D0 Note XXXX Version 1.9

1 Measurement of σ(pp̄ → tt̄X) in τ + jets channel using 5.0 fb^{−1} of data

2 Dhiman Chakraborty (NIU), Phillip Gutierrez (Oklahoma), Diego Menezes (NIU)

3 (Dated: May 18, 2011)

This note presents a new measurement of pp̄ → tt̄X production at \sqrt{s} = 1.96 TeV using 4951.86 pb^{−1} of data collected with the DØ detector between 2002 and 2010. We focus on the final state where the W boson from one of the top quarks decays into a τ lepton and its associated neutrino, while the other W boson decays into a quark-antiquark pair. We aim to select those events in which the τ lepton subsequently decays hadronically, meaning to one or three charged hadrons, zero or more neutral hadrons and a tau neutrino. We use a neural network b-tagging algorithm as well as a topological neural network to enhance signal over the background. For a top quark mass of 172.5 GeV the preliminary result for the measured cross section is:

σ(t\overline{t}) = 8.46 _{−1.04}^{+1.06} (stat) _{−0.88}^{+0.92} (syst) ± 0.3 (lumi) pb.

Contents

I. Introduction 4

II. Dataset 6 A. Data Sample 6 B. Backgrounds 7 C. Monte Carlo Samples 7 D. MC samples corrections 9

III. Trigger Parametrization 9 A. Level 1 10 B. Level 2 10 C. Level 3 11

IV. Object Identification 12 A. Taus 12 B. Jets 12 C. E̸_{T} 13 D. The Neural Network b-tagging Algorithm 13

V. Analysis outline 14

VI. Preselection 14

VII. b and τ selections 17

VIII. Neural Network Analysis 21 A. Variables for NN training 21 B. Topological NN 21 C. NN optimization 24

IX. Topological variables 29 A. Signal sample plots 29 B. b-veto control sample plots 32

X. Cross section 35

XI. Systematic uncertainties 41 A. JES 41 B. TES 41 C. Jet Energy Resolution and Jet ID 41 D. Trigger 41 E. b-quark fragmentation 41 F. b-tagging 41 G. τ ID systematics 42 H. QCD systematics 42 I. W and Z scale factors 42 J. Template statistics 42 K. tt̄ contamination in the loose-tight sample 42 L. PDF 42 M. Luminosity 43

References 44

A. Trigger Efficiencies 45 1. Trigger Efficiencies for τ + jets 45 2. Trigger Efficiencies for e + jets 45 3. Trigger Efficiencies for μ + jets 46 4. Trigger Efficiencies for dilepton 46 5. Trigger Efficiencies for alljets 47 6. Trigger Efficiencies for W jj + jets 47 7. Trigger Efficiencies for W bb + jets 48 8. Trigger Efficiencies for W cc + jets 48 9. Trigger Efficiencies for Zjj + jets → ee + jj + jets 49 10. Trigger Efficiencies for Zbb + jets → ee + bb + jets 49 11. Trigger Efficiencies for Zcc + jets → ee + cc + jets 50 12. Trigger Efficiencies for Zjj + jets → μμ + jj + jets 50 13. Trigger Efficiencies for Zbb + jets → μμ + bb + jets 51 14. Trigger Efficiencies for Zcc + jets → μμ + cc + jets 51 15. Trigger Efficiencies for Zjj + jets → ττ + jj + jets 52 16. Trigger Efficiencies for Zbb + jets → ττ + bb + jets 52 17. Trigger Efficiencies for Zcc + jets → ττ + cc + jets 53 18. Trigger Efficiencies for Zjj + jets → νν + jj + jets 53 19. Trigger Efficiencies for Zbb + jets → νν + bb + jets 54 20. Trigger Efficiencies for Zcc + jets → νν + cc + jets 54

B. Turn on curves for trigger JT2 3JT15L IP VX 54 1. Level 1 jet turn on curves for trigger JT2 3JT15L IP VX 55 2. Level 2 jet turn on curves for trigger JT2 3JT15L IP VX 57 3. Level 2 H_{T} turn on curves for trigger JT2 3JT15L IP VX 57 4. Level 2 E̸_{T} turn on curves for trigger JT2 3JT15L IP VX 58 5. Level 2 Sphericity turn on curves for trigger JT2 3JT15L IP VX 59 6. Level 2 STTIP turn on curves for trigger JT2 3JT15L IP VX 59 7. Level 3 jet turn on curves for trigger JT2 3JT15L IP VX 60 8. Level 3 b-tag on curves for trigger JT2 3JT15L IP VX 61

C. Discriminant variables 64

D. Set optimization 65

E. Set optimization continued 67

F. E̸_{T} significance optimization 68

G. Cross section measurements when signal contamination is ignored 69

1. Results for Set = metl, H_{T}, topmassl, aplan, sqrts, metl > 4.0, lumi = 4951.86/pb, VC jets and NNelec > 0.9 69

2. Results for Set = metl, H_{T}, topmassl, aplan, sqrts, metl > 4.0, lumi = 4951.86/pb, VC jets and no NNelec cut 70 4 I. INTRODUCTION

5 Since its discovery at the Fermilab TEVATRON collider in 1995, the top quark has been one of the most 6 important topics in High Energy Physics. The study of its production rate and properties allows us to 7 perform precision tests of standard model (SM) predictions as well as represents a chance of observing 8 possible deviations from such predictions. Amongst all subsequent top decays, the process t → W b → τν_{τ} b 9 represents one of the most important tools for probing beyond-SM physics. For instance, the MSSM (Minimal 10 Supersymmetric Standard Model) [1] predicts the existence of the decay t → H^{+}b if m_{H_{−}^{+}} < m_{t} − m_{b}. As 11 the Higgs-fermion coupling is proportional to the latter’s mass, the subsequent decay of a charged Higgs 12 boson into a τ lepton is much more favored than its decays into e’s and μ’s. Therefore, for high values of tan 13 β (the ratio of the vacuum expectation values of the two Higgs doublets) the charged Higgs preferentially 14 decays to τν_{τ}, which increases the branching ratio (BR) of t → τν_{τ} b relative to the SM prediction. Thus, 15 any non-standard flavor- and mass-dependent could produce a significant effect on the τ production channel. 16 In this respect, the work presented here represents an important test of the SM predictions as well as one 17 step further on the investigation of non-SM processes. 18 In this analysis we study the process when the W boson from one of the top quarks decays into a τ lepton 19 and its associated neutrino, while the other W boson decays into a quark-antiquark pair. The τ is the 20 heaviest lepton and its prompt decay into other particles and the probability of being faked by electrons, 21 muons and jets makes its reconstruction and identification much more difficult than other top decays. 22 Here we focus on events where the τ decays hadronically, meaning to one or three charged hadrons, zero 23 or more neutral hadrons and a tau neutrino. This implies that our signal consists of a final state with four or 24 more jets. Figures 1 and 2 show respectively the Feynman diagram that decribes the process tt̄ → τ + jets 25 and the pie chart of top decay. In Section II we discuss or signal and main backgrounds.

FIG. 1: Feynman diagram for tt̄→ τ + jets .

FIG. 2: Top quark decay pie chart.

26 The present work is the third measurement of the tt̄ cross section in the τ + jets channel performed with 27 the DØ detector. Previous results [2, 3] used using p14 RunI and p17 RunIIa Data and are summarized in 28 Table I (only statistical uncertainties are shown).

Data set (pb^{−1}) cross section (pb)
p14 (349.0)  5.05 _{−3.46}^{+4.31}
p17 (974.2)  6.90 _{−1.20}^{+1.20}

TABLE I: Previous tt̄ cross section measurements in the τ + jets channel

29 The main improvements upon previous p17 analysis are listed below: 30 • 5 times more data (RunIIb1, RunIIb2 and RunIIb3). 31 • Trigger used: we use a new set of multijet triggers that represents a gaim of 10% in the final efficiency. 32 • Use of vertex confirmed jets. 33 • Tau energy scale added to the analysis. 34 • Improved neural net (NN) optimization. 35 • New set of p20 b-tag TRF’s.

36 II. DATASET

37 A. Data Sample

38 For this analysis the framework used was vjets cafe v04-00-08 (Release p21.18.00) and the data set consisted 39 of 3JET skim produced by the commom samples group [4] and recorded between August 2002 and May 2010 40 (runs 151817 - 258547).

41 • CSG CAF 3JET PASS2 p21.10.00

42 • CSG CAF 3JET PASS4 p21.10.00 p20.12.00

43 • CSG CAF 3JET PASS4 p21.10.00 p20.12.01

44 • CSG CAF 3JET PASS4 p21.10.00 p20.12.02

45 • CSG CAF 3JET PASS4 p21.10.00 p20.12.04

46 • CSG CAF 3JET PASS4 p21.12.00 p20.12.05 allfix

47 • CSG CAF 3JET PASS4 p21.10.00 p20.16.07 fix

48 • CSG CAF 3JET PASS4 p21.12.00 p20.16.07 summer2010

49 In this analysis we chose the three jets trigger JT2 3JT15L IP VX. 50 This particular trigger was chosen based on our needs of looking for events with multiple jets and the fact 51 that it represents a gain of 20% efficiency on signal selection if compared to previous p17 analysis. Since the 52 efficiencies for such trigger are not currently part of caf trigger package, in this analysis we benefit from the 53 trigger modelling provided by the hbb group [5] for the ϕb → bb̄b analysis. Trigger weight distributions for 54 all MC samples used in the analysis as a function of the number of b-tagged jets are found in Appendix A 55 and Table II summarizes their mean values:

Process  0 tags 1 tag 2 tags 3 or more tags
t\overline{t} → τ + jets  0.7923 0.8620 0.8953  0.9039
t\overline{t} → e + jets  0.7902 0.8599 0.8933  0.9020
t\overline{t} → μ + jets  0.7942 0.8639 0.8973  0.9058
t\overline{t} → l + l  0.7274 0.7915 0.8223  0.8302
W jj + jets → lν + jj + jets 0.5821 0.6337 0.6586  0.6652
W bb + jets → lν + bb + jets 0.5948 0.6475 0.6729  0.6796
W cc + jets → lν + cc + jets 0.5912 0.6435 0.6687  0.6754
Zjj + jets → ee + jj + jets 0.6769 0.7363 0.7646  0.7719
Zbb + jets → ee + bb + jets 0.4331 0.4712 0.4895  0.4943
Zcc + jets → ee + cc + jets 0.6167 0.6746 0.7035  0.7127
Zjj + jets → μμ + jj + jets 0.6641 0.7233 0.7520  0.7598
Zbb + jets → μμ + bb + jets 0.6057 0.6598 0.6860  0.6931
Zcc + jets → μμ + cc + jets 0.5817 0.6335 0.6585  0.6653
Zjj + jets → ττ + jj + jets 0.5712 0.6220 0.6465  0.6530
Zbb + jets → ττ + bb + jets 0.6049 0.6586 0.6845  0.6914
Zcc + jets → ττ + cc + jets 0.5889 0.6410 0.6661  0.6727
Zjj + jets → νν + jj + jets 0.5739 0.6241 0.6480  0.6541
Zbb + jets → νν + bb + jets 0.6012 0.6539 0.6790  0.6854
Zcc + jets → νν + cc + jets 0.6360 0.6914 0.7177  0.7242

TABLE II: Mean values of the trigger weight for all MC samples.

56 For this trigger we also measured the luminosity of our data sample. Table III shows the results for both 57 v15 and v16 trigger versions.

Trigger version  Trigger name Delivered L (pb^{−1}) Recorded L (pb^{−1}) Reconstructed L (pb^{−1})
V15.0 - V15.99 JT2 3JT15L IP VX  1682.08  1544.71  1385.99
V16.0 - V16.99 JT2 3JT15L IP VX  4059.92  3887.95  3565.86
T O T A L  5742.00  5432.66  4951.85

TABLE III: The results of luminosity calculation for the Run2b 3JET data skim for different D0 trigger list versions

58 B. Backgrounds

59 In this analysis the largest background sources are QCD (“fake τ”), which is estimated from data and 60 W/Z+jets, which are simulated Monte Carlo samples. Other backgrounds that were not included in this 61 analysis due to their small contribution are single top and diboson production. A list of backgrounds sources 62 is found in Section III of [3]. In the following sections we describe both signal and background simulation.

63 C. Monte Carlo Samples

64 We use p20 certified MC samples as produced by CSG and caffed with p21.11.00 (version3) [6]. All W/Z and 65 tt̄ were generated with ALPGEN v2.11 [7] interfaced with Pythia v6.409 [8] for production of parton-level 66 showers and hadronization. EvtGen [9] is used to model b hadrons decays and TAUOLA [10] used to model 67 tau leptons decays. 68 ALPGEN is a leading order (LL) generator. In order to correct it to match with next-to-leading order (NLO) 69 cross sections we apply correction factors and then provide a correct normalization. These correction factors 70 were taken from vjets cafe framework and are described in Ref.[11]. There are two kinds of correction 71 factors: k-factors, which are the result of the ratio between NLO and LL cross sections (σ_{NLO}/σ_{LL}) and 72 heavy flavor factors, which are in turn the ratio between k-factors for HF + 0lp(incl) and 2lp(incl) process 73 from MCFM [12]. Here HF denotes Z + bb, Z + cc, W + bb or W + cc and lp stands for light parton. Heavy 74 flavor factors are applied on the top of k-factors in order to provide the correct normalization for process 75 where heavy quarks are present. For Z production, samples are split into Z + light jets, Z + bb and Z + cc. 76 Z + light parton cross sections are multiplied by a k-factor of 1.3, while Z + bb and Z + cc are multiplied by 77 additional heavy flavor factors of 1.52 and 1.67 respectively. W + jets samples are also split the same way: 78 W + light jets, W + bb and W + cc. In W + light jets case a k-factor of 1.3 is applied while an additional 79 heavy flavor factor of 1.47 is applied to both W + bb and W + cc samples. 80 Table IV summarizes the correction factors applied.

Process  k-factor
W + light partons 1.3
W + bb  1.3×1.47
W + cc  1.3×1.47
Z + light partons  1.3
Z + bb  1.3×1.52
Z + cc  1.3×1.67

TABLE IV: k-factors for MC.

81 All MC samples used in this analysis are shown in Table V with theirs respective cross sections and number 82 of events. The cross sections shown are the averages of the cross-sections of each set of MC process generated 83 and are calculated from /caf mc util/mc sample info/MC.list

Sample  σ(pb) # of Events
t + t + 0lp − lν + 2b + 2lpc excl m172  1.392196  793267
t + t + 1lp − lν + 2b + 3lpc excl m172  .576927  456317
t + t + 2lp − lν + 2b + 4lpc incl m172  .281831  277912
W + 0lp → lnu + 0lp excl  4530.269741 47070044
W + 1lp → lnu + 1lp excl  1283.094130 20683540
W + 2lp → lnu + 2lp excl  306.073315 19686862
W + 3lp → lnu + 3lp excl  73.494491  4269023
W + 4lp → lnu + 4lp excl  16.958254  3084707
W + 5lp → lnu + 5lp incl  5.218917  2565942
W + 2b + 0lp → lν + 2b + 0lp excl  9.315458  1120570
W + 2b + 1lp → lν + 2b + 1lp excl  4.288365  812095
W + 2b + 2lp → lν + 2b + 2lp excl  1.554786  563315
W + 2b + 3lp → lν + 2b + 3lp incl  0.716175  464475
W + 2b + 0lp → lν + 2c + 0lp excl  24.404153  934253
W + 2b + 1lp → lν + 2c + 1lp excl  13.486806  738709
W + 2b + 2lp → lν + 2c + 2lp excl  5.459005  554236
W + 2b + 3lp → lν + 2c + 3lp incl  2.526973  469900
γZ + 0lp → ee + 0lp excl 75 130  132.086811  1212214
γZ + 1lp → ee + 1lp excl 75 130  40.060963  599588
γZ + 2lp → ee + 2lp excl 75 130  9.981935  298494
γZ + 3lp → ee + 3lp incl 75 130  3.297072  150267
γZ + 2b + 0lp → ee + 2b + 0lp excl 75 130  0.400826  200121
γZ + 2b + 1lp → ee + 2b + 1lp excl 75 130  0.173438  97474
γZ + 2b + 2lp → ee + 2b + 2lp incl 75 130  0.107248  48269
γZ + 2c + 0lp → ee + 2c + 0lp excl 75 130  0.900923  182485
γZ + 2c + 1lp → ee + 2c + 1lp excl 75 130  0.506337  89293
γZ + 2b + 2lp → ee + 2b + 2lp incl 75 130  0.285871  47357
γZ + 0lp → μμ + 0lp excl 75 130  133.850906  1553222
γZ + 1lp → μμ + 1lp excl 75 130  41.677185  639392
γZ + 2lp → μμ + 2lp excl 75 130  9.822132  446737
γZ + 3lp → μμ + 3lp incl 75 130  3.195801  172628
γZ + 2b + 0lp → μμ + 2b + 0lp excl 75 130 0.424239  210139
γZ + 2b + 1lp → μμ + 2b + 1lp excl 75 130 0.195271  101055
γZ + 2b + 2lp → μμ + 2b + 2lp incl 75 130 0.099004 49600
γZ + 2c + 0lp → μμ + 2c + 0lp excl 75 130 0.932203  193928
γZ + 2c + 1lp → μμ + 2c + 1lp excl 75 130 0.548182  92744
γZ + 2b + 2lp → μμ + 2b + 2lp incl 75 130  0.280795  51277
γZ + 0lp → ττ + 0lp excl 75 130  131.564780  1556389
γZ + 1lp → ττ + 1lp excl 75 130  40.300291  595169
γZ + 2lp → ττ + 2lp excl 75 130  10.072067  305312
γZ + 3lp → ττ + 3lp excl 75 130  3.089442  205365
γZ + 2b + 0lp → ττ + 2b + 0lp excl 75 130  0.423679  196943
γZ + 2b + 1lp → ττ + 2b + 1lp excl 75 130  0.196527  103105
γZ + 2b + 2lp → ττ + 2b + 2lp incl 75 130  0.103561  48476
γZ + 2c + 0lp → ττ + 2c + 0lp excl 75 130  0.898135  260243
γZ + 2c + 1lp → ττ + 2c + 1lp excl 75 130  0.487548  100802
γZ + 2b + 2lp → ττ + 2b + 2lp incl 75 130  0.297808  50711
γZ + 0lp → νν + 0lp excl  806.552968  2368495
γZ + 1lp → νν + 1lp excl  244.651772  2591505
γZ + 2lp → νν + 2lp excl  61.014112  657110
γZ + 3lp → νν + 3lp excl  14.091090  194705
γZ + 4lp → νν + 4lp excl  3.277295  100158
γZ + 5lp → νν + 5lp incl  0.936465  49660
γZ + 2b + 0lp → νν + 2b + 0lp excl  2.562976  375572
γZ + 2b + 1lp → νν + 2b + 1lp excl  1.143703  180558
γZ + 2b + 2lp → νν + 2b + 2lp incl  0.617265  91588
γZ + 2c + 0lp → νν + 2c + 0lp excl  5.634504  376456
γZ + 2c + 1lp → νν + 2c + 1lp excl  3.002712  199012
γZ + 2b + 2lp → νν + 2b + 2lp incl  1.635746  96147

TABLE V: MC Samples. Here l stands for the three lepton flavor (e, μ and τ). τ decays are not restricted.

84 D. MC samples corrections

85 Standard DØ corrections are applied to MC in order to obtain a better MC-data agreement [13]. 86 Trigger efficiency: an additional scale factor (weight) is applied to MC to account for the trigger efficiency 87 in data. Further details are given in Section III. 88 Luminosity reweighting: in order to reproduce luminosity effects from real data, simulated samples are 89 overlaid to Zero Bias data Due to a difference in intantaneous luminosity between the overlay and real data, 90 the luminosity profile of all MC samples is reweighted to match the luminosity profile in data [14]. 91 Primary vertex reweighting: z vertex distributions are different between data and MC.This difference 92 is corrected by reweighting MC z vertex distributions using the reweight processor from the caf mc util 93 package [15]. 94 W and Z p_{T} reweighting: for both W + jets and Z + jets, the p_{T} distribution from MC samples is 95 reweighted to match the equivalent distribution in data, accordingly to the standard way [16]. 96 b fragmentation: the systematics on the reweight of the b-fragmentation function from the default in 97 Pythia to the value tuned to reproduce collider data was assumed to be the symmetrized difference between 98 the AOD and SLD tunes [17]. 99 Jet Shifting Smearing and Removing (JSSR): due to differences in energy scale, resolution, recon-100 struction and identification between data and MC, MC jets are shifted, smeared and possibly removed using 101 standard JSSR processor [18]. In this analysis shifting is turned off to signal tt̄ and on to W/Z + jets 102 samples. 103 Tau Energy Scale (TES): due to the analysis sensitivity to any difference between data and MC in the 104 energy scale of taus decaying hadronically we apply a E/p correction to this energy scale as described in 105 [19].

106 III. TRIGGER PARAMETRIZATION

107 As aforementioned the trigger used in this analysis is JT2 3JT15L IP VX. In both v15 and v16 trigger 108 versions, this trigger has 4 terms at level 2. Currently, only three of these, the L2 H_{T}, missing E_{T} (E̸_{T}) and 109 sphericity based branches have been modelled by the hbb group [5]. Therefore these are the ones used in 110 this analysis. The missing term is the acoplanarity term, namely, L2JET(1,20,2.4) L2HT(35,6) MJT(20,10) 111 L2ACOP(168.75), which is the same in both v15 and v15 trigger lists. 112 Table VI shows the L1, L2 and L3 requirements of the trigger. 113 In its work, the hbb group has parametrized the trigger in three instantaneous luminosity (10^{32})regions: 114 low (L_{int} < 77 ), medium ( 77 ≤ L_{int} < 124 ) and high ( L_{int} ≥ 124 ). The final goal is to measure the 115 total trigger efficiency for our events. In order to do so we take into account both the trigger probabilities 116 and the b-tag probabilities. Thus, the trigger probabilities for 0, 1, 2 and 3 or more b-tagged jets are then 117 multiplied by the probabilities of 0, 1, 2 and 3 or more jets being tagged, which are themselves got from 118 TRF’s, as described in section IV D. 119 The trigger efficiency is computed as a probability (TrigWeight) which we associate to each MC event 120 with:

P = P_{t0} ∗ P_{b0} + P_{t1} ∗ P_{b1} + P_{t2} ∗ P_{b2} + P_{t≥3} ∗ P_{b≥3}  (1)

121 where P_{ti} is the trigger probability for the event if it has i b-tags and P_{bi} is in turn the probability of having 122 i b-tags in the event offline reconstruction.

123

124 What follows is a brief description of how the trigger probabilities at each level were calculated. Single-125 object turn-on curves were determined using muon triggered events from the TOPJETTRIG skim. Some 126 turn-on curves are found in Appendix B. A more complete description can be found in [5].

Level  v15
L1  CSWJT(3,8,3.2)CSWJT(2,15,2.4)CSWJT(1,30,2.4)
L2  L2JET(3,6) L2HT(75,6) SPHER(0.1) OR

L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(75,6) MJT(10,10) OR L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(100,6)

L3  L3JET(3,15,3.6) L3JET(2,25,3.6) |z_{PV}| < 35 cm BTAG(0.4)
Name  JT2 3JT15L IP VX
Level  v16
L1  CSWJT(3,8,3.2)CSWJT(2,15,2.4)CSWJT(1,30,2.4)
L2  L2JET(3,6) L2HT(75,6) SPHER(0.1) STTIP(1,5.5,3) OR

L2JET(1,30,2.6) L2JET(2,15,2.6) L2JET(3,8) L2HT(75,6) MJT(20,10) OR L2JET(1,30,2.4) L2JET(2,15,2.4) L2JET(3,8,2.4) L2HT(75,6) STTIP(1,5.5,3)

L3  L3JET(3,15,3.6) JT(2,25,3.6) |z_{PV}| < 35 cm BTAG(0.4)
Name  JT2 3JT15L IP VX

TABLE VI: Level-by-level description of trigger JT2 3JT15L IP VX. The CSWJT(x,y,z) term corresponds to x L1 jets above y GeV and within |η| < z. The JT(x,y,z) term corresponds to x jets reconstructed at L2 or L3 with p_{T} > y GeV and |η| < z. The HT(x,y) term is used only at L2 and requires that the sum of the transverse momenta of L2 jets with p_{T} > y GeV is above x GeV. The SPHER(0.1) term requires the event sphericity calculated from L2 jets to be greater than 0.1. The MJT(x,y) term corresponds to a missing transverse energy > x GeV calculated from jets with E_{T} > y GeV. The STTIP(1,5.5,3) term requires one L2STT track with an impact parameter significance greater than or equal to three and a χ^{2} < 5.5. The |z_{PV}| < 35 cm term requires the primary vertex reconstructed at L3 to be within 35 cm of the center of the detector and the BTAG(0.4) term is used only at L3 and corresponds to a cut of 0.4 on the probability for the event to not contain a b-quark.

127 A. Level 1

128 Level 1 consists of jet terms only: 1 jet with E_{T} > 30 GeV and |η| < 2.4, a second jet with E_{T} > 15 GeV 129 and |η| < 2.4 and a third jet with E_{T} > 8 GeV and |η| < 3.2. The total L1 probability is given by

P (L1) = [P (≥ 3jets) + P (= 2jets) ∗ P (≥ 1noise jet) + P (= 1jet) ∗ P (≥ 2noise jets) + P (= 0jets) ∗ P (≥ 3noise jets)]

∗ [P (≥ 2jets) + P (= 1jet) ∗ P (≥ 1noise jet) + P (= 0jets) ∗ P (≥ 2noise jets)]

∗ [P (≥ 1jet) + P (= 0jets) ∗ P (≥ 1noise jet)] (2)

130 where P (≥ xjets) is the probability of having x or more jets present in the event and P (= xjets) is 131 the probability of having exactly x jets in the event. The term noise jets refers to all those L1 jets 132 that didn’t match to an offline jet within ΔR < 0.5. In the equation above the first line corresponds 133 to the term CSWJT(3,8,|η| < 3.2), the second to the term CSWJT(2,15,|η| < 2.4) and the third to the term 134 CSWJT(1,30,|η| < 2.4). L1 jets that matched offline ones had their turn-on curves parametrized as functions 135 of offline jet pT ’s. The number of noise jets per event was parametrized as a function of offline H_{T}. All L1 136 turn-on curves are found in Appendix B 1.

137 B. Level 2

138 Level 2 part of this trigger consists of an OR of three terms (here classified as top, hbb and mjt), each with 139 a variation for v15 and v16:

140 v15 top: 3 jets with p_{T} >8 GeV, 2 with p_{T} >15 GeV, 1 with p_{T} >30 GeV and H_{T} >100 GeV

141 v16 top: 3 jets with p_{T} >8 GeV, 2 with p_{T} >15 GeV, 1 with p_{T} >30 GeV, H_{T} >75 GeV and STT IP with 142 IPSIG ≥ 3 and χ^{2} < 5.5.

143 v15 hbb: 3 jets with p_{T} >6 GeV, H_{T} >75 GeV and sphericity > 0.1

144 v16 hbb: 3 jets with p_{T} >6 GeV, H_{T} >75 GeV, sphericity > 0.1 and STT IP with IPSIG ≥ 3 and χ^{2} < 5.5.

145 v15 mjt: 3 jets with p_{T} >8 GeV, 2 jets with p_{T} >15 GeV, 1 jet with p_{T} >30 GeV, H_{T} >75 GeV and E̸_{T} 146 > 10 GeV.

147 v16 mjt: 3 jets with p_{T} >8 GeV, 2 jets with p_{T} >15 GeV, 1 jet with p_{T} >30 GeV, H_{T} >75 GeV and E̸_{T} 148 > 20 GeV.

149 For this level the net trigger probability is

\begin{aligned}P (L2) & = P (hbb ∪ mht ∪ top) \\ & = P (top) + P (hbb) + P (mht) − P (top ∩ hbb) − P (top ∩ mht) − P (hbb ∩ mht) + P (hbb ∩ mht ∩ top) \end{aligned} ; (3)

150 where P(x) corresponds to the probability of either L2, the mht, hbb or the top term firing. 151 Level 2 jet terms: from Table VI we see that for v15 trigger version, L2 jets terms are actually subsets of 152 L1. As here conditional probability is used, it means that the probability of L2 jet terms firing if L1 terms 153 fired is unity. However in v16 the Pt requirement of jets in the first trigger term was loosened from 8 to 6 154 GeV and η requirement on 8 GeV jets in the third trigger term was tightened from |η| < 3.2 to |η| < 2.4. 155 As in the L1 case, all L2 jets matching offline ones had their turn-on curves parametrized as functions of 156 offline jet p_{T} ’s, except for noise jets, whose number in each event which paratrized as funcions of offline H_{t}. 157 Turn-on curves for these cases are found in Appendix B 2. 158 Level 2 H_{T} term: this term consists of a cut of H_{T} > 75 GeV for v15 and H_{T} > 100 GeV for v16). 159 Correspondent turn-on curves are shown in Appendix B 3. 160 Level 2 E̸_{T} term: the correspondent E̸_{T} cuts are > 10 GeV and > 20 GeV for v15 and v16 respectively. 161 Their turn-on are shown in Appendix B 4. 162 L2 Sphericity Term: this term requires a sphericity cut of > 0.1. Corresponding turn-on curves are shown 163 in Appendix B 5. 164 L2 STT: the L2STTIP efficiency was measured for events in v16 which have passed the rest of the L1, 165 L2 (L2top OR L2hbb) and L3 (except L3 b-tag) trigger requirements and the offline three to five jet selec-166 tion. The efficiency was measured versus the invariant mass of the two leading jets, separately for 0, 1, 2 167 and 3 offline tight NN b-tagged events, in the three different luminosity regions. Appendix B 6 shows the 168 STTIP(1,5.5,3) efficiency versus the leading invariant di-jet mass in the low, medium and high luminosity 169 range for different number of offline b-tags.

170 C. Level 3

171 L3 consists of a jet part and a b-tag one. For the jet part of L3, turn-on curves were determined for events 172 passing both L1 and L2 requirements. Corresponding probability is given the equation below

P (L3) = [P (≥ 3jets) + P (= 2jets) ∗ P (≥ 1noise jet) + P (= 1jet) ∗ P (≥ 2noise jets) + P (= 0jets) ∗ P (≥ 3noise jets)]

∗ [P (≥ 2jets) + P (= 1jet) ∗ P (≥ 1noise jet) + P (= 0jets) ∗ P (≥ 2noise jets)] (4)

173 In the equation above the first line corresponds to the term JT(3,15,|η| < 3.6), the second to the term 174 JT(2,25,|η| < 3.6). Here was applied the same treatment to L3 jets matching offline ones and to noise jets 175 as in L1 and L2 jet terms. Corresponding turn-on curves are shown in Appendix B 1. 176 Efficiencies for the b-tag part of L3 were measured in two different ways depending whether the trigger list 177 was v15 or v16. In the v15 case events were recorded with the JT2 4JT20 and JT2 3JT12L MM3 V triggers, 178 since their L1 and L2 conditions were exactly the same. Events were further required to pass the rest of L3 179 conditions of JT2 3JT15L IP VX and the offline event selection. In the v16 case efficiencies were measured 180 in a similar fashion, but using trigger JT4 3JT15L VX (which has no L2STT or L3BTAG requirements). 181 Events were then required to have fired one of the three L2 branches of JT2 3JT15L IP VX and to pass the 182 offline three to five jet selection. All turn-on curves for both trigger lists are found in Appendix B 8.

183 IV. OBJECT IDENTIFICATION

184 In this section we describe the main objects used in this study: E̸_{T} , jets and hadronic tau candidates.

185 A. Taus

186 Taus are reconstructed in the DØ detector from energy in the calorimeter and one or more tracks.The tau 187 reconstruction algorithm uses a cone of ΔR = \sqrt{δη^{2} + δϕ^{2}} < 0.5 and an inner cone of ΔR < 0.3 is used to 188 calculate tau isolation variables. 189 For us, the most important discriminating variables for τ-leptons are [20]:

190 • Profile - \frac{E_{T}^{1} +E_{T}^{2}}{∑_{i} E_{T}^{i}} , where E_{T}^{i} is the E_{T} of the i^{th} highest E_{T} tower in the cluster.

191 • Isolation, defined as \frac{E(0.5)−E(0.3)}{E(0.3)}, where E(R) is the energy contained in a y, ϕ of radius R around the 192 calorimeter cluster centroid.

193 • Track isolation, defined as scalar sum of the p′_{T} of non-τ tracks in a η, ϕ cone of 0.5 around the 194 calorimeter cluster centroid divided by similar sum for tracks associated with τ.

195 Such variables are chosen based on the possible tau decays:

196 • electron or muon (τ → eν_{e}ν_{τ} or τ → μν_{μ}ν_{τ}), BR = 35% .

197 • single charged hadron and no neutral hadrons (τ → π^{−}ν_{τ}), BR =12% .

198 • single charged hadron + ≥ 1 neutral hadron (i.e., τ → ρ^{−}ν_{τ} → (π^{0} + π^{−})ν_{τ}) , BR = 38% .

199 • 3 charged hadrons + ≥ 0 neutral hadrons, BR = 15% (so-called “3-prong” decays).

200 which leads us classificate reconstructed taus into three different types depending on the number of tracks 201 and electromagnetic (EM) clusters [21]:

202 1. Type1: calorimeter cluster, one matched charged track and no associated EM subcluster. Mainly 203 τ → π^{−}ν_{τ}.

204 2. Type2: calorimeter cluster, one matched charged track and one or more associated EM subclusters. 205 Mainly τ → ρ^{−}ν_{τ} → π^{0}π^{−}ν_{τ}.

206 3. Type3: calorimeter cluster, two or more matched charged tracks and with or without EM subcluster. 207 Mainly τ → π^{−}π^{−}π^{+}(π^{0})ν_{τ}.

208 In order to provide an optimal tau identification,three Neural Networks (NNs) are trained to identify the 209 three types of the taus (1,2 and 3). 210 The output of these NNs provides a set of three variables (nnout = 1,2,3) to be used to select the tau in 211 the event. The types roughly correspond to the τ lepton decay modes. High values of NN correspond to the 212 physical taus, while low ones should indicate jets misidentified as taus (fakes).

213 B. Jets

214 Jets are identified using the RunII cone algorithm [22] with cone size of ΔR < 0.5. The jet algorithm T42 215 [23] is ran before jet reconstruction to remove isolated small energy deposits due to noise. DØ standard jet 216 quality cuts [24] include L1 Trigger information, calorimeter electromagnetic fraction and coarse hadronic 217 fraction. 218 Jets used in this analysis are required to have at least two primary vertex tracks associated to them 219 (vertex confirmed jets). It implies that although a calorimeter cluster is still reconstructed as a jet, it will 220 be discarded if it has less than 2 associated PV tracks. In order to correct the energies of reconstructed 221 jets in data and MC back to parton-level energies, we apply certified jet energy scale correction (JES)[25]. 222 Additionally, jets containing a muon with ΔR(μ, jet) < 0.5 from a b-quark decay are corrected to take into 223 account the momentum carried away by the muon and the neutrino [26].

224 C. E̸_{T}

225 Presence of neutrinos in an event causes an imbalance of energy in the transverse plane (E̸_{T} ). This quantity 226 is calculated from the transverse energies of all calorimeter cells that pass the T42 algorithm, except those 227 of the coarse hadronic layers due to high noise level. However, they are included in the case that they are 228 clustered within a reconstructed jet. This raw E̸_{T} is corrected for the energies of other objects like photons, 229 electrons, taus and jets. As muons deposit only a small portion of their energy in the calorimeter, their 230 momenta is subtracted from the E̸_{T} vector.

231 D. The Neural Network b-tagging Algorithm

232 Being QCD and W + jets the main sources of backgrounds in this analysis, requiring the presence of 233 at least one jet coming from a b-quark is a very powerful method of background rejection. The b-tagging 234 algorithm used in this measurement is a Neural Network (NN) tagging algorithm developed by the b-ID 235 group [27], which combines 7 characteristic variables of SVT, JLIP and CSIP tagging algorithms into the 236 NN discriminant. As in the previous analysis we have chosen the operating point TIGHT, which is equivalent 237 to requiring the NN discriminant output to be greater than 0.775. Both the average efficiency and fake rate 238 are comparable between this p20 version of the algorithm and the version used in p17 [28]. 239 a. b-tagging efficiency In data we apply the b-tagging algorithm directly to jets selected in our sample. 240 In MC such “direct tag” is not done. Instead we have to apply a certain efficiency to MC samples. This 241 inclusive b-decay efficiency (ϵ_{b}) is measured in data and it is the product of the probability to tag a b-jet in 242 an MC sample (ϵ_{b}^{MC}) containing inclusive decays of the b quark times a scale factor. This data/MC scale 243 factor is given by the ratio of data semileptonic efficiency (ϵ_{b→μ}^{DAT A}) and a MC semileptonic efficiency (ϵ_{b→μ}^{MC}). 244 This scale factor, that measures the effect on the tagging rate caused by the differences in tracking between 245 data and MC, is then used to properly scale the MC-derived efficiency. It is assumed that such factor could 246 be applied to any MC tagging efficiency [27]. 247 b. c-tagging efficiency It is assumed that the same procedure adopted in the b-jet case is also valid for 248 c-jets, namely, a c-jet scale factor (ϵ_{b→μ}^{DAT A})/(ϵ_{b→μ}^{MC}) multiplies the probability to tag a c-jet in an MC sample 249 (ϵ_{b}^{MC}) to get the c-tagging efficiency. 250 c. Light jet tagging efficiency The b-tag fake rate from light quarks is computed by measuring the 251 negative tag rate as defined in [29]. The method uses fits of b-, c- and light jets tagging rates to binned data 252 combined with sample composition estimated from data. Binned NN output (NN_{out}) distributions for b, c 253 and light jets is fitted to data distribution using b- and c-jet efficiencies provided by standard bID TRF’s. 254 d. Taggability b-tag algorithm can’t be applied to any jet, but only the ones that contain tracks. Such 255 jets are called “taggable” and are defined by matching within ΔR < 0.5 to a track jet, composed of at 256 least two tracks. Just like b-tagging, taggability is different in data and MC, due to imperfect simulation of 257 tracking system. To account for this, taggability rate functions are applied to MC events. Such functions 258 are parametrized in terms of jet p_{T}, jet η and primary vertex z. They were derived on the single top loose 259 data samples, where the isolation quality of the lepton is loose.The validity of these functions is tested 260 by comparing observed and predicted taggability to tight samples. The results show a good agreement as 261 described in [30].

262 V. ANALYSIS OUTLINE

263 Up to this point we have presented the data sample used in this analysis (Section II A) the Monte Carlo 264 samples and corrections applied to them (Sections II C and II D), the trigger used and its simulation (Section 265 III) and the object ID method (Section IV). Now we describe the next steps of the analysis towards the final 266 crosse section measurement:

267 • Preselection (section VI): at least 4 jets, at least one τ with NN>0.3 and p_{T} > 10 GeV/c, 15 GeV ≤ 268 E̸_{T} ≤ 500 GeV and E̸_{T} significance >4.0.

269 • τ- and b-ID cuts (section VII): at least one good τ lepton candidate and at least one tight NN b-tag 270 are required.

271 • Topological NN (section VIII B): a feed-forward NN’s is trained in order to provide signal-background 272 separation. The NN was optimized by testing different sets of topological variables as its inputs and 273 by applying different E̸_{T} significance cuts.

274 • Topological Variables (section IX): section showing final analysis plots of topological variables of 275 interest.

276 • Cross Section (section X) The signal fraction determination is combined with integrated luminosity 277 measurement to calculate the cross section. Systematic uncertainties are determined by fluctuating the 278 significant components up and down by one standard deviation one at a time, propagating it through 279 the entire procedure.

280 VI. PRESELECTION

281 The preselection is the first step of the analysis. The cuts presented here were chosen in order to provide 282 the best background reduction and enhance the tt̄ content at this point. The cuts are the similar to those 283 used in the p17 analysis [3] except that for this time we opted to optimize the value of E̸_{T} significance along 284 with the sets of variables we used as inputs to NN training (Section VIII). Cuts shown below were applied 285 to samples shown in Table V as well as to data as shown in Section II A.

286 • At least 4 jets with p_{T} > 15 GeV and η <2.5, with leading (in p_{T}) jet p_{T} > 35 GeV and second and 287 third jets have p_{T} > 25 GeV

288 • at least one τ with NN>0.3 and p_{T} > 10 GeV

289 • 15 GeV ≤ E̸_{T} ≤ 500 GeV

290 • E̸_{T} significance ≥ 4.0

291 • No isolated electron or muon. This is done in order to ensure orthogonality with other DØ measure-292 ments ([31] and [32]) - events that pass the lepton preselection cuts from these measurements were 293 vetoed. Also events that pass the all-jets analysis preselection cuts (described in the alljet analysis 294 note [33]) are rejected here.

295 Among all preselection cuts one of them requires a more detailed description at this point since it represents 296 an improvement upon the old p17 analysis: E̸_{T} significance. Missing transverse energy significance is a 297 measure of the likelihood of E̸_{T} arising from physical sources. It is computed from calculated resolutions 298 of physical objects (jets, electrons, muons and unclustered energy) [3, 34]. Initially no E̸_{T} significance was 299 applied neither on MC nor on data. In this analysis we decided to optimize the E̸_{T} significance cut along 300 with the NN optimization itself. After finishing the E̸_{T} significance optimization part we went back and 301 applied the optimized cut along with the non-optimized NNelec cut only to MC. The entire optimization 302 procedure is described in Section VIII C. 303 In data, initially the sample contained approximately 650 million events and the number of preselected 304 events (once again, without E̸_{T} significance applied) is approximately 2.8 million events. 305 Another relevant aspect of the preselection is the usage of Particle Selector (only applied to MC samples). 306 In this step we aimed to select a particular tt̄ final state, namely, we split W decay into W → e/μ/τ and 307 tracked separate efficiencies for each of these processes. In this step we selected hadronic decays of tau, and 308 at the same events where tau decays into electrons and muons were put into e + jets and μ + jets samples. 309 As in p17, we decided to do not split the dilepton sample in different lepton flavors. 310 Before proceeding to the next step, it is important to describe the result of the preselection in terms of 311 its efficiencies since all the rest of analysis strongly depends on the cuts applied at this level. As previously 312 described, tt̄ were generated by ALPGEN. In ALPGEN, different process with different numbers of partons 313 have different cross-sections and number of events. This fact must be taken into account when calculating 314 the efficiencies, namely, efficiencies must be properly scaled to the luminosity (4951.85 pb^{−1}) of the sample. 315 Tables VI and III show the number beforementioned for tt̄→ lepton + jets and tt̄→ dilepton respectively.

Process  # of events cross-section (pb) alpgen weight
0 light parton  777068  1.4  0.00892
1 light parton  457782  0.577  0.00624
≥ 2 light partons 321166  0.267  0.00412

TABLE VII: tt̄→ lepton + jets ALPGEN weights.

Process  # of events cross-section (pb) alpgen weight
0 light parton  749642  0.352  0.00233
1 light parton  452177  0.142  0.00156
≥ 2 light partons 281453  0.068  0.00119

TABLE VIII: tt̄→ dilepton ALPGEN weights.

316 Tables IX, X, XI and XII show cut flows for all preselection cuts applied to different tt̄ decays (only 317 statistical uncertainties are shown).

Selection  Events Relative  Cumulative
Initial  11164
Particle selector  2412 21.60 ± 0.03 % 21.60 ± 0.03 %
Duplicate events removal 2411 99.98 ± 0.01 % 21.60 ± 0.03 %
Event quality  2315 96.00 ± 0.04 % 20.74 ± 0.03 %
Jet selection  1307 59.45 ± 0.09 % 11.70 ± 0.03 %
Vertex selection  1296 99.18 ± 0.02 % 11.61 ± 0.03 %
Electron veto  1282 98.93 ± 0.01 % 11.49 ± 0.03 %
Muon veto  1282 99.93 ± 0.01 % 11.48 ± 0.03 %
MET selection  1218 95.05 ± 0.05 % 10.91 ± 0.02 %
MET significance  772 63.39 ± 0.12 % 6.92 ± 0.02 %
NN tau cut  394 53.51 ± 0.15 % 3.70 ± 0.02 %
TABLE IX: Preselection t\overline{t} → τ + jets cut flow

Selection  Events Relative  Cumulative
Initial  11164
Particle selector  4385 39.28 ± 0.04 % 39.28 ± 0.04 %
Duplicate event removal 4383 99.96 ± 0.01 % 39.26 ± 0.04 %
Event quality  4207 95.97 ± 0.03 % 37.68 ± 0.04 %
Jet selection  1923 45.71 ± 0.07 % 17.22 ± 0.03 %
Vertex selection  1907 99.20 ± 0.02 % 17.08 ± 0.03 %
Electron veto  1048 54.94 ± 0.10 % 9.39 ± 0.02 %
Muon veto  1047 99.95 ± 0.01 % 9.38 ± 0.02 %
MET selection  1002 95.64 ± 0.05 % 8.97 ± 0.02 %
MET significance  669 66.74 ± 0.13 % 5.99 ± 0.02 %
NN tau cut  395 59.12 ± 0.16 % 3.54 ± 0.02 %
TABLE X: Preselection t\overline{t} → e + jets cut flow

Selection  Events Relative  Cumulative
Initial  11164
Particle selector  4367 39.12 ± 0.04 % 39.12 ± 0.04 %
Duplicate event removal 4366 99.96 ± 0.04 % 39.10 ± 0.04 %
Event quality  4189 95.95 ± 0.03 % 37.52 ± 0.04 %
Jet selection  1990 47.52 ± 0.07 % 17.83 ± 0.03 %
Vertex selection  1975 99.23 ± 0.02 % 17.69 ± 0.03 %
Electron veto  1967 99.59 ± 0.01 % 17.62 ± 0.03 %
Muon veto  1170 59.48 ± 0.09 % 10.48 ± 0.02 %
MET selection  1127 96.31 ± 0.04 % 10.09 ± 0.02 %
MET significance  812 72.06 ± 0.11 % 7.27 ± 0.02 %
NN tau cut  186 22.95 ± 0.13 % 1.67 ± 0.01 %
TABLE XI: Preselection t\overline{t} → μ + jets cut flow

Selection  Events  Relative  Cumulative
Initial  2799
Particle selector  2799 100.00 ± 0.00 % 100.00 ± 0.00 %
Duplicate event removal 2799 100.00 ± 0.00 % 100.00 ± 0.00 %
Event quality  2685 95.92 ± 0.02 % 95.92 ± 0.02 %
Jet selection  145 5.41 ± 0.02 % 5.19 ± 0.02 %
Vertex selection  144 99.32 ± 0.03 % 5.16 ± 0.02 %
Electron veto  110 76.14 ± 0.13 % 3.93 ± 0.01 %
Muon veto  83 75.08 ± 0.16 % 2.95 ± 0.01 %
MET selection  80 96.45 ± 0.08 % 2.84 ± 0.01 %
MET significance  60 75.32 ± 0.19 % 2.14 ± 0.01 %
NN tau cut  38 63.21 ± 0.24 % 1.35 ± 0.01 %
TABLE XII: Preselection t\overline{t} → l + l cut flow

318 VII. b AND τ SELECTIONS

319 In the next step we applied the requirements of tight τ- and b-tagging. Table XIII shows the selection 320 criteria that we applied to data and MC. The b-tag operating point used was TIGHT, which corresponds 321 to NNbtag > 0.775. We chose the τ with the highest NN_{τ} as the τ candidate. At this stage of the analysis 322 we separated the events dataset we deal with into parts, according to which type of τ the candidate with 323 highest NN belongs. This was done primarily to separate the type 3 tau events (which are expected to 324 have much higher fake rate and thus weaker tt̄ cross section result) from the type 2 events. The separate 325 measurement channels were later combined to get the final result (Section X). In principle, types 1 and 2 326 should be separated as well but as there exists a considerable cross-migration between them [20] and type 327 1 is a small fraction of the total (10% of type 1, 54.5% of type 2 and 35.5% of type 3), they were taken 328 togetther in this analysis. The topological NN used to enhance the signal content is described in section 329 VIII B . 330 At this point, we used these ID algorithms to define 3 mutually exclusive and exhastive subsamples out 331 of the original preselected data sample:

332 • The “non-b veto” or “signal” sample - the τ candidate has NN_{τ} > 0.90 (NN_{τ} denotes the NN cut 333 commonly applied to all taus) for taus types 1 and 2 and NN(τ) > 0.95 for taus type 3, and at least 334 one NN b-tag (as in Table XIII). These NN(τ) cuts were chosen based on previous studies involving 335 hadronic decays of taus [19, 37]. This is the sample used to extract the cross section. Jets matched to 336 τ candidates are not b-tagged, althought they still count as jets.

337 • The “τ veto sample” or “loose-tight τ sample” - Same selection, but with 0.3 < NN_{τ} < 0.7 for all 338 taus. τ NN lower cut of 0.3 instead of 0.0 was chosen to bias their jet properties closer to those of 339 tight tau candidates, in particular, so they have narrow showers. The upper cut is at 0.7 and not 0.95 340 or 0.90 to reduce signal contamination. In this sample, 1400000 events were used for NN training for 341 taus type 1 and 2 and 600000 events were used in the case of type 3 taus. In both cases, the rest of 342 the samples served as QCD template.

343 • The “b veto” sample - Require exactly 0 tight b-tags. This is the control sample used to verify the 344 validity of the QCD modelling method. The b veto requirement implies this sample is almost purely 345 background.

346 Along with the NN_{τ} cut described above, we also applied the cut NNelec > 0.9 only to type 2 taus since 347 these are more likely to be faked by electrons. The cut NNelec > 0.9 was chosen in order to match the lowest 348 cut of NN_{τ} > 0.9 applied to type 2 taus (Section VII). 349 As both b and τ ID is the step immediately after the preselection, the number of events available is 2800000 350 million events. As explained above 1400000 events were used for taus type 1 and 2 NN training and 600000 351 for type 3 taus NN training. Thus, there are 1400000 events available in each sample for the measurement 352 in the case of types 1 and 2 and 2200000 in the case of type 3. Details on NN training are given in Section 353 VIII B. 354 The QCD modelling method used here is the same as used in p17 and is described in Section IXA of [3]. 355 The final number of events in each channel for both signal and b veto samples is shown on Tables XIV, 356 XV, XVI and XVII (only statistical uncertainties are shown). 357 As important as determining the subsamples to be used in this analysis, a determination as precise as 358 possible of both signal and electroweak contamination in the “loose-tight τ sample” had be done in order 359 to know whether this sample is totally QCD dominated or not. Numbers showing the composition of such 360 sample are shown on Tables XVIII and XIX with their respective statistical uncertainties. From the tt̄content 361 in each case we are able estimate the signal contamination in the loose-tight sample. Such contaminations 362 are 5.4% and 3.0% for taus type 1 and 2 and type 3 respectively when a cross section of 7.46 pb is assumed 363 (Section II C). Likewise we see that electroweak contaminations are 2.2% and 0.9%. As this is the sample 364 used to model the QCD background both signal and electroweak contaminations were taken into account 365 when measuring the cross section in Section X.

data  taggingMC
≥ 1 τ with |η| < 2.5 and p_{T} > 20 GeV  ≥ 1 τ with |η| < 2.5 and p_{T} > 20 GeV
≥ 1 NN b-tag  mcweight · T rigW eight · bT agP rob · lumiReW eight · P V zReW eight · bF ragW eight
·W ZP tReweight
≥ 4 jets with |η| < 2.5 and p_{T} > 20 GeV  ≥ 4 jets with |η| < 2.5 and p_{T} > 20 GeV

TABLE XIII: b-tagging and τ ID. In the MC, we use the b-tagging certified parameterization rather than actual b-tagging, that is, we applied the b-tagging weight. We also used the triggering weight as computed by the trigger efficiency parameterization as well as luminosity profile and P V_{Z} reweighting weights. mcweight is the MC normalization factors (to luminosity), which are different for MC samples with different parton multiplicities in ALPGEN MC samples.

Sample  # events
data  386
t\overline{t} → τ + jets  48.03 ± 0.53
t\overline{t} → e + jets  25.57 ± 0.36
t\overline{t} → μ + jets  3.21 ± 0.14
t\overline{t} → l + l  4.01 ± 0.07
W bb + jets → lν + bb + jets 7.48 ± 0.30
W cc + jets → lν + cc + jets 4.68 ± 0.17
W jj + jets → lν + jj + jets 5.66 ± 0.11
Zbb + jets → ττ + bb + jets 0.93 ± 0.08
Zcc + jets → ττ + cc + jets 0.51 ± 0.04
Zjj + jets → ττ + jj + jets 1.07 ± 0.10
Zbb + jets → ee + bb + jets 0.03 ± 0.01
Zcc + jets → ee + cc + jets 0.00 ± 0.00
Zjj + jets → ee + jj + jets 0.02 ± 0.01
Zbb + jets → μμ + bb + jets 0.07 ± 0.02
Zcc + jets → μμ + cc + jets 0.02 ± 0.01
Zjj + jets → μμ + jj + jets 0.01 ± 0.01
Zbb + jets → νν + bb + jets 0.08 ± 0.03
Zcc + jets → νν + cc + jets 0.00 ± 0.00
Zjj + jets → νν + jj + jets 0.04 ± 0.01

TABLE XIV: Final number of events in each channel for taus types 1 and 2 τ after b-tagging, τ ID and trigger in the signal sample when the assumed cross section is 7.46 pb. An estimate of QCD background is not included.

Sample  # of events
data  459
t\overline{t} → τ + jets  25.88 ± 0.39
t\overline{t} → e + jets  4.35 ± 0.16
t\overline{t} → μ + jets  3.43 ± 0.14
t\overline{t} → l + l  2.80 ± 0.06
W bb + jets → lν + bb + jets 3.92 ± 0.17
W cc + jets → lν + cc + jets 3.26 ± 0.15
W jj + jets → lν + jj + jets 4.08 ± 0.11
Zbb + jets → ττ + bb + jets 0.74 ± 0.07
Zcc + jets → ττ + cc + jets 0.41 ± 0.03
Zjj + jets → ττ + jj + jets 0.80 ± 0.10
Zbb + jets → ee + bb + jets 0.00 ± 0.00
Zcc + jets → ee + cc + jets 0.01 ± 0.01
Zjj + jets → ee + jj + jets 0.01 ± 0.01
Zbb + jets → μμ + bb + jets 0.04 ± 0.02
Zcc + jets → μμ + cc + jets 0.01 ± 0.01
Zjj + jets → μμ + jj + jets 0.00 ± 0.00
Zbb + jets → νν + bb + jets 0.12 ± 0.04
Zcc + jets → νν + cc + jets 0.19 ± 0.04
Zjj + jets → νν + jj + jets 0.06 ± 0.01

TABLE XV: Final number of events in each channel for taus type 3 τ After b-tagging, τ ID and trigger in the signal sample when the assumed cross section is 7.46 pb. An estimate of QCD background is not included.

Sample  # of events
data  2494
t\overline{t} → τ + jets  33.57 ± 0.34
t\overline{t} → e + jets  15.67 ± 0.23
t\overline{t} → μ + jets  2.30 ± 0.09
t\overline{t} → l + l  2.69 ± 0.04
W bb + jets → lν + bb + jets 9.29 ± 0.27
W cc + jets → lν + cc + jets 31.63 ± 0.90
W jj + jets → lν + jj + jets 169.95 ± 2.68
Zbb + jets → ττ + bb + jets 1.30 ± 0.11
Zcc + jets → ττ + cc + jets 3.15 ± 0.20
Zjj + jets → ττ + jj + jets 16.86 ± 1.14
Zbb + jets → ee + bb + jets 0.02 ± 0.01
Zcc + jets → ee + cc + jets 0.00 ± 0.00
Zjj + jets → ee + jj + jets 0.74 ± 0.33
Zbb + jets → μμ + bb + jets 0.08 ± 0.02
Zcc + jets → μμ + cc + jets 0.07 ± 0.03
Zjj + jets → μμ + jj + jets 0.38 ± 0.22
Zbb + jets → νν + bb + jets 0.10 ± 0.03
Zcc + jets → νν + cc + jets 0.00 ± 0.00
Zjj + jets → νν + jj + jets 1.36 ± 0.49

TABLE XVI: b-veto data set composition for types 1 and 2 τ when the assumed cross section is 7.46 pb.

Sample  # of events
data  3688
t\overline{t} → τ + jets  19.85 ± 0.27
t\overline{t} → e + jets  3.53 ± 0.13
t\overline{t} → μ + jets  2.80 ± 0.10
t\overline{t} → l + l  1.81 ± 0.03
W bb + jets → lν + bb + jets 5.26 ± 0.19
W cc + jets → lν + cc + jets 22.43 ± 0.80
W jj + jets → lν + jj + jets 126.41 ± 2.60
Zbb + jets → ττ + bb + jets 0.92 ± 0.09
Zcc + jets → ττ + cc + jets 2.86 ± 0.20
Zjj + jets → ττ + jj + jets 14.53 ± 1.15
Zbb + jets → ee + bb + jets 0.00 ± 0.00
Zcc + jets → ee + cc + jets 0.08 ± 0.04
Zjj + jets → ee + jj + jets 0.31 ± 0.18
Zbb + jets → μμ + bb + jets 0.04 ± 0.02
Zcc + jets → μμ + cc + jets 0.05 ± 0.02
Zjj + jets → μμ + jj + jets 0.05 ± 0.04
Zbb + jets → νν + bb + jets 0.16 ± 0.05
Zcc + jets → νν + cc + jets 0.83 ± 0.15
Zjj + jets → νν + jj + jets 2.31 ± 0.46

TABLE XVII: b-veto data set composition for type 3 τ when the assumed cross section is 7.46 pb.

Sample  # of events
data  1217
t\overline{t} → τ + jets  32.94 ± 0.48
t\overline{t} → e + jets  17.02 ± 0.34
t\overline{t} → μ + jets  14.37 ± 0.32
t\overline{t} → l + l  2.43 ± 0.06
W bb + jets → lν + bb + jets 6.33 ± 0.23
W cc + jets → lν + cc + jets 4.63 ± 0.19
W jj + jets → lν + jj + jets 11.34 ± 0.26
Zbb + jets → ττ + bb + jets 0.50 ± 0.06
Zcc + jets → ττ + cc + jets 0.58 ± 0.06
Zjj + jets → ττ + jj + jets 1.10 ± 0.13
Zbb + jets → ee + bb + jets 0.01 ± 0.01
Zcc + jets → ee + cc + jets 0.01 ± 0.01
Zjj + jets → ee + jj + jets 0.00 ± 0.00
Zbb + jets → μμ + bb + jets 0.03 ± 0.01
Zcc + jets → μμ + cc + jets 0.04 ± 0.01
Zjj + jets → μμ + jj + jets 0.02 ± 0.01
Zbb + jets → νν + bb + jets 1.07 ± 0.17
Zcc + jets → νν + cc + jets 0.57 ± 0.10
Zjj + jets → νν + jj + jets 0.36 ± 0.04

TABLE XVIII: loose-tight data set composition for types 1 and 2 τ when the assumed cross section is 7.46 pb.

Sample  # of events
data  4733
t\overline{t} → τ + jets  51.16 ± 0.57
t\overline{t} → e + jets  40.02 ± 0.50
t\overline{t} → μ + jets  48.00 ± 0.56
t\overline{t} → l + l  2.16 ± 0.05
W bb + jets → lν + bb + jets 8.95 ± 0.27
W cc + jets → lν + cc + jets 7.80 ± 0.23
W jj + jets → lν + jj + jets 16.32 ± 0.30
Zbb + jets → ττ + bb + jets 0.52 ± 0.05
Zcc + jets → ττ + cc + jets 0.46 ± 0.04
Zjj + jets → ττ + jj + jets 1.16 ± 0.12
Zbb + jets → ee + bb + jets 0.00 ± 0.00
Zcc + jets → ee + cc + jets 0.00 ± 0.00
Zjj + jets → ee + jj + jets 0.01 ± 0.01
Zbb + jets → μμ + bb + jets 0.06 ± 0.01
Zcc + jets → μμ + cc + jets 0.07 ± 0.01
Zjj + jets → μμ + jj + jets 0.11 ± 0.02
Zbb + jets → νν + bb + jets 2.49 ± 0.24
Zcc + jets → νν + cc + jets 1.90 ± 0.14
Zjj + jets → νν + jj + jets 1.28 ± 0.08

TABLE XIX: loose-tight data set composition for type 3 τ when the assumed cross section is 7.46 pb.

366 VIII. NEURAL NETWORK ANALYSIS

367 A. Variables for NN training

368 Following the same procedure as in the previous analysis, we determine the content of signal and background 369 in the preselected sample, increase signal/background rate and from this, measure the cross-section. The 370 procedure adopted in the p17 analysis was feed a set of topological variables into an artificial neural network 371 in order to provide the best possible separation between signal and background. As before, the criteria for 372 choosing such variables were: power of discrimination and τ-uncorrelated variables. The set is presented 373 below:

374 • H_{T} - the scalar sum of all jet’s p_{T} (here and below including τ lepton candidates).

375 • E̸_{T} significance - As being the variable that provides the best signal-background separation we 376 decided to optimize it.

377 • Aplanarity [35] - the normalized momentum tensor is defined as

M = \frac{∑_{o} p_{i}^{o}p_{j}^{o}}{∑_{o} |\overrightarrow{p^{o}}|}  (5)

378 where \overrightarrow{p^{0}} is the momentum-vector of a reconstructed object o and i and j are cartesian coordinates. 379 From the diagonalization of M we find three eigenvalues λ_{1} ≥ λ_{2} ≥ λ_{3} with the constraint λ_{1}+λ_{2}+λ_{3} = 380 1. The aplanarity A is given by A = \frac{3}{2}λ_{3} and measures the flatness of an event. Hence, it is defined 381 in the range 0 ≤ M ≤ 0.5. Large values of A correspond to more spherical events, like tt̄ events for 382 instance, since they are typical of decays of heavy objects. On the other hand, both QCD and W +jets 383 events are more planar since jets in these events are primarily due to initial state radiation.

384 • Sphericity [35] - being defined as S = \frac{3}{2}(λ_{2} + λ_{3}), and having a range 0 ≤ S ≤ 1.0, sphericity is a 385 measure of the summed p_{⊥}^{2} with respect to the event axis. In this sense a 2-jets event corresponds to 386 S ≈ 0 and an isotropic event S ≈ 1. tt̄ events are very isotropic as they are typical of the decays of 387 heavy objects and both QCD and W + jets events are less isotropic due to the fact that jets in these 388 events come primarily from initial state radiation.

389 • Top and W mass likelihood - a χ^{2}-like variable. L ≡ (\frac{M_{3j}−m_{t}}{σ_{t}} )^{2} + (\frac{M_{2j}−M_{W}}{σ_{W}} )^{2}, where 390 m_{t}, M_{W} , σ_{t}, σ_{W} are top and W masses (172.4 GeV and 81.02 GeV respectively) and resolution val-391 ues (19.4 GeV and 8.28 GeV respectively). M_{3j} and M_{2j} are invariant masses composed of the jet 392 combinations. We choose combination that minimizes L.

393 • Centrality, defined as \frac{H_{T}}{H_{E}} , where H_{E} is sum of energies of the jets.

394 • cos(θ∗) - The angle between the beam axis and the highest-p_{T} jet in the rest frame of all the jets in 395 the event.

396 • \sqrt{(}s) - The invariant mass of all jets and τs in the event.

397 The chosen variables are in the end a consequence of the method employed in this analysis: use events 398 from the QCD-enriched loose-tight sample to model QCD events in the signal-rich sample, and use a b-tag 399 veto sample as an independent control sample to check the validity of such background modeling.

400 B. Topological NN

401 For training the Neural Network we used the Multilayer Perceptron algorithm, as described in [38]. As 402 explained before in Section VII, the first 1400000 events in the “loose-tight” sample were used as background 403 for NN training for taus types 1 and 2, and the first 600000 of the same sample for NN training for type 3 404 taus. This means that different tau types are being treated separately in the topological NN. In both cases 405 1/3 of the Alpgen sample of tt̄ → τ + jets was used for NN training and 2/3 of it for the measurement. 406 When doing the measurement later on (Section X) we pick the tau with the highest NN(τ) in the signal 407 sample as the tau cadidate at same time that taus in the loose-tight sample are picked at random since all 408 of them are regarded as fake taus by being below the cut NN(τ) = 0.7. By doing this we expect to avoid 409 any bias when selecting real taus for the measurement. Figures 3 and 4 show the effect of each of the chosen 410 the topological event NN input variables on the final output. 411 Figures 5 and 6 show the NN output as a result of the training described above. It is evident from both 412 pictures that high values of NN correspond to the signal-enriched region.

FIG. 3: Training of topological Neural Network output for type 1 and 2 τ channel. Upper left: relative impact of each of the input variables; upper right: topological structure; lower right: final signal-background separation of the method; lower left: convergence curves.

FIG. 4: Training of topological Neural Network output for type 3 τ channel. Upper left: relative impact of each of the input variables; upper right: topological structure; lower right: final signal-background separation of the method; lower left: convergence curves.

FIG. 5: The topological Neural Network output for type 1 and 2 τ channel

FIG. 6: The topological Neural Network output for type 3 τ channel

413 C. NN optimization

414 One difference between this present analysis and the previous p17 is that we performed a NN optimization 415 along with a E̸_{T} significance optimization. Previously a cut of > 3.0 was applied to E̸_{T} significance at 416 the preselection stage and then it was included as one of the variables for NN training. This time as we 417 chose to optimize it, since it is still a good variable to provide signal-background discrimination (Figure 7). 418 It is important to stress out that after the optimization we performed the analysis with the optimized E̸_{T} 419 significance cut applied when doing both τ and b ID (Section VII), therefore after the preselection where no 420 E̸_{T} significance cut was applied. We then went back anp reprocessed (preselected) all MC samples with the 421 optimized cut. Both results, with E̸_{T} significance applied during and after preselectio were identical. We 422 then chose to present this analyis with this cut applied at the preselection level in order to have a consistent 423 cut flow throughout the analysis(Section VI).

FIG. 7: E̸_{T} significance distribution for signal and backgrounds.

424 Below we describe how we split this part of the analysis into two parts: 425 1. Set optimization: We applied an arbitrary cut on E̸_{T} significance of ≥ 4.0 and varied the set of 426 varibles going into NN training 427 2. E̸_{T} significance optimization: After chosing the best set based on the lowest RMS, we then varied 428 the E̸_{T} significance cut 429 For this part of the analysis we present the sets of variables that were taken into account to perform the 430 NN traning 431 • Set I : H_{T}, aplan (aplanarity), sqrts (\sqrt{s}) 432 • Set II : H_{T}, aplan, cent (centrality) 433 • Set III : H_{T}, aplan, spher (spherecity) 434 • Set IV : H_{T}, cent, spher 435 • Set V : aplan, cent, spher 436 • Set VI : H_{T}, aplan, sqrts, spher 437 • Set VII : H_{T}, aplan, sqrts, cent 438 • Set VIII : H_{T}, aplan, sqrts, costhetastar (cos(θ^{∗}) 439 • Set IX : H_{T}, aplan, sqrts, cent, spher 440 • Set X : H_{T}, aplan, sqrts, cent, costhetastar 441 • Set XI : H_{T}, aplan, sqrts, spher, costhetastar 442 • Set XII : metl, H_{T}, aplan, sqrts 443 • Set XIII : metl, H_{T}, aplan, cent 444 • Set XIV : metl, H_{T}, aplan, spher 445 • Set XV : metl, H_{T}, cent, spher 446 • Set XVI : metl, H_{T}, aplan 447 • Set XVII : metl, H_{T}, sqrts 448 • Set XVIII : metl, aplan, sqrts 449 • Set XIX : metl, H_{T}, cent 450 • Set XX : metl, H_{T}, aplan, sqrts, cent 451 • Set XXI : metl, H_{T}, aplan, cent, spher 452 • Set XXII : metl, H_{T}, aplan, sqrts, spher 453 • Set XXIII : metl, H_{T}, aplan, sqrts, costhetastar 454 • Set XXIV : metl, sqrts, cent, spher, costhetastar 455 • Set XXV : metl, H_{T}, cent, spher, costhetastar 456 • Set XXVI : metl, aplan, cent, spher, costhetastar 457 • Set XXVII : metl, H_{T}, aplan, cent, costhetastar 458 • Set XXVIII : H_{T}, aplan, topmassl 459 • Set XXIX : H_{T}, aplan, sqrts, topmassl 460 • Set XXX : H_{T}, aplan, sqrts, cent, topmassl

461 • Set XXXI : H_{T}, aplan, sqrts, costhetastar, topmassl

462 • Set XXXII : metl, H_{T}, topmassl, aplan, sqrts

463 • Set XXXIII : metl, spher, costhetastar, aplan, cent

464 The criteria used for making a decision on which variable should be used follow:

465 • No more than 5 variables to keep NN simple and stable. More variables leads to instabilities (different 466 result after each retraining) and require larger training samples.

467 • We do not want to use highly correlated variables in same NN.

468 • We want to use variables with high discriminating power.

469 In order to make the decision about which of these 11 choices is the optimal we created an ensemble of 470 20000 pseudo-datasets each containing events randomly (according to a Poisson distribution) picked from 471 QCD, EW and tt̄ templates. Each of these datasets was treated like real data, meaning applying all the cuts 472 and doing the shape fit of event topological NN. QCD templates for fit were made from the same “loose-tight 473 τ sample” from which the QCD component of the “data” was drawn. The figure of merit chosen is given by 474 Equation 6 below:

f = \frac{(N_{fit} − N_{true})}{N_{true}}  (6)

475 where N_{fit} is the number of tt̄ pairs given by the fit and N_{true} is the number of tt̄ pairs from the Poisson 476 distribution. In both Set and E̸_{T} significance optimization, the lowest RMS was used to caracterize which 477 configuration is the best in each case. 478 The plots showing results concerning the set optimizations are found in Appendix E and are summarized 479 in Table XX below, where each RMS and mean are shown. For NN training is standard to choose the number 480 of hidden nodes as being twice the number the number of variables used for the training. The parenthesis 481 after each set ID show the number of hidden nodes in NN training. 482 From Table XX we see that Set I has the lowest RMS, thus we chose it as the set to be used in E̸_{T} 483 significance optimization part, whose results are shown in Appendix F and then summarized in Table XXI 484 below 485 Combined results from Tables XX and XXI show that the best configuration found was Set I with E̸_{T} sig-486 nificance ≥ 4.0. Therefore, this was the configuration used to perform the cross-section measurement.Figure 487 8 shows the variation of the RMS as function of the E̸_{T} significance we applied.

FIG. 8: Plot of RMS as a function the E̸_{T} significance applied

Set of variables RMS mean
Set1(6)  0.1642 0.0265
Set2(6)  0.1840 0.0054
Set3(6)  0.1923 0.0060
Set4(6)  0.1978 0.0175
Set5(6)  0.2385 0.0022
Set6(8)  0.1687 0.0115
Set7(8)  0.1667 0.0134
Set8(10)  0.1668 0.0162
Set9(10)  0.1721 0.0102
Set10(10) 0.1722 0.0210
Se11(10) 0.1716 0.0180
Set12(8)  0.1662 0.0039
Set13(8)  0.1819 0.0018
Set14(8)  0.1879 0.0019
Set15(8)  0.1884 -0.0004
Set16(6)  0.1912 0.0034
Set17(6)  0.1768 0.0074
Set18(6)  0.2216 -0.0030
Set19(6)  0.1921 0.0015
Set20(10) 0.1620 0.0262
Set21(10) 0.1753 0.0010
Set22(10) 0.1646 0.0086
Set23(10) 0.1683 0.0132
Set24(10) 0.2053 0.0122
Set25(10) 0.1906 0.0038
Set26(10) 0.2130 0.0028
Set27(10) 0.1859 0.0004
Set28(6)  0.1910 -0.0022
Set29(8)  0.1587 0.0214
Set30(10) 0.1546 0.0148
Set31(10) 0.1543 0.0203
Set32(10) 0.1468 0.0172
Set33(10) 0.2201 0.0081

TABLE XX: Results for set optimization part whit E̸_{T} significance > 4.0 applied to all sets. The number in parenthesis refers to number of hidden nodes in each case.

Set of variables E̸_{T} significance cut RMS mean
Set32(10)  3.0  0.1507 0.0157
Set32(10)  3.5  0.1559 0.0189
Set32(10)  4.0  0.1468 0.0172
Set32(10)  4.5  0.1511 0.0153
Set32(10)  5.0  0.1552 0.0205

TABLE XXI: Results for E̸_{T} significance optimization part when varying the E̸_{T} significance cut The number in parenthesis refers to number of hidden nodes in each case.

FIG. 9: Distribution of the output “measurement” for an ensemble with 116.9 tt̄ events.

FIG. 10: The ensemble test’s pull.

488 In order to check the validity of our emsemble tests procedure, it is instructive to plot both the distribution 489 of the predicted number of tt̄ and what is called “pull”, defined in Equation 7 below:

p = \frac{(N_{fit} − N_{true})}{σ_{fit}}  (7)

490 where σ_{fit} is the error on the number of tt̄ pairs given by the fit. 491 Figures 9 and 10 show both beforementioned distributions. 492 From Figure 9 we see a good agreement between the number of tt̄ pairs initially set in the ensemble and 493 the measured value. And Figure 10 shows a nice gaussian curve, that indicates a good behaviour of the fit 494 uncertainties in the ensembles.

495 IX. TOPOLOGICAL VARIABLES

496 In this section we show plots of the topological variables used in this analysis in order to check the 497 agreement between data and Monte Carlo in all cases. Plots are separated in two kinds: signal sample and 498 b-veto control plots.

499 A. Signal sample plots

500 As stated in Section VII the signal sample is the one we used to perform the measurement. The cuts here 501 consist of NN(τ) > 0.90 for taus types 1 and 2, NN(τ) > 0.95 for taus type 3, and at least one NN b-tag. 502 This sample contains a good amount of tt̄ (19.7% for types 1 and 2 and 8.6% for type 3) as shown in Tables 503 XIV and XV. Next we show the plots of the topological variables for this sample. The error bars represent 504 the statistical uncertainties only.

FIG. 11: The topological variables in the signal sample (τ types 1 and 2). The Kolmogorov-Smirnov (KS) probabilities are shown, indicating the level of agreement.

FIG. 12: The topological variables in the signal sample (τ types 1 and 2). The Kolmogorov-Smirnov (KS) probabilities are shown, indicating the level of agreement.

FIG. 13: The topological variables in the signal sample (τ types 3). The Kolmogorov-Smirnov (KS) probabilities are shown, indicating the level of agreement.

FIG. 14: The topological variables in the signal sample (τ types 3). The Kolmogorov-Smirnov (KS) probabilities are shown, indicating the level of agreement.

505 B. b-veto control sample plots

506 The b-veto sample is the one used to test our QCD modelling VII. As it requires no NN b-tags it is 507 QCD-dominated and has a tiny amount of tt̄ (1.9% for types 1 and 2 and 0.7% for type 3) as shown in 508 Tables XVI and XVII. It consists of an ideal sample to make sure that the QCD modelling works and can 509 be used in the measurement. Next we show the plots of the topological variables for this sample. The error 510 bars represent the statistical uncertainties only.

FIG. 15: The topological variables in the b-veto control sample (τ types 1 and 2). The Kolmogorov-Smirnov (KS) probabilities are shown, indicating how good the agreement is.

FIG. 16: The topological variables in the b-veto control sample (τ types 1 and 2). The Kolmogorov-Smirnov (KS) probabilities are shown, indicating how good the agreement is.

FIG. 17: The topological variables in the b-veto control sample (τ types 3). The Kolmogorov-Smirnov (KS) probabilities are shown, indicating how good the agreement is.

FIG. 18: The topological variables in the b-veto control sample (τ types 3). The Kolmogorov-Smirnov (KS) probabilities are shown, indicating how good the agreement is.

511 X. CROSS SECTION

512 Having presented the preselection yelds on Section VI we now show the results of the efficiencies for τ ID, 513 b-tagging and trigger for all tt̄ channels

Selection Relative(%) Cumulative(%)
τ ID 22.20 ± 0.24 22.20 ± 0.24
Trigger 84.54 ± 0.55 18.77 ± 0.22
b-tagging 61.82 ± 0.55 11.61 ± 0.16

TABLE XXII: t\overline{t} → τ + jets final cut flow for taus types 1 and 2

Selection Relative(%) Cumulative(%)
τ ID 12.37 ± 0.21 12.37 ± 0.21
Trigger 84.79 ± 0.75 10.49 ± 0.19
b-tagging 59.63 ± 0.75 6.26 ± 0.13

TABLE XXIII: t\overline{t} → τ + jets final cut flow for taus type 3

Selection Relative(%) Cumulative(%)
τ ID 10.81 ± 0.20 10.81 ± 0.20
Trigger 83.40 ± 0.81 9.02 ± 0.18
b-tagging 61.30 ± 0.82 5.52 ± 0.12

TABLE XXIV: t\overline{t} → e + jets final cut flow for taus types 1 and 2

Selection Relative(%) Cumulative(%)
τ ID 2.25 ± 0.11 2.25 ± 0.11
Trigger 83.62 ± 1.77 1.88 ± 0.09
b-tagging 58.26 ± 1.76 1.10 ± 0.06

TABLE XXV: t\overline{t} → e + jets final cut flow for taus type 3

Selection Relative(%) Cumulative(%)
τ ID 3.38 ± 0.19 3.38 ± 0.19
Trigger 84.44 ± 2.13 2.86 ± 0.17
b-tagging 61.25 ± 2.16 1.75 ± 0.11

TABLE XXVI: t\overline{t} → μ + jets final cut flow for taus types 1 and 2.

Selection Relative(%) Cumulative(%)
τ ID 3.88 ± 0.21 3.88 ± 0.21
Trigger 82.79 ± 2.04 3.21 ± 0.18
b-tagging 58.11 ± 2.05 1.87 ± 0.11

TABLE XXVII: t\overline{t} → μ + jets final cut flow for taus type 3

Selection Relative(%) Cumulative(%)
τ ID 21.18 ± 0.37 21.18 ± 0.37
Trigger 79.56 ± 0.90 16.85 ± 0.34
b-tagging 62.83 ± 0.92 10.59 ± 0.25

TABLE XXVIII: t\overline{t} → dilepton final cut flow for taus types 1 and 2

Selection Relative(%) Cumulative(%)
τ ID 14.73 ± 0.34 14.73 ± 0.34
Trigger 78.78 ± 1.08 11.60 ± 0.30
b-tagging 63.62 ± 1.11 7.38 ± 0.22

TABLE XXIX: t\overline{t} → dilepton final cut flow for taus type 3.

514 After having computed all efficiencies it is worthy to summarize all of them (in %) for the different tau 515 types:

Channel Preselection  τ ID  Trigger  b-tag
t\overline{t} → τ + jets 3.70 ± 0.02 22.20 ± 0.24 18.77 ± 0.22 11.61 ± 0.16
t\overline{t} → e + jets 3.54 ± 0.02 10.80 ± 0.20 9.02 ± 0.18 5.53 ± 0.12
t\overline{t} → μ + jets 1.67 ± 0.01 3.38 ± 0.19 2.86 ± 0.17 1.75 ± 0.11
t\overline{t} → dilepton 1.36 ± 0.01 21.18 ± 0.37 16.85 ± 0.34 10.59 ± 0.25

TABLE XXX: Summary of all selections for taus type 1 & 2.

Channel Preselection  τ ID  Trigger  b-tag
t\overline{t} → τ + jets 3.70 ± 0.02 12.37 ± 0.21 10.49 ± 0.19 6.26 ± 0.13
t\overline{t} → e + jets 3.54 ± 0.02 2.25 ± 0.11 1.88 ± 0.09 1.10 ± 0.06
t\overline{t} → μ + jets 1.67 ± 0.01 3.88 ± 0.21 3.21 ± 0.18 1.87 ± 0.11
t\overline{t} → dilepton 1.36 ± 0.01 14.73 ± 0.34 11.60 ± 0.30 7.38 ± 0.22

TABLE XXXI: Summary of all selections for taus type 3.

516 Table below summarizes the number of events in each channel after final selection.

TABLE XXXII: Final number of events in the two analysis channels.

τ type I,II τ type I,II (fitted) τ type III τ type III (fitted)
data 386 459
t\overline{t} → τ + jets 72.04 ± 0.53  38.82 ± 0.39
t\overline{t} → e + jets 38.35 ± 0.36  6.52 ± 0.16
t\overline{t} → μ + jets 4.81 ± 0.14  5.14 ± 0.14
t\overline{t} → l + l  6.02 ± 0.07  4.20 ± 0.06
t\overline{t} total MC  121.22 ± 0.43  54.68 ± 0.20
t\overline{t} total fitted  133.04 ± 17.09  33.12 ± 15.04
W +jets  17.82 ± 0.33  11.26 ± 0.23
Z+jets  2.78 ± 0.14  2.39 ± 0.12
QCD  232.35 ± 17.09  412.22 ± 15.04
Signal significance  6.77  1.54
S/B ratio  0.52  0.08

517 The cross section was measured by minimizing the sum of the negative log-likelihood functions for each 518 bin of both the types 1 and 2 channel and the type 3 τ channel. These are functions used by MINUIT to 519 perform fits shown in Figs 5 and 6 in Section VIII B. But there L was function of f(QCD) and now we want 520 to use it to measure the cross section, so we must express it in terms of σ(tt̄):

L(σ, Ñ_{i}, N_{i}^{obs}) ≡ −log(∏_{i} \frac{Ñ_{i}^{N_{i}^{obs}}}{N_{i}^{obs}!} e^{−Ñ_{i}})  (8)

521 where Ñ_{i} = σ×BR×L×ϵ(tt̄)_{i}+N_{bkg} is number events predicted in bin i of the data NN distribution and N_{i}^{obs} 522 is the actual count observed in that bin. The cross-section is then the minimum value of each function. But, 523 as stressed out in Section VII, we have to take into account both signal (tt̄) and electroweak contamination 524 in the loose-tight sample we use to model QCD in the high NN region used for the measurement. The 525 electroweak component is small and therefore it is kept fixed during the fit and subtracted from the loose-526 tight sample. However, as dicussed before, the numbers for signal contamination are 5.4% and 3.0% for taus 527 types 1 and 2 and type 3 respectively when we assumed a tt̄ cross section of 7.46 pb. This means that 5.4% 528 (12.55 events) of 232.35 QCD events for taus types 1 and 2 are actually tt̄ events and 3.0% (12.37 events) 529 of 412.22 QCD events for taus type 3 are actually tt̄ events. 12.55 and 12.37 events represent increases of 530 9.43% and 37.35% on the number of signal events for types 1 and 2 and type 3 respectively. However this is 531 not the final measurement yet since the cross-section measurement only makes sense if the cross-section we 532 measure in the and is the same as the one we have assumed to normalize tt̄ MC samples. This means that 533 we had to iterate back by normalizing the signal samples until we found a convergence of the cross-section. 534 Table XXIII summarizes the iteration process.

Assumed σ(tt̄) (pb) signal contamination for types 1 & 2 (%) signal contamination for type 3 (%) measured σ(tt̄) (pb)
7.46  5.4  3.0  8.37
8.37  6.1  3.3  8.42
8.42  6.2  3.4  8.46
8.46  6.2  3.4  8.46

TABLE XXXIII: Cross-section iteration process.

535 Table above shows that when we assumed a cross-section of 8.46 pb we measured the exact same value, 536 which means that we had to take into account signal contaminations of 6.2% (14.40 events) and 3.4% (14.02 537 events) for taus types 1 and 2 and 3 respectively. This represents an increase in the number of signal events 538 of 10.82% for types 1 and 2 and 42.33% for type 3. By considering such events as part of the signal tt̄ sample 539 we measure for the cross-sections:

τ+jets types 1 and 2 cross section:

σ(t\overline{t}) = 8.83 _{−1.12}^{+1.14} (stat) _{−0.94}^{+0.89} (syst) ± 0.3 (lumi) pb,

τ+jets type 3 cross section:

σ(t\overline{t}) = 6.06 _{−2.62}^{+2.77} (stat) _{−0.99}^{+0.94} (syst) ± 0.3 (lumi) pb,

Combined cross section:

σ(t\overline{t}) = 8.46 _{−1.04}^{+1.06} (stat) _{−0.88}^{+0.92} (syst) ± 0.3 (lumi) pb.

540 The correspondent likelihoods of these measurements are shown in Figures 19, 20 and 21. Figures 22, 23 541 and 24 show zoomed in graphs of the same likelihood functions described above. 542 All associated systematics concerning this measurement can be seen in Table XXXVI.

FIG. 19: The log likelihood function for type 1 and 2 τ channel

FIG. 20: The log likelihood function for type 3 τ channel FIG. 21: The log likelihood function for all three types combined FIG. 22: Zoom in of the log likelihood function for type 1 and 2 τ channel

FIG. 23: Zoom in of the log likelihood function for type 3 τ channel

FIG. 24: Zoom in of the log likelihood function for all three types combined

543 After measuring the combined cross section we observed a significant higher statistical uncertainty value if 544 compared to the one we expected to see based on the fact that we have approximately 5 times more data than 545 in p17, where the signal contamination was not taken into account (see Appendix G). Further investigation 546 showed that the cut NNelec > 0.9 applied to taus type 2 only was responsible for such discrepancy. Below 547 we show the same measurement as done above but now with no NNelec cut applied. 548 Table below summarizes the number of events in each channel after final selection.

TABLE XXXIV: Final number of events in the two analysis channels.

τ type I,II τ type I,II (fitted) τ type III τ type III (fitted)
data 583 459
t\overline{t} → τ + jets 85.46 ± 0.58  38.82 ± 0.39
t\overline{t} → e + jets 175.23 ± 0.85  6.52 ± 0.16
t\overline{t} → μ + jets  8.98 ± 0.19  5.14 ± 0.14
t\overline{t} → l + l  12.62 ± 0.10  4.18 ± 0.06
t\overline{t} total MC  282.27 ± 1.05  54.67 ± 0.41
t\overline{t} total fitted  260.71 ± 20.74  35.73 ± 15.28
W +jets  39.65 ± 0.50  11.26 ± 0.25
Z+jets  4.56 ± 0.10  2.38 ± 0.11
QCD  278.04 ± 20.74  409.62 ± 15.28
Signal significance  10.80  1.67
S/B ratio  0.80  0.08

549 Table below shows the iteration process in this case and and the cross section measurement follows:

Assumed σ(tt̄) (pb) signal contamination for types 1 & 2 (%) signal contamination for type 3 (%) measured σ(tt̄) (pb)
7.46  6.0  3.0  6.84
6.84  5.4  2.7  6.91
6.91  5.5  2.8  6.92
6.92  5.5  2.8  6.92

TABLE XXXV: Cross-section iteration process.

τ+jets types 1 and 2 cross section:

σ(t\overline{t}) = 7.03 _{−0.56}^{+0.54} (stat) _{−0.61}^{+0.65} (syst) ± 0.3 (lumi) pb,

τ+jets type 3 cross section:

σ(t\overline{t}) = 4.36 _{−2.50}^{+2.62} (stat) _{−0.61}^{+0.62} (syst) ± 0.3 (lumi) pb,

Combined cross section:

σ(t\overline{t}) = 6.92 _{−0.54}^{+0.54} (stat) _{−0.60}^{+0.62} (syst) ± 0.3 (lumi) pb,

550 As we can see the statistical uncertainty decreases to 0.54 pb which is in a good agreement to what we 551 would expect if compared to 1.2 pb measured in p17. Appendix G shows cross sections measurements when 552 signal contamination is not taken into account for both NNelec > 0.9 and no NNelec cut applied. Once again 553 we observed a discrepancy when NNelec is applied and the expected value when NNelec is not applied.

554 XI. SYSTEMATIC UNCERTAINTIES

555 Several factors contribute to systematic uncertainties in the measurement. Here we describe such uncer-556 tainties.

557 A. JES

558 The jet energy scale (JES) systematic is determined by shifiting the jet energy scale by ±1σ in all MC 559 samples.

560 B. TES

561 The tau energy scale (TES) systematic is determined by shifiting the tau energy scale by its uncertainty as 562 given in [36].

563 C. Jet Energy Resolution and Jet ID

564 The jet energy resolution (JER) systematic is determined by shifiting the jet energy resolution by ±1σ in 565 all MC samples.

566 D. Trigger

567 Each event was corrected by the ratio of the actual and predicted trigger result as a function of H_{T}, which 568 was used based on the fact that the agreement varies as function of it.

569 E. b-quark fragmentation

570 This uncertainty is estimated using the standard procedure described in [17] by reweighting tt̄ events using 571 different fragmentation functions.

572 F. b-tagging

573 b-tagging uncertainty effects are taken into account by varying the systematic and statistical errors on the 574 MC tagging weights. 575 These errors (which are computed using standard DØ b ID group tools) arise form several independent 576 sources [27]:

577 • B-jet tagging parameterization.

578 • C-jet tagging parameterization.

579 • Light jet tagging parameterization (negative tag rate).

580 • Semi-leptonic b-tagging efficiency parameterization in MC and in data (System 8).

581 • Taggability. This includes the statistical error due to finite statistic in the samples from which it had 582 been derived and systematic, reflecting the (neglected) taggability dependence on the jet multiplicity.

583 G. τ ID systematics

584 Here we include systematics associated to the NN cut (NN > 0.90 for taus types 1 and 2 and NN > 0.95 for 585 taus type 3) applied to select hadronic taus. As recommended by the τ-ID group these systematics are 9.5%, 586 3.5% and 5.0% for taus type 1, 2 and 3 respectively. However in this analysis we chose treat taus types 1 587 and 2 together. This led us to combine their uncertainties in the following way

sys_{12} = \sqrt{ϵ_{1}^{2} ∗ f_{1}^{2} + ϵ_{2}^{2} ∗ f_{2}^{2}}  (9)

588 where ϵ_{1} and ϵ_{2} are the τ ID efficiencies for taus types 1 and 2 respectively and f_{1} and f_{2} are the fractions 589 of taus types 1 (0.16) and 2 (0.84) respectively.

590 H. QCD systematics

591 As explained in the section VIII A we use the control (b-veto) data set to validate our method of modeling 592 the multijet background. Therefore we have to use the same sample to evaluate the associated uncertainties. 593 The way it was done is by reweighting topological event NN for QCD template (“loose-tight” τ), so that it 594 matches the one for “tight” τ data exactly (electroweak beckgrounds were subtracted).

595 I. W and Z scale factors

596 We apply a ascale factor of 1.47 to both W + bb and W + cc events with an uncertainty of 15%. At the 597 same time a scales factors of 1.52 and 1.67 are applied to Z + bb and Z + cc events, both with an uncertainty 598 of 20%.

599 J. Template statistics

600 When we performed the template fit to data (Section VIII) the QCD template had limited statistics (1132 601 events for taus types 1 and 2 and 4487 events for taus type 3). We have to take the statistical uncertainty 602 in this histogram as one of the cross section systematics. It was calculated by varying the content of each 603 bin of the QCD template NN distribution within its uncertainty and observing how the cross section result 604 changed.

605 K. tt̄ contamination in the loose-tight sample

606 When measuring the cross-section we had to take into account the signal contamination in the loose-tight 607 sample we use to model QCD in the high NN region. The systematic uncertainty in this case is calculated by 608 varying the final assumed cross section by ±1σ, re-estimating the signal contamination and finally measuring 609 the up and down values of the cross section.

610 L. PDF

611 Systematics on Parton Distribution Functions (PDF) are estimated by reweighting signal tt̄ MC from 612 CTEQ6L1 to CTEQ6.1m and its twenty error PDF’s. The reweighting of the PDF’s is done by using 613 caf pdfreweight package tool on Pythia tt̄ MC. We then assigned the relative PDF uncertainty obtained 614 with Pythia on the Alpgen tt̄ MC.

615 M. Luminosity

616 Here we take the DØ standard measured uncertainty on luminosity of 6.1% . 617 Tables XXXVI and XXXVII summarize all of these uncertainty sources and shows how the resulting cross 618 section shifts.

TABLE XXXVI: Systematic uncertainties on σ(tt̄) (in pb) for NNelec > 0.9.

Channel  τ+jets types 1 and 2 τ+jets type 3 Combined
Tau Energy Scale  _{+0.068,−0.102}  _{+0.340,−0.306} _{+0.136,−0.136}
Jet Energy Scale  _{+0.051,−0.034}  _{+0.051,−0.085} _{+0.051,−0.000}
Jet Energy Resolution  _{+0.102,−0.051}  _{+0.204,−0.034} _{+0.119,−0.052}
Jet ID  _{+0.204,−0.204}  _{+0.153,−0.153} _{+0.204,−0.204}
b-tag  _{+0.562,−0.493}  _{+0.493,−0.426} _{+0.544,−0.477}
b-fragmentation  _{+0.102,−0.102}  _{+0.068,−0.068} _{+0.085,−0.085}
QCD Modeling  _{+0.340,−0.340}  _{+0.221,−0.221} _{+0.324,−0.305}
τ ID  _{+0.272,−0.272}  _{+0.306,−0.306} _{+0.290,−0.290}
Trigger  _{+0.256,−0.256}  _{+0.238,−0.238} _{+0.256,−0.256}
W Scale Factor  _{+0.034,−0.034}  _{+0.034,−0.034} _{+0.034,−0.034}
Z Scale Factor  _{+0.072,−0.072}  _{+0.072,−0.072} _{+0.048,−0.048}
Template statistics  _{+0.156,−0.156}  _{+0.204,−0.204} _{+0.168,−0.168}
Signal contamination  _{+0.153,−0.153}  _{+0.255,−0.272} _{+0.188,−0.170}
PDF  _{+0.097,−0.084}  _{+0.188,−0.198} _{+0.092,−0.081}

TABLE XXXVII: Systematic uncertainties on σ(tt̄) (in pb) when no NNelec cut is applied.

Channel  τ+jets types 1 and 2 τ+jets type 3 Combined
Tau Energy Scale  _{+0.101,−0.002}  _{+0.238,−0.255} _{+0.102,−0.017}
Jet Energy Scale  _{+0.016,−0.001}  _{+0.017,−0.000} _{+0.016,−0.000}
Jet Energy Resolution  _{+0.084,−0.086}  _{+0.017,−0.034} _{+0.068,−0.085}
Jet ID  _{+0.169,−0.169}  _{+0.017,−0.017} _{+0.153,−0.153}
b-tag  _{+0.424,−0.375}  _{+0.358,−0.306} _{+0.425,−0.375}
b-fragmentation  _{+0.069,−0.069}  _{+0.102,−0.102} _{+0.068,−0.068}
QCD Modeling  _{+0.271,−0.273}  _{+0.153,−0.136} _{+0.225,−0.256}
τ ID  _{+0.220,−0.220}  _{+0.204,−0.204} _{+0.221,−0.221}
Trigger  _{+0.204,−0.204}  _{+0.170,−0.170} _{+0.204,−0.204}
W Scale Factor  _{+0.034,−0.034}  _{+0.034,−0.034} _{+0.034,−0.034}
Z Scale Factor  _{+0.072,−0.072}  _{+0.072,−0.072} _{+0.048,−0.048}
Template statistics  _{+0.118,−0.118}  _{+0.170,−0.170} _{+0.102,−0.102}
Signal contamination  _{+0.050,−0.052}  _{+0.136,−0.187} _{+0.051,−0.051}
PDF  _{+0.097,−0.084}  _{+0.188,−0.198} _{+0.092,−0.081}

619 [1] J. A. Coarasa, J. Guasch, and J. Sola, Report No. UAB-FT-451, 1999, hep-ph/9903212 620 [2] Measurement of top pair production cross section from the tau + jets channel, DØ Note 5158. 621 [3] Measurement of σ(pp̄ → tt̄X) in τ + jets channel using 1 fb^{−1} of data, DØ Note 5765.

622 [4] Commom Sample Group, http://www-d0.fnal.gov/Run2Physics/cs/index.html

623 [5] Search for neutral Higgs bosons in ϕb → bb̄b using RunIIb data, DØ Note 5709

624 [6] Commom Sample Group, http://www-d0.fnal.gov/Run2Physics/cs/MC/MC.html

625 [7] M.L. Mangano et al., “ALPGEN: a generator for hard multiparton process in hadronic collisions”, JHEP 0307, 626 001 (2003); 627 [8] T. Sjostrand, P. Eden, C. Friberg, L. Lonnblad, G. Miu, S. Mrenna and E. norbin, Computer Phys. Commun. 628 135, 238 (2001). 629 [9] http://charm.physics.ucsb.edu/people/lange/EvtGen/ 630 [10] S. Jadach, Z. Was, R. Decker, J.H. Kuehn, Comp. Phys. Commun. , 361 (1993) (CERN TH-6793 preprint).

631 [11] http://www-d0.hef.ru.nl//askArchive.php?base=agenda&categ=a081895&id=a081895s0t3/transparencies.

632 [12] S. Muanza, A compilation of MCFM v5.1 Cross Sections. DØ Note 5300. 633 [13] Systematics Uncertainties in Top Quark Measurements, DØ Note 6024.

634 [14] https://plone4.fnal.gov/P1/D0Wiki/comp/caf/MCreweighting/lumiprofile-reweighting.

635 [15] H. Schellman, The longitudinal shape of the luminous regions at DØ DØ Note 5885. 636 [16] D. Price, W. Fisher, and J. Haley, Studies of Alpgen parameters corrections and uncertainties, DØ Note 5966. 637 [17] Y. Peters, M. Begel, K. Hamacher, and D. Wicke, Reweighting of the fragmentation function for the DØ Monte 638 Carlo, DØ Note 5325. 639 [18] N. Makovec and J.F. Grivaz, Shifiting, smearing, and removing simulated jets, DØ Note 4914. 640 [19] Search For MSSM Higgs Boson Production in the Decay h → τ_{μ}τ_{had} with the DØ Detector at at \sqrt{1.96} TeV, DØ 641 Note 5708. 642 [20] DØ τ ID certification, DØ Note 4773. 643 [21] S.Eldelman et al. (Particle Data Group), Phys. Lett. B 592, 1(2004) and 2005 644 [22] G.C. Blazey et al., arXiv.hep-ex/0005012 (2000). 645 [23] G.Bernardi, E. Busato and J.R. Vlimant, Improvements from the T42 Algorithm on calorimeter objects recon-646 struction, DØ Note 4335. 647 [24] A. Harel, Jet ID Optimization, DØ note 4919. 648 [25] Jet Energy Scale Determination at DØ Run II, DØ Note 5382. 649 [26] A. Harel, Capping the JES muon corrections, DØ Note 5563. 650 [27] T. Gadfort, A. Haas, D. Johnston, D. Lincoln, T. Scalon and S. Schlobohm Performance of the DØ NN b-tagging 651 Tool on p20 Data, DØ Note 5554 652 [28] M. Anastasoaie, S. Robinson, T. Scalon, Performance of the NN b-tagging Tool on p17 Data, DØ Note 5213 653 [29] T. Scalon and S. Greder, Measurement of the p20 Fake Rate using Binned Fits do Data, DØ Note 6046 654 [30] Search for Single Top Quark Production with 1.0 fb^{−1}, DØ Note 5285 655 [31] Measurement of the ttbar cross section in the lepton+jets channel with 5.3 fb^{−1} , DØ Note 6028. 656 [32] DØ Note 5350 and DØ Note 5360 657 [33] Measurement of the tt̄→ all − jets production cross section using Secondary Vertex Tagging, DØ Note 4830 658 [34] E̸_{T} significance Algorithm in RunII Data, DØ Note 4254 659 [35] Measurement of the top-antitop quark pair production cross section in proton-antiproton collisions at \sqrt{1.96} TeV 660 in the lepton + jets final state, DØ Note 5262

661 [36] http://www-d0.hef.kun.nl//fullAgenda.php?ida=a092001&fid=57.

662 [37] DØ Search for Neutral Higgs Bosons at high tan β in the final state τ_{μ}τ_{h}b with 4.3 fb^{−1} of Run2b Data , DØ 663 Note 6077. 664 [38] http://schwind.home.cern.ch/schwind/MLPfit.html 665 APPENDIX A: TRIGGER EFFICIENCIES

666 In this appendix we present the trigger weight distributions of all MC samples for different numbers of 667 b-tagged jets. These are the weight distributions we referred to in Sections II A and III.

668 1. Trigger Efficiencies for τ + jets

FIG. 25: Trigger Efficiencies for τ + jets.

669 2. Trigger Efficiencies for e + jets FIG. 26: Trigger Efficiencies for e + jets.

670 3. Trigger Efficiencies for μ + jets

FIG. 27: Trigger Efficiencies for μ + jets.

671 4. Trigger Efficiencies for dilepton FIG. 28: Trigger Efficiencies for dilepton.

672 5. Trigger Efficiencies for alljets

FIG. 29: Trigger Efficiencies for alljets.

673 6. Trigger Efficiencies for W jj + jets FIG. 30: Trigger Efficiencies for W jj + jets.

674 7. Trigger Efficiencies for W bb + jets

FIG. 31: Trigger Efficiencies for W bb + jets.

675 8. Trigger Efficiencies for W cc + jets FIG. 32: Trigger Efficiencies for W cc + jets.

676 9. Trigger Efficiencies for Zjj + jets → ee + jj + jets

FIG. 33: Trigger Efficiencies for Zjj + jets → ee + jj + jets.

677 10. Trigger Efficiencies for Zbb + jets → ee + bb + jets

FIG. 34: Trigger Efficiencies for Zbb + jets → ee + bb + jets.

678 11. Trigger Efficiencies for Zcc + jets → ee + cc + jets

FIG. 35: Trigger Efficiencies for Zcc + jets → ee + cc + jets.

679 12. Trigger Efficiencies for Zjj + jets → μμ + jj + jets

FIG. 36: Trigger Efficiencies for Zjj + jets → μμ + jj + jets.

680 13. Trigger Efficiencies for Zbb + jets → μμ + bb + jets

FIG. 37: Trigger Efficiencies for Zbb + jets → μμ + bb + jets.

681 14. Trigger Efficiencies for Zcc + jets → μμ + cc + jets

FIG. 38: Trigger Efficiencies for Zcc + jets → μμ + cc + jets.

682 15. Trigger Efficiencies for Zjj + jets → ττ + jj + jets

FIG. 39: Trigger Efficiencies for Zjj + jets → ττ + jj + jets.

683 16. Trigger Efficiencies for Zbb + jets → ττ + bb + jets

FIG. 40: Trigger Efficiencies for Zbb + jets → ττ + bb + jets.

684 17. Trigger Efficiencies for Zcc + jets → ττ + cc + jets

FIG. 41: Trigger Efficiencies for Zcc + jets → ττ + cc + jets.

685 18. Trigger Efficiencies for Zjj + jets → νν + jj + jets

FIG. 42: Trigger Efficiencies for Zjj + jets → νν + jj + jets.

686 19. Trigger Efficiencies for Zbb + jets → νν + bb + jets

FIG. 43: Trigger Efficiencies for Zbb + jets → νν + bb + jets.

687 20. Trigger Efficiencies for Zcc + jets → νν + cc + jets

FIG. 44: Trigger Efficiencies for Zcc + jets → νν + cc + jets.

688 APPENDIX B: TURN ON CURVES FOR TRIGGER JT2 3JT15L IP VX

689 Here it is shown all turn-on curves for all three levels of the trigger JT2 3JT15L IP VX as described in 690 Section III.

691 1. Level 1 jet turn on curves for trigger JT2 3JT15L IP VX

(a) p_{T} > 8 GeV  (b) p_{T} > 15 GeV  (c) p_{T} > 30 GeV

FIG. 45: Level 1 jet turn-on curves, low luminosity.

(a) p_{T} > 8 GeV  (b) p_{T} > 15 GeV  (c) p_{T} > 30 GeV

FIG. 46: Level 1 jet turn-on curves, medium luminosity.

(a) p_{T} > 8 GeV  (b) p_{T} > 15 GeV  (c) p_{T} > 30 GeV

FIG. 47: Level 1 jet turn-on curves, high luminosity.

692 2. Level 2 jet turn on curves for trigger JT2 3JT15L IP VX

(a) Low luminosity p_{T} > 8 GeV (b) Medium luminosity p_{T} > 8 GeV (c) high luminosity p_{T} > 8 GeV

FIG. 48: Level 2 p_{T} > 8 GeV jets turn-on curves.

693 3. Level 2 H_{T} turn on curves for trigger JT2 3JT15L IP VX

(a) H_{T} > 75 GeV  (b) H_{T} > 100 GeV

FIG. 49: L2 H_{T} turn-on curves, low luminosity.

(a) H_{T} > 75 GeV  (b) H_{T} > 100 GeV

FIG. 50: L2 H_{T} turn-on curves, medium luminosity.

(a) H_{T} > 75 GeV  (b) H_{T} > 100 GeV

FIG. 51: L2 H_{T} turn-on curves, high luminosity.

694 4. Level 2 E̸_{T} turn on curves for trigger JT2 3JT15L IP VX

(a) E̸_{T} > 10 GeV  (b) E̸_{T} > 20 GeV

FIG. 52: L2 E̸_{T} turn-on curves, low luminosity.

(a) E̸_{T} > 10 GeV  (b) E̸_{T} > 20 GeV

FIG. 53: L2 E̸_{T} turn-on curves, medium luminosity.

(a) E̸_{T} > 10 GeV  (b) E̸_{T} > 20 GeV

FIG. 54: L2 E̸_{T} turn-on curves, high luminosity.

695 5. Level 2 Sphericity turn on curves for trigger JT2 3JT15L IP VX

(a) Sphericity > 0.1 turn-on curve, low luminosity (b) Sphericity > 0.1 turn-on curve, medium luminosity (c) Sphericity > 0.1 turn-on curve, high luminosity

FIG. 55: L2 Sphericity turn-on curves.

696 6. Level 2 STTIP turn on curves for trigger JT2 3JT15L IP VX

(a) L2STTIP, 0 and 1 tight NN tags (b) L2STTIP, 2 and 3 tight NN tags

FIG. 56: L2STTIP efficiency in the low luminosity range. Left: events with 0 (red) and 1 (black) tight NN b-tags. Right: events with 2 (red) and 3 (black) tight NN b-tags.

(a) L2STTIP, 0 and 1 tight NN tags (b) L2STTIP, 2 and 3 tight NN tags

FIG. 57: L2STTIP efficiency in the medium luminosity range. Left: events with 0 (red) and 1 (black) tight NN b-tags. Right: events with 2 (red) and 3 (black) tight NN b-tags.

(a) L2STTIP, 0 and 1 tight NN tags (b) L2STTIP, 2 and 3 tight NN tags

FIG. 58: L2STTIP efficiency in the high luminosity range. Left: events with 0 (red) and 1 (black) tight NN b-tags. Right: events with 2 (red) and 3 (black) tight NN b-tags.

697 7. Level 3 jet turn on curves for trigger JT2 3JT15L IP VX

(a) p_{T} > 15 GeV  (b) p_{T} > 25 GeV

FIG. 59: L3 jet turn-on curves, low luminosity.

(a) p_{T} > 15 GeV  (b) p_{T} > 25 GeV

FIG. 60: L3 jet turn-on curves, medium luminosity.

(a) p_{T} > 15 GeV  (b) p_{T} > 25 GeV

FIG. 61: L3 jet turn-on curves, high luminosity.

698 8. Level 3 b-tag on curves for trigger JT2 3JT15L IP VX

(a) 0 and 1 b-tags.  (b) 2 and 3 b-tags.

FIG. 62: (a) Efficiency of the L3 b-tag (Level3 Event b-tag< 0.4) for the low luminosity range in triggerlist v15. The selected events passed the rest of the trigger and offline event selection and had zero (red) or one (black) offline NN (TIGHT) b-tags. (b) Same for events with 2(red) and 3(black) offline NN (TIGHT) b-tags.

(a) 0 and 1 b-tags.  (b) 2 and 3 b-tags.

FIG. 63: (a) Efficiency of the L3 b-tag (Level3 Event b-tag< 0.4) for the medium luminosity range in triggerlist v15. The selected events passed the rest of the trigger and offline event selection and had zero (red) or one (black) offline NN (TIGHT) b-tags. (b) Same for events with 2(red) and 3(black) offline NN (TIGHT) b-tags.

(a) 0 and 1 b-tags.  (b) 2 and 3 b-tags.

FIG. 64: (a) Efficiency of the L3 b-tag (Level3 Event b-tag< 0.4) for the high luminosity range in triggerlist v15. The selected events passed the rest of the trigger and offline event selection and had zero (red) or one (black) offline NN (TIGHT) b-tags. (b) Same for events with 2(red) and 3(black) offline NN (TIGHT) b-tags.

(a) 0 and 1 b-tags.  (b) 2 and 3 b-tags.

FIG. 65: (a) Efficiency of the L3 b-tag (Level3 Event b-tag< 0.4) for the low luminosity range in triggerlist v16. The selected events passed the rest of the trigger and offline event selection and had zero (red) or one (black) offline NN (TIGHT) b-tags. (b) Same for events with 2(red) and 3(black) offline NN (TIGHT) b-tags.

(a) 0 and 1 b-tags.  (b) 2 and 3 b-tags.

FIG. 66: (a) Efficiency of the L3 b-tag (Level3 Event b-tag< 0.4) for the medium luminosity range in triggerlist v16. The selected events passed the rest of the trigger and offline event selection and had zero (red) or one (black) offline NN (TIGHT) b-tags. (b) Same for events with 2(red) and 3(black) offline NN (TIGHT) b-tags.

(a) 0 and 1 b-tags.  (b) 2 and 3 b-tags.

FIG. 67: (a) Efficiency of the L3 b-tag (Level3 Event b-tag< 0.4) for the high luminosity range in triggerlist v16. The selected events passed the rest of the trigger and offline event selection and had zero (red) or one (black) offline NN (TIGHT) b-tags. (b) Same for events with 2(red) and 3(black) offline NN (TIGHT) b-tags.

699 APPENDIX C: DISCRIMINANT VARIABLES

700 This appendix shows normalized plots of signal and background samples for all discriminant variables tested 701 for this analysis.

FIG. 68: Discriminant variables.

702 APPENDIX D: SET OPTIMIZATION

703 In this appendix it is shown plots of the figure of merit (Equation 6) used to perform the NN variables set 704 optimization as described in Section VIII C.

66

FIG. 69: Sets of NN inputs variables with E̸_{T} significance > 4.0 for set optimization.

705 APPENDIX E: SET OPTIMIZATION CONTINUED

706 In this appendix it is shown plots of the figure of merit (Equation 6) used to perform the NN variables set 707 optimization as described in Section VIII C.

FIG. 70: Sets of NN inputs variables with E̸_{T} significance > 4.0 for set optimization.

708 APPENDIX F: E̸_{T} SIGNIFICANCE OPTIMIZATION

FIG. 71: Variation of E̸_{T} significance cut for Set XXXII = metl, H_{T}, topmassl, aplan, sqrts.

709 APPENDIX G: CROSS SECTION MEASUREMENTS WHEN SIGNAL CONTAMINATION IS 710 IGNORED

711 In this appendix it is shown plots of the figure of merit (Equation 6) used to perform the NN variables set 712 optimization as described in Section VIII C.

713 1. Results for Set = metl, H_{T}, topmassl, aplan, sqrts, metl > 4.0, lumi = 4951.86/pb, VC jets and 714 NNelec > 0.9

715 Table below summarizes the number of events in each channel after final selection.

TABLE XXXVIII: Final number of events in the two analysis channels.

τ type I,II τ type I,II (fitted) τ type III τ type III (fitted)
data 386 459
t\overline{t} → τ + jets 72.04 ± 0.53  38.82 ± 0.39
t\overline{t} → e + jets 38.35 ± 0.36  6.52 ± 0.16
t\overline{t} → μ + jets 4.81 ± 0.14  5.14 ± 0.14
t\overline{t} → l + l  6.02 ± 0.07  4.20 ± 0.06
t\overline{t} total MC  121.22 ± 0.43  54.68 ± 0.20
t\overline{t} total fitted  133.04 ± 17.09  33.12 ± 15.04
W +jets  17.82 ± 0.33  11.26 ± 0.23
Z+jets  2.78 ± 0.14  2.39 ± 0.12
QCD  232.35 ± 17.09  412.22 ± 15.04
Signal significance  6.77  1.54
S/B ratio  0.52  0.08

716 Without taking into account the signal contamination the result is (only statistical uncertainties are shown)

τ+jets types 1 and 2 cross section:

σ(t\overline{t}) = 8.05 _{−1.02}^{+1.04} (stat) ± 0.3 (lumi) pb,

τ+jets type 3 cross section:

σ(t\overline{t}) = 4.24 _{−1.80}^{+1.94} (stat) ± 0.3 (lumi) pb,

Combined cross section:

σ(t\overline{t}) = 7.26 _{−0.92}^{+0.92} (stat) ± 0.3 (lumi) pb,

717 2. Results for Set = metl, H_{T}, topmassl, aplan, sqrts, metl > 4.0, lumi = 4951.86/pb, VC jets and 718 no NNelec cut

719 Table below summarizes the number of events in each channel after final selection.

TABLE XXXIX: Final number of events in the two analysis channels.

τ type I,II τ type I,II (fitted) τ type III τ type III (fitted)
data 583 459
t\overline{t} → τ + jets 85.46 ± 0.58  38.82 ± 0.39
t\overline{t} → e + jets 175.23 ± 0.85  6.52 ± 0.16
t\overline{t} → μ + jets  8.98 ± 0.19  5.14 ± 0.14
t\overline{t} → l + l  12.62 ± 0.10  4.18 ± 0.06
t\overline{t} total MC  282.27 ± 1.05  54.67 ± 0.41
t\overline{t} total fitted  260.71 ± 20.74  35.73 ± 15.28
W +jets  39.65 ± 0.50  11.26 ± 0.25
Z+jets  4.56 ± 0.10  2.38 ± 0.11
QCD  278.04 ± 20.74  409.62 ± 15.28
Signal significance  10.80  1.67
S/B ratio  0.80  0.08

720 Without taking into account the signal contamination the result is (only statistical uncertainties are shown)

τ+jets types 1 and 2 cross section: σ(t\overline{t}) = 6.47 _{−0.53}^{+0.53} (stat) ± 0.3 (lumi) pb, τ+jets type 3 cross section: σ(t\overline{t}) = 4.58 _{−1.85}^{+1.96} (stat) ± 0.3 (lumi) pb, Combined cross section: σ(t\overline{t}) = 6.35 _{−0.51}^{+0.51} (stat) ± 0.3 (lumi) pb,