Usage of Jet Charge to Improve the Up/Down-type Quark Separation146

9. Results 135

9.2. Constraints on W tb Vertex

10.1.2. Usage of Jet Charge to Improve the Up/Down-type Quark Separation146

In order to make use of the hadronic analyser in the measurement of the W boson polarisation, the separation between the up- and down-type quarks is essential. As explained in Section6.2.2, ap_Tdependent MV1 weights distribution obtained for different jet flavours is used to discriminate between up- and down-type jets.

Another discriminant that could serve the mentioned separation is the use ofjet charge.

Given the conservation of charge in the hadronisation process, the charge of the origi-nating parton could be identified by the identification of the charge of the hadrons to which a jet is fragmented [181,182]. Similar methods are used to measure the charge of the top quark by both ATLAS and CMS [183, 184] to exclude the BSM processes with exotic top quark charge of−4/3.

However, the light jets originating from the hadronic W boson decay have same sign charges, some discriminating variables such as the tracks with maximump_Tand weighted jet charge proposed in [85], could be defined and utilised in a multi-variate technique to construct a final discriminant variable, which potentially can improve the current up-and down-type quark discriminant. In former method the charge of the track within the jet that has the highestpT is used to assign the jet charge, while in the latter method a weighted charge using all tracks are used according to their momentum contribution.

10.1.3. Usage of Up-type Quark in the Hadronic Analyser

As discussed in Section 3.2.3, the jets with higher transverse momentum have higher energy resolution, and therefore, have lower uncertainty in measuring their energy. Due to theV−Astructure of theW tbvertex as discussed in Section2.2.3, the up-type quark originating from theW boson hadronic decay is preferably propagated in the direction of theW boson. Thus, on average the up-type quark acquires a higher transverse momen-tum with respect to the down-type quark, and consequently it has on average a higher reconstruction efficiency compared to the down-type quark.

On the other hand, the hadronic analyser is defined as the angle between the down-type

10.1. Outlook

quark and the inverse direction of theb-quark in theW boson rest frame. However, one could use the inverse direction of the up-type quark with higher reconstruction efficiency rather than the direct usage of the down-type quark direction, knowing that the light jets are propagated back-to-back in theW boson rest frame.

Acknowledgements

This thesis would not have been possible without the support and guidance of many people to whom I owe my gratitude. At first, I would like to express my gratitude to my supervisor, Arnulf Quadt, for inviting me to join his research group, for all his kind support and guidances during this journey and for the opportunity that he gave me to understand the priceless joy of research. Thank you for believing in me. It was an honer for me to be a member in this institute and your research group. I would also like to thank Stan Lai for agreeing to be the co-referee of this thesis, and thanks for spreading positive energy to everyone he meets.

There are no words to express how thankful I am to Boris Lemmer. Thank you for a lot of discussions and advice and your continued encouragement and all the positive energy I got from you, and for all your kind help in the hard moments. Lisa Shabalina, thank you for all the support during my stay at CERN, for your patience and kindness. Without your support and encouragement this success wouldn´t have been possible. You gave me enthusiasm and taught me how to think analytically. I am proud that I worked with you and under your supervision. Thank you for everything you have done for me. Thanks to the tireless and energetic friend, Maria Moreno Llacer, for her kind support during my stay at CERN. Thanks to Jörn Grosse-Knetter, for supervising my first project in particle physics hardware with ATLAS during my Pixel detector Qualification task, for his patience and support. I would like to take the opportunity to express my sincere appreciation to all my friends and colleagues at the II. Institute of Physics with whom I shared nice moments along the way. Thank you for all the support, insights, and help you have provided me over the past 4 years. Especially I want to thank Ms. Hamdi, Ms.

Tyson, Ms. Lange and Ms. Afshar.

My special feelings and thanks to my dear wife, Nibras, who has been with me all these years and has made them the best years of my life. Her support, encouragement, patience and unwavering love were undeniably the bedrock upon which this success have been built. Thanks to my little daughter Fatema, for coming to my life. You are the best daughter I could ever have. Thanks for your smiles that encouraged me to efficiently overcome the difficulties encountered in my pursuit of the Ph.D. degree.

My final words go to my bleeding homeland. I am greatly honoured to have received the Ph.D. scholarship from the Iraqi ministry of higher education and scientific research (MOHESR). Thanks for supporting me during all these years despite the pain and suf-fering of the war.

Appendices

A

Systematic Uncertainties - Full Tables

This appendix presents the tables of significant systematic uncertainties in the measure-ment of W boson helicity fractions. The systematic uncertainties are evaluated via the ensemble test method using 5000 sets of pseudo-data. The results here quoted for the leptonic analyser with ≥2 b-tags, hadronic analyser with≥ 2 b-tags, and the hadronic analyser with 1 b-tag + ≥2 b-tags. The algorithm discussed in Section8.2.6 is used to determine which systematics are considered significant. The uncertainties are split ac-cording detector and modelling systematics, and three tables are provided (one for each helicity fraction).

Table A.1.: Change in the mean value of fitted helicity fraction, F₀, due to systematic variations up and down. The fits are performed using 5000 sets of pseudo-data and correspond to the leptonic analyser with≥2b-tags, hadronic anal-yser with ≥ 2 b-tags, and the leptonic+hadronic analysers with 1 b-tag +

≥2 b-tags.

Systematic uncertainty Up/Down Leptonic 2incl Had 2incl Had 1excl+2incl Modeling

Radiation radHi -0.0025 -0.0382 -0.0108

radLo 0.0033 0.048 0.0178

Reconstructed Objects

BTAG_bTagVar_0 up -0.0001 -0.0007 -0.0012

down 0.0 -0.0 0.0001

BTAG_bTagVar_1 up -0.001 -0.0021 0.0014

down 0.0008 0.0012 -0.0026

BTAG_bTagVar_2 up 0.0001 -0.0002 -0.0069

down -0.0004 -0.0006 0.0059

BTAG_bTagVar_3 up 0.0005 0.0008 0.0081

down -0.0011 -0.0014 -0.0093

BTAG_bTagVar_4 up 0.0005 0.0003 -0.0005

down -0.0008 -0.0008 -0.0006

BTAG_bTagVar_5 up -0.0001 -0.0002 0.0246

down 0.0004 -0.0006 -0.0262

BTAG_cTagVar_0 up -0.0005 -0.0006 -0.0009

down -0.0003 -0.0002 -0.0003

BTAG_cTagVar_1 up 0.0005 0.0014 0.004

down -0.0004 -0.0021 -0.0051

BTAG_cTagVar_2 up 0.0001 -0.0007 -0.0022

down 0.0001 0.0002 0.0011

BTAG_cTagVar_3 up 0.0006 0.0033 0.0076

down -0.0006 -0.004 -0.0084

BTAG_misTagVar_0 up -0.0002 -0.0006 -0.0007

down -0.0003 -0.0003 -0.0003

BTAG_misTagVar_1 up -0.0003 -0.0005 -0.0003

down -0.0 -0.001 -0.0011

BTAG_misTagVar_10 up -0.0002 -0.0007 -0.0016

down 0.0001 0.0009 0.0015

BTAG_misTagVar_11 up -0.0005 -0.0021 -0.0053

down 0.0008 0.0021 0.0047

BTAG_misTagVar_2 up 0.0002 -0.0008 -0.0009

down 0.0001 -0.0007 -0.0012

BTAG_misTagVar_3 up -0.0 -0.0004 -0.0005

down -0.0003 -0.0006 -0.0007

BTAG_misTagVar_4 up -0.0001 -0.0003 -0.0008

down -0.0001 -0.0003 -0.0001

Systematic uncertainty Up/Down Leptonic 2incl Had 2incl Had 1excl+2incl

BTAG_misTagVar_5 up -0.0 -0.0003 -0.0007

down -0.0001 -0.0006 -0.0004

BTAG_misTagVar_6 up -0.0001 0.0 0.0003

down -0.0002 -0.0 -0.0008

BTAG_misTagVar_7 up -0.0 0.0002 -0.0003

down -0.0003 0.0002 -0.0002

BTAG_misTagVar_8 up 0.0001 -0.0001 0.0001

down -0.0002 -0.0002 -0.0006

BTAG_misTagVar_9 up 0.0 0.0008 0.001

down 0.0001 -0.0008 -0.0013

ELE_ID up -0.0028 -0.0027 -0.0023

down 0.003 0.0027 0.0021

ELE_RECO up -0.0003 -0.0003 -0.0007

down 0.0002 -0.0 -0.0001

ELE_TRIGGER up -0.0003 -0.0007 -0.0008

down 0.0 0.0008 0.0004

MUON_ID up 0.0006 0.0008 0.001

down -0.0009 -0.0014 -0.0014

MUON_RECO up 0.0 -0.0001 -0.0002

down -0.0003 -0.0013 -0.0009

MUON_TRIGGER up 0.0024 0.0031 0.0024

down -0.0028 -0.0039 -0.0034

jer_DataMC_Difference -0.0021 -0.0096 -0.0096

jer_NP0 up 0.0013 -0.0003 -0.0043

down -0.0021 -0.0096 -0.0096

jer_NP1 up -0.0021 -0.0096 -0.0101

down -0.0019 -0.0069 -0.0088

jer_NP2 up -0.0013 -0.0043 -0.0069

down -0.0018 -0.0101 -0.0104

jer_NP3 up -0.0025 -0.0088 -0.0096

down -0.0004 -0.0056 -0.0077

jer_NP4 up -0.0013 -0.0094 -0.0098

down -0.0024 -0.008 -0.0101

jer_NP5 up -0.002 -0.0095 -0.0117

down -0.0018 -0.0063 -0.0084

jer_NP6 up -0.0025 -0.008 -0.0094

down -0.0006 -0.0086 -0.0088

jer_NP7 up -0.0028 -0.0089 -0.0086

down -0.0013 -0.0076 -0.0091

jer_NP8 up -0.0021 -0.0096 -0.0097

down -0.0018 -0.0084 -0.0092

jer_Noise_ForwardRegion -0.002 -0.0101 -0.0104

Systematic uncertainty Up/Down Leptonic 2incl Had 2incl Had 1excl+2incl jes_EtaIntercalibration_TotalStat up -0.0007 0.0031 0.0013

down -0.0007 -0.0035 -0.0026

jes_FlavourComp up -0.0042 0.0096 0.0054

down 0.0018 -0.0077 -0.003

jes_FlavourResponse up -0.0024 -0.0003 0.0038

down -0.0005 -0.0003 -0.0056

jes_Modelling1 up -0.003 0.0046 -0.0005

down 0.0014 -0.0041 0.0016

jes_RhoTopology up -0.0021 0.0047 0.0014

down 0.0022 -0.0045 -0.0003

jes_Statistical1 up -0.0015 0.0023 -0.0002

down 0.0006 -0.0011 -0.0003

jvf up -0.0036 -0.0152 -0.0129

down -0.0017 0.0105 0.0092

Total Syst. +0.0149 +0.067 +0.0518

-0.0136 -0.0673 -0.0541

Table A.2.: Change in the mean value of fitted helicity fraction, F_L, due to systematic variations up and down. The fits are performed using 5000 sets of pseudo-data and correspond to the leptonic analyser with ≥2 b-tags, hadronic anal-yser with ≥2 b-tags, and the leptonic+hadronic analysers with 1b-tag +≥2 b-tags.

Systematic uncertainty Up/Down Leptonic 2incl Had 2incl Had 1excl+2incl Modeling

Radiation radHi 0.0058 -0.0089 -0.0115

radLo -0.0032 0.0376 0.0393

Reconstructed Objects

BTAG_bTagVar_0 up 0.0001 -0.001 -0.0003

down -0.0002 0.0007 0.0007

BTAG_bTagVar_1 up 0.0007 -0.0014 -0.0019

down -0.0007 0.0001 0.0019

BTAG_bTagVar_2 up -0.0003 0.0022 0.0021

down 0.0004 -0.0026 -0.0023

BTAG_bTagVar_3 up -0.0006 -0.0013 -0.0007

down 0.0007 0.0013 0.0007

BTAG_bTagVar_4 up -0.0006 -0.0008 0.0

down 0.0006 0.0006 0.0005

BTAG_bTagVar_5 up -0.0002 0.0009 -0.0013

down -0.0002 -0.0012 0.0022

BTAG_cTagVar_0 up 0.0003 0.0025 0.002

down -0.0 -0.003 -0.0021

BTAG_cTagVar_1 up -0.0002 0.0024 0.0014

down 0.0 -0.0025 -0.0013

BTAG_cTagVar_2 up 0.0 0.0018 0.0025

down -0.0 -0.0023 -0.0012

BTAG_cTagVar_3 up -0.0001 0.0084 0.0078

down 0.0001 -0.0089 -0.0075

BTAG_misTagVar_0 up 0.0001 -0.0008 -0.0

down 0.0 -0.0006 -0.0004

BTAG_misTagVar_1 up 0.0001 -0.0003 0.0005

down -0.0001 -0.0003 0.0001

BTAG_misTagVar_10 up 0.0001 -0.0033 -0.0033

down 0.0001 0.0035 0.0039

BTAG_misTagVar_11 up -0.0001 -0.0098 -0.0086

down -0.0002 0.0103 0.0103

BTAG_misTagVar_2 up -0.0 0.0005 0.0

down -0.0001 -0.0001 0.0001

BTAG_misTagVar_3 up 0.0 -0.0007 -0.0004

down 0.0002 -0.0 0.0001

BTAG_misTagVar_4 up 0.0 0.0003 0.0004

down -0.0 -0.0004 -0.0006

Systematic uncertainty Up/Down Leptonic 2incl Had 2incl Had 1excl+2incl

BTAG_misTagVar_5 up -0.0001 -0.0008 -0.0012

down 0.0 0.0003 0.0008

BTAG_misTagVar_6 up 0.0001 0.0002 0.0009

down 0.0002 0.0004 0.0004

BTAG_misTagVar_7 up -0.0 -0.0001 0.0002

down 0.0001 0.0007 0.0004

BTAG_misTagVar_8 up -0.0001 0.0024 0.0019

down 0.0001 -0.0013 -0.0013

BTAG_misTagVar_9 up 0.0001 -0.0005 0.0002

down -0.0001 0.0004 0.001

ELE_ID up 0.0018 -0.0021 -0.0028

down -0.002 0.0026 0.0034

ELE_RECO up 0.0002 -0.0005 0.0005

down -0.0003 0.0009 0.0003

ELE_TRIGGER up 0.0 -0.0009 -0.0002

down 0.0002 0.0003 0.0015

MUON_ID up -0.0002 0.0016 0.0014

down 0.0003 -0.0014 -0.0014

MUON_RECO up -0.0001 0.0007 0.0005

down 0.0 -0.0005 -0.0006

MUON_TRIGGER up -0.0012 0.0031 0.0044

down 0.0015 -0.0035 -0.0031

jer_DataMC_Difference 0.0002 -0.0125 -0.0114

jer_NP0 up -0.0044 -0.002 0.0026

down 0.0002 -0.0125 -0.0114

jer_NP1 up 0.0002 -0.012 -0.0122

down -0.0003 -0.0138 -0.0099

jer_NP2 up -0.0016 -0.0002 0.0071

down 0.0 -0.0141 -0.0125

jer_NP3 up 0.0001 -0.0152 -0.0145

down -0.0012 -0.0076 -0.0014

jer_NP4 up -0.0001 -0.0139 -0.0141

down -0.0006 -0.0164 -0.0143

jer_NP5 up -0.0004 -0.0078 -0.0048

down -0.0003 -0.013 -0.0125

jer_NP6 up 0.0004 -0.013 -0.013

down -0.0009 -0.014 -0.0131

jer_NP7 up -0.0 -0.0125 -0.012

down -0.0005 -0.0143 -0.0133

jer_NP8 up 0.0002 -0.0125 -0.0114

down -0.0001 -0.0153 -0.0156

jer_Noise_ForwardRegion 0.0003 -0.0136 -0.0137

Systematic uncertainty Up/Down Leptonic 2incl Had 2incl Had 1excl+2incl jes_EtaIntercalibration_TotalStat up 0.0001 -0.0022 -0.0022

down 0.0002 -0.0012 -0.0002

jes_FlavourComp up 0.0017 -0.0 0.0034

down -0.0013 0.0059 0.0029

jes_FlavourResponse up 0.0013 0.004 -0.0031

down -0.0002 0.004 0.0055

jes_Modelling1 up 0.0013 0.0054 0.0103

down -0.0008 0.0013 -0.0025

jes_RhoTopology up 0.0009 0.0012 0.0027

down -0.0018 0.0012 -0.0014

jes_Statistical1 up 0.0008 -0.0 0.0015

down -0.0008 -0.0032 -0.0036

jvf up 0.0019 0.0041 0.0012

down 0.0013 -0.0062 -0.0046

Total Syst. +0.0129 +0.0596 +0.0625

-0.012 -0.0672 -0.0667

Table A.3.: Change in the mean value of fitted helicity fraction, F_R, due to systematic variations up and down. The fits are performed using 5000 sets of pseudo-data and correspond to the leptonic analyser with≥2b-tags, hadronic anal-yser with≥2b-tags, and the leptonic+hadronic analysers with 1 b-tag +≥2 b-tags.

Systematic uncertainty Up/Down Leptonic 2incl Had 2incl Had 1excl+2incl Modeling

Radiation radHi -0.0034 0.047 0.022

radLo -0.0001 -0.0855 -0.0573

Reconstructed Objects

BTAG_bTagVar_0 up 0.0 0.0016 0.0018

down 0.0001 -0.0009 -0.001

BTAG_bTagVar_1 up 0.0002 0.0034 0.0003

down -0.0 -0.0017 0.0011

BTAG_bTagVar_2 up 0.0003 -0.0022 0.0048

down 0.0001 0.0029 -0.0035

BTAG_bTagVar_3 up -0.0 0.0003 -0.0076

down 0.0004 0.0003 0.0084

BTAG_bTagVar_4 up 0.0001 0.0006 0.0003

down 0.0001 -0.0 0.0001

BTAG_bTagVar_5 up 0.0003 -0.0009 -0.0232

down -0.0002 0.0017 0.0238

BTAG_cTagVar_0 up 0.0003 -0.0023 -0.0013

down 0.0002 0.0028 0.0024

BTAG_cTagVar_1 up -0.0003 -0.0043 -0.0056

down 0.0004 0.0044 0.0062

BTAG_cTagVar_2 up 0.0001 -0.0014 -0.0001

down 0.0001 0.0018 0.0003

BTAG_cTagVar_3 up -0.0005 -0.0119 -0.0156

down 0.0007 0.0126 0.0162

BTAG_misTagVar_0 up 0.0002 0.0012 0.0005

down 0.0001 0.0007 0.0007

BTAG_misTagVar_1 up 0.0002 0.0006 -0.0

down 0.0002 0.0009 0.0009

BTAG_misTagVar_10 up 0.0002 0.0038 0.005

down -0.0 -0.0046 -0.0053

BTAG_misTagVar_11 up 0.0006 0.0116 0.014

down -0.0006 -0.0126 -0.0149

BTAG_misTagVar_2 up 0.0 0.0001 0.0006

down 0.0001 0.0004 0.0011

BTAG_misTagVar_3 up 0.0001 0.0006 0.0008

down 0.0003 0.0004 0.0005

BTAG_misTagVar_4 up 0.0001 -0.0003 0.0005

down 0.0001 0.0006 0.0007

Systematic uncertainty Up/Down Leptonic 2incl Had 2incl Had 1excl+2incl

BTAG_misTagVar_5 up 0.0001 0.0009 0.0018

down 0.0001 0.0001 -0.0003

BTAG_misTagVar_6 up 0.0001 -0.0003 -0.0009

down 0.0002 -0.0004 0.0003

BTAG_misTagVar_7 up 0.0001 -0.0002 0.0

down 0.0001 -0.001 0.0001

BTAG_misTagVar_8 up -0.0 -0.0025 -0.0022

down 0.0002 0.0015 0.0018

BTAG_misTagVar_9 up -0.0001 -0.0005 -0.0011

down 0.0001 0.0002 0.0004

ELE_ID up 0.001 0.0042 0.005

down -0.0011 -0.005 -0.0054

ELE_RECO up 0.0001 0.0006 0.0

down -0.0 -0.0007 -0.0003

ELE_TRIGGER up 0.0003 0.0013 0.001

down -0.0002 -0.0012 -0.0019

MUON_ID up -0.0002 -0.0025 -0.0024

down 0.0005 0.0028 0.0026

MUON_RECO up -0.0 -0.0007 -0.0005

down 0.0002 0.0016 0.0016

MUON_TRIGGER up -0.001 -0.0062 -0.0068

down 0.0013 0.007 0.0066

jer_DataMC_Difference 0.0019 0.0219 0.021

jer_NP0 up 0.0031 0.0021 0.0018

down 0.0019 0.0219 0.021

jer_NP1 up 0.0019 0.0212 0.022

down 0.002 0.0207 0.0187

jer_NP2 up 0.003 0.0042 -0.0001

down 0.0017 0.0238 0.0225

jer_NP3 up 0.0025 0.0239 0.0242

down 0.0015 0.0128 0.009

jer_NP4 up 0.0014 0.0231 0.0236

down 0.0031 0.0242 0.0243

jer_NP5 up 0.0026 0.017 0.0166

down 0.0023 0.0191 0.0208

jer_NP6 up 0.0021 0.0209 0.0222

down 0.0016 0.0225 0.0217

jer_NP7 up 0.0028 0.0213 0.0207

down 0.0017 0.0216 0.0222

jer_NP8 up 0.0019 0.0219 0.0212

down 0.002 0.0238 0.0248

jer_Noise_ForwardRegion 0.0019 0.0235 0.024

Systematic uncertainty Up/Down Leptonic 2incl Had 2incl Had 1excl+2incl jes_EtaIntercalibration_TotalStat up 0.0006 -0.0011 0.0006

down 0.0006 0.0045 0.0027

jes_FlavourComp up 0.0026 -0.0098 -0.0089

down -0.0003 0.002 -0.0

jes_FlavourResponse up 0.0011 -0.0039 -0.0007

down 0.0008 -0.0039 0.0002

jes_Modelling1 up 0.0018 -0.0102 -0.0097

down -0.0007 0.0026 0.0013

jes_RhoTopology up 0.0012 -0.0063 -0.0042

down -0.0005 0.0031 0.0019

jes_Statistical1 up 0.0007 -0.0023 -0.0013

down 0.0 0.0042 0.0041

jvf up 0.0017 0.011 0.0114

down 0.0006 -0.0046 -0.0045

Total Syst. +0.0125 +0.1208 +0.101

-0.0116 -0.1277 -0.1084

B

Systematics: Covariance Matrix

The covariance matrix for each systematic uncertainty component, k, is defined as:

C_syst,k =





 σ_F²

0 cF₀F_L cF₀F_R cF0FL σ²_F

L cFLFR

cF₀F_R cF_LF_R σ_F²





, (B.1)

whereσ_F_i is the uncertainty in measuring the helicity fraction,F_i, for a given system-atic component. Since each systemsystem-atic is assumed to be correlated across the different helicity fractions, the off-diagonal terms are written as:

cF_iF_j =σ_F_iσ_F_j. (B.2)

The signs of the components σ_F_i reflects whether the up/down variation has a posi-tive/negative effect on a given helicity fraction measurement with respect to the nominal measurement. For every systematic uncertainty there should be at least one positive error and at least one negative error, such that the overall normalisationF0 +FL+FR

= 1 is respected.

Once all component matrices are calculated, the full covariance matrix, C can be constructed as the sum of the statistical covariance matrix (C_stat) and the direct sum of all systematic matrices (assuming each systematic uncertainty component is uncorrelated from all others). The final covariance matrix,C, is expressed mathematically as:

C=C_stat+X

C_syst,k. (B.3)

For the fully combined measurement, i.e., the eight-channel combination of the electron

and muon channels of leptonic and hadronic analysers with 1 b-tag + ≥2 b-tags, the summed systematic matrix obtained as

Csyst=







0.00166 −0.00050 −0.00114

−0.00050 0.00034 0.00021

−0.00114 0.00021 0.00098





. (B.4)

The information for the statistical covariance matrix, Cstat, is obtained directly from the fit, and the final covariance matrix,Cstat + syst is found as

Cstat + syst=







0.00175 −0.00053 −0.00117

−0.00053 0.00035 0.00022

−0.00117 0.00022 0.00098





 (B.5)

The total covariance matrix is used as input to the EFTfitter tool, used to place limits on anomalous couplings of the W tb vertex. Since the fitter takes the correlation coefficients between the fractions as the input, the covariance matrix, C, is translated into the correlation matrix, S, via introducing the diagonal matrix Das

D=sqrt(diag(C)) (B.6)

Indeed Dis the square root of the diagonal matrix obtained fromC. From there,S is obtained via

S =D⁻¹CD⁻¹ (B.7)

The correlation coefficients, ρ can then be read from the off-diagonal elements of S.

Performing this procedure, the correlation fractions for the eight-channel combination is found as

ρ(F₀, F_L) = −0.68 ρ(F0, FR) = −0.89 ρ(F_L, F_R) = 0.37

(B.8)

The sensitivity of anomalousW tb limits derived using the eight-channel combination can be compared with the limits derived from any other region given the central values obtained from the template fit and the correlation coefficients obtained from the above procedure.

The corresponding correlation coefficients obtained from the measurement using the leptonic analyser with ≥2 b-tags results in

ρ(F0, FL) = −0.55 ρ(F₀, F_R) = −0.75 ρ(FL, FR) = 0.16

(B.9)

And finally, the correlation coefficients obtained from the hadronic analyser with 1 b-tag + ≥2 b-tags are

ρ(F₀, F_L) = 0.56 ρ(F0, FR) = −0.91 ρ(F_L, F_R) = −0.92

(B.10)

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Im Dokument Measurement of the W Boson Helicity Fractions in Top/anit-Top Events at 8 TeV in the Lepton + Jets Channel with the ATLAS Detector (Seite 156-200)