Dkg
DkZ
lg = lZ
Dg1Z
Infinity CTEQ6M
(6-bin with errors)
[-0.181,0.227]
[-0.068,0.054]
[-0.071,0.059]
[-0.027,0.086]
H. Yang - Anomalous TGC Limits

9. Log-likelihood(LEP) vs ATGC
H. Yang - Anomalous TGC Limits

10. Log-likelihood vs ATGC
H. Yang - Anomalous TGC Limits

11. H. Yang - Anomalous TGC Limits
2D Contour limits
H. Yang - Anomalous TGC Limits

12. H. Yang - Anomalous TGC Limits
2D contour limits
H. Yang - Anomalous TGC Limits

13. Comparisons of ATGC Limits
CDF, PRL.104, (2010)
D0 PRL.103, (2009)
CERN-PH-EP/
hep-ex/
CMS PLB 699 (2011) 25–47
H. Yang - Anomalous TGC Limits

14. H. Yang - Anomalous TGC Limits
Summary
 95% C.L. limits on the anomalous TGCs are obtained using WW candidates with 1.02 fb-1 at 7 TeV based on LEP scenario.
H. Yang - Anomalous TGC Limits

15. Backup

16. PDF/Scale Uncertainty vs Lepton Pt
Cutoff Infinity, default scale with different PDFs
Cutoff Infinity, default PDF(CTEQ6M) with different scales

17. Theoretical Uncertainties (from Liu Lulu)
From PDF (CTEQ6M,MRST2002NLO,MRST2002NNLO)
From factorization/renormalization scale
Total
Pt (GeV)
20-30
30-40
40-50
50-60
60-70
70-80
80-90
90-100
>120
Uncert.
0.0687%
0.0277%
0.0020%
0.0123%
0.0275%
0.0223%
0.0194%
0.0237%
0.0735%
0.1378%
Pt (GeV)
20-30
30-40
40-50
50-60
60-70
70-80
80-90
90-100
>120
Uncert. 
0.0560%
0.0481%
0.0552%
0.1337%
0.1547%
0.2102%
0.2462%
0.0961%
0.4786%
3.4619%
Pt (GeV)
20-30
30-40
40-50
50-60
60-70
70-80
80-90
90-100
>120
0.09%
0.06%
0.13%
0.16%
0.21%
0.25%
0.10%
0.48%
3.46%

18. Experimental uncertainties (Jianbei Liu)
20-30
30-40
40-50
50-60
60-70
70-80
80-90
90-100
>120
Electron Reconstruction SF
-0.58
-0.62
-0.63
-0.64
-0.65
-0.67
-0.66
3.08
1.43
1.36
1.55
1.93
2.4
2.96
3.65
3.06
3.3
Electron Identification SF
-1.72
-1.4
-1.28
-1.37
-1.36
-1.38
-1.39
-1.35
Electron Et Resolution
-0.6
-0.14
0.2
0.21
-0.04
0.25
0.28
-0.97
-0.25
0.26
1.92
2.41
2.95
3.66
Electron Et Scale
0.08
0.18
-0.48
-0.02
-1.17
-1.47
-1.1
-0.09
-1.31
2.94
3.67
3.29
Muon Identification SF
-0.83
-0.79
-0.78
-0.77
-0.81
Muon Scale/Resolution from ID
-0.17
-0.03
0.06
0.09
0.03
-0.52
0.13
0.38
3.07
3.05
Muon Scale/Resolution from MS
-0.39
0.17
0.12
-0.2
0.36
0.41
-0.01
Jet Energy Scale
6.89
6.24
6.94
7.05
6.05
7.29
7.43
7.08
9.56
7.02
3.09
Jet Energy Resolution
-3.01
-1.84
-2.21
-3.03
-2.31
-2.06
-0.57
-4.71
-2.54
6.12
2.84
2.7
3.83
4.79
5.89
7.27
6.06
6.55
Total
7.81
6.74
7.48
7.87
6.81
7.82
8.08
7.47
10.8
7.78
Pt (GeV)
Syst. Uncert.
Associated Stat.
Total Syst. Uncert.

19. H. Yang - Anomalous TGC Limits
BHO NLO Generator with Anomalous TGCs (Ref: Baur, Han, Ohnemus, Phys. Rev. D53, 1098, 1996)
Three different constraints:
LEP assumption (three free parameters)
HISZ scenario (two free parameters)
Equal couplings assumption (two free parameters)
Input parameters to BHO (L (cutoff) = 3,∞ TeV; PDF = CTEQ6M, MRST2002)
CME = GeV Mass_Z = GeV
Gamma_Z = GeV Mass_W = GeV
Gamma_W = GeV Mass_top = GeV
Sin2qW = a = 1/128
Br (Wln) =
H. Yang - Anomalous TGC Limits 19

20. Cross-Check: BHO NLO vs MC@NLO
Check the SM coupling between and BHO
Kinematic distributions from BHO and are consistent.
H. Yang - Anomalous TGC Limits 20

21. Anomalous TGCs Reweighting Method
Ref: V.M. Abazov et al. (D0), Phys. Rev. D80, (2009)
Basic idea: differential cross section has quadratic dependence on anomalous TGCs, X is a set of kinematic distributions:
LEP parameterization (eg.):
Points
DKZ
DlZ
Dg1Z 1
+0.4 2
-0.4 3
+0.5 4
-0.5 5 6 7 8 9
Test for LEP
Method using nine ATGCs points:
H. Yang - Anomalous TGC Limits 21

22. BHO ATGC Points for HISZ/EQUAL Parameterization
ATGC points, L = 3, ∞ TeV for HISZ scenario parameterization
Points
DKZ
DlZ 1
+0.4 2
-0.4 3
+0.5 4
-0.5 5
0.5
0.4
Test point
for HISZ
-0.3
Points
DKZ
DlZ 1
+0.4 2
-0.4 3
+0.5 4
-0.5 5
Test point
for EQUAL
ATGC points, L = 3, ∞ TeV for EQUAL scenario parameterization
H. Yang - Anomalous TGC Limits 22

23. Validation of 3D Reweighting
LEP Scenario:
DKZ = +0.1
DlZ = +0.0
Dg1z = -0.1
lep_pT>20 GeV
fabs(eta)<1.37 ||
( fabs(eta)<2.47 && fabs(eta) >1.52)
L1Pt>25 GeV
Mll>15 GeV
fabs( Mll-Mz)>15 GeV
METRel>40 GeV SM
aTGC
SM_reweighted
N_total
443.5
100%
514.2
513.6
N_2l
214.9
48.5%
268.4
52.2%
267.4
52.1%
N_L1Pt
211.9
47.8%
265.4
51.6%
264.4
51.5%
N_Mll
209.3
47.2%
262.7
51.1%
261.7
51.0%
N_MzVeto
160.2
36.1%
209.8
40.8%
209.1
40.7%
N_METRel
99.4
22.4%
134.2
26.1%
133.8
H. Yang - Anomalous TGC Limits

24. Validation of 3D Reweighting
Pt(ll)
Lepton Eta
Mll
MtWW
H. Yang - Anomalous TGC Limits

25. Validation of 3D Reweighting
MET
METRel
H. Yang - Anomalous TGC Limits

26. WW Production at 7 TeV with 1.02 fb-1
 Raise leading lepton Pt cut (20GeV  25 GeV) – remove wjets/QCD
 Lower jet pt threshold cut (30 GeV  25 GeV) and b-tag veto cut – suppress ttbar, single top and drell-yan background
325 WW events observed using revised WW selection cuts, expect WW (SM WW cross section 44.4 pb) and background of 86.6.
H. Yang - Anomalous TGC Limits 26

27. Methods to Determine 95% C.L. Limits
Log-likelihood Function (Fmin )
Bayesian Estimator
< DkZ < 0.065
+1.92
< DkZ < 0.068
95% C.L. Limits determined from
two methods are consistent.
H. Yang - Anomalous TGC Limits 27