Top quark spin in 2HDM models

Alberto Prades Ibanez, University of Valencia, Spain

Supervisors: Cecile Deterre and Roger Naranjo (DESY ATLAS Group)

September 6, 2017

Abstract

The SM is a powerful theory that describes an enormous variety of physicsprocesses. However, it has limitations that points to the necessity of searchingmore completed theories. In many of them, the top quark plays an important roledue to its great mass. In this project, we have worked with a simple extensionof the SM Higgs, the Two Higgs-Doublet Model (2HDM). This model proposesfive Higgs boson and two of them contribute to the production of tt pair. Ouraim is, using a new set of polarization of spin correlation observables, to performcomprisons between 2HDM predictions and ATLAS data to exclude or constrainthe free parameters of this model.

1

Contents

1 Introduction 3

2 Theory 42.1 The Top Quark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Two-Higgs-Doublet model . . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 Polarization and spin correlation . . . . . . . . . . . . . . . . . . . . . . . 82.4 Chi-squared test with correlations between the bins . . . . . . . . . . . . 11

3 Results and discussion 123.1 Compatibility between the SM and the 2HDM . . . . . . . . . . . . . . . 123.2 Compatibility between the ATLAS data and the different models . . . . 16

4 Conclusions 19

References 24

2

1 Introduction

The Standard Model of particle physics (SM) is a quantum field theory that describesthe elementary particles and their interactions at a subatomic level. The SM assumesthat all matter is formed by elementary particles that are characterized by their quan-tum numbers. The elementary particles are classified in two types according to the SM:fermions (spin 1

2, described by the Fermi-Dirac statistics) and bosons (integer spin, de-

scribed by the Bose-Einstein statistics). Fermions are divided into three families formedby three charged leptons, three neutrinos, and six quarks. For each of these particles,there exists an antiparticle with the same mass and opposite quantum numbers. Thisgives a total of 24 fermionic particles. The bosons are classified into two groups, thosewhich are associated with fundamental interactions between fermions, and the Higgsboson. There are three fundamental interactions in the SM: the strong force, the weakforce and the electromagnetism mediated by the gluon (g), the bosons W±, Z and thephoton respectively. The Higgs boson is responsible for the mass of the particles [1, 2, 3].

The SM is a powerful theory that describes an enormous variety of physics processes.However, it has limitations that points to the necessity of searching more completed the-ories. These new theories might unify weak and strong interactions with gravity (whichis not included in the SM). Moreover, the SM does not explain the neutrino masses [4]and there is no candidate for dark matter.

Theories Beyond the Standard Model (BSM) propose new ways to solve these limita-tions. For example, supersymmetry (SUSY) [5] proposes the existence of a supersym-metric particle for each particle of the SM. This theory solves some problems of the SMlike renormalization and it gives a candidate for dark matter. Other theories, like theGreat Unification Theories (GUT), try to unify the three interactions described by theSM in a unique interaction at high energies and predict the existence of new bosons suchas Z’ and W’. It also explains the masses of the neutrinos [6, 7].

A way for testing these theories is studying the properties of particles. For example, aset of observables that caracterize the top spin structure were proposed in [9] and mea-sured, for the first time, by the ATLAS collaboration [10] that have not been comparedyet with BSM theories.

In this report we compare the behaviour of those observables in the SM with one classof BSM models, the two Higgs-Doublet model (2HDM). We also compare the measuredvalues with the predictions of all those models to try to constrain the free parametersof the 2HDM that we study.

3

2 Theory

2.1 The Top Quark

The top quark is a fermion of spin s = 1/2 and charge Q = +2/3 discovered at Fermilabin 1995 [11, 12]. It was predicted by the Standard Model as the companion of isospinof the bottom quark belonging to the third generation of fermions. It is the heaviestelementary particle of the SM. Its mass is about 35 times the mass of the second heavi-est quark (the bottom quark). This very large mass comes from the coupling with theHiggs boson (the top quark has the highest coupling with this boson). A more detailedexplanation of its properties can be found in the Particle Data Group book [1].

Since the lifetime of the top quark is ' 0.5 10−24s and the typical hadronization timeis ' 3fm/c ' 3.3 10−24s [13], the top quark decays before hadronization and beforeany consequent spin-flip can take place. This offers a unique opportunity to study theproperties of a bare quark and the properties of its spin.

At hadron colliders, top quarks are mainly produced in tt pairs via the strong interac-tion. The quarks and gluons of the initial state are unpolarised, which means that theirspins are not preferentially aligned with any given direction. The top quarks producedvia QCD are expected to be almost unpolarized but their spins are expected to be cor-related. The spins of the top quarks do not become decorrelated due to hadronization,so their spin information is transfered to their decay products. This makes it possibleto measure the top quark pair’s spin structure using angular observables of their decayproducts. In this report we are going to use the 15 observables defined and measured in[10]. These observables are related with the top quark pair’s spin density matrix thatis presented in section 2.3. In order to measure all observables, the final-state particlesof the decay chains of the pair tt have to be reconstructed and identified correctly. Thetop quark decays in almost all cases via electroweak interaction into a b quark and a Wboson (the CKM matrix element is |Vtb| = 0.99914± 0.00005 [1]). The W boson decayseither leptonically (to one lepton and one neutrino) or hadronically (to one quark andone antiquark). As charged leptons retain more information about the spin state of thetop quarks, and they can be precisely reconstructed, the measurements of these observ-ables were performed in the dileptonic final state (both W decay leptonically, leading toa final state with two quarks, two charged leptons, and two neutrinos). The dileptonicchannel offers a pure sample since the background contribution is smaller than in theother channels (fully hadronic or semileptonic).

2.2 Two-Higgs-Doublet model

The two Higgs Doublet Model is a simple extension of SM Higgs, with two complexHiggs field-doublets and five Higgs bosons of spin 0 [14]. Those bosons are h (CP-even,neutral, SM like), H(CP-even, neutral, high mass), A (CP-odd, neutral, high mass), H+

4

and H- (charged, high mass). This theory has 7 free parameters: mh, mA, mH = mH+

= mH−, the mixing angle α among the neutral Higgs bosons, the ratio of the vacuumexpectation values of the two Higgs doublets fields Φ1 and Φ2, tan β = ν1/ν2, and thepotential m2

12 of the softly break term.

In this model, the tt pair could be produced via the following Feynman diagrams:

Figure 1: Feynman diagrams for tt production in 2HDM.

The usual way to discover those new particles would be to look for a bump in the tt pairinvariant mass distribution but the interference of the other Feynman diagrams makeour mesurement less sensitive. Those interferences deform the usual bump that becomesa dip and a bump as we see in Figures 2, 3 and 4. Due to the limited resolution on thett invariant mass, the shape of the signal makes it more difficult to detect as we see in.For this reason, the authors [15] could only exclude a few models in their analysis as wecan see in Figure 5 where just the models below the blue line are excluded. For solvingthis problem, we have to look in other top properties. In this report we will look in thespin polarization and correlation of the top pair. In the next section a set of polarizationand spin correlation observables will be presented. We will study the behaviour of theseobservables in different 2HDM models to try to exclude some of them and constraintheir free parameters.

5

Figure 2: tt pair invariant mass distribution fot the process H → tt with mH = 500 GeVoverlayed with the signals of different widths (1%, 5% and 10%).

Figure 3: Pure resonance signal (S) and signal+interference (S+I) for mtt distributionsfor mA = 500 GeV.

6

Figure 4: Pure resonance signal (S) and signal+interference (S+I) for mtt distributionsfor mA = 500 GeV at reconstruction level.

Figure 5: Exclusion plots obtained by [15] using the tt invariant mass for the differentmodels that we study in this report. The models below the blue line areexcluded.

Several MC simulations have been performed for this model changing the different freeparameters for the processes gg → A→ tt and gg → H → tt [15]. Table 1 shows the listof ntuples that we use in the data analysis. The parameters of the model that we change

7

for the comparison with the data and the SM are tan β (between 0.40− 9.00), mA (500and 750 GeV) and mH (500 and 750 GeV). The rest of the parameters are known fromthe SM or we fix them.

2.3 Polarization and spin correlation

The degree of polarization of a particle (P ) is the expectation value of the helicity ofthe particle:

P =⟨−→S · p

⟩(1)

where−→S is the spin of the particle and p is a unitary vector in the direction of the

momentum of the particle.

The spin correlation (C) can be expressed as the ratio of the difference of spin-alignedpairs and spin anti-aligned pairs in a given frame of reference (spin-quantization axis):

C =N(↑↑) +N(↓↓)−N(↑↓)−N(↓↑)N(↑↑) +N(↓↓) +N(↑↓) +N(↓↑)

(2)

Tthe squared spin density matrix of tt production is defined as:

|M |2 ∝ A+ B+ · s+ + B− · s− + Cijs1is2j (3)

where A fixes the cross section of tt production, B± corresponds to the polarizationvectors for the top and antitop quark, s± denote the spin vectors of those quarks andCij is the spin correlation matrix [2, 9].

The equation (3) can be rewritten in terms of its angular distributions with respect tothe production angles of the leptons which come from the top and antitop quark as:

1

σ

d2σ

d cos θad cos θb=

1

4

(1 +Ba

+ cos θa+ +Bb− cos θb− − C(a, b) cos θa+ cos θb−

)(4)

where Ba, Bb and C(a, b) are the polarization and spin correlation along the spin quan-tization axes a and b. The angles θa and θb are the angles between the momentumdirection of a top quark decay particle in its parent top quark’s rest frame and the axisa or b. The subscript +(-) refers to the top (antitop) quark. From equation (4) one can

8

Table 1: Signal+interference (S+I) sample parameters, for the pseudoscalar Higgs bosonA and the scalar H. The cross-sections are from MadGraph, for the processesgg → A → tt and gg → H → tt in the semileptonic+dileptonic channels,sin(β − α) = 1. The samples were simulated in ATLFAST-II. Table obtainedfrom [15]

Higgs boson Mass Higgs boson tan β Γ MG σ S+I[GeV] [GeV] [pb]

pseudoscalar A

500

0.40 142.950 0.34492000.50 91.489 0.52275000.68 49.467 0.47779991.40 11.687 0.16208982.00 5.754 0.08055555.00 1.144 0.00373209.00 1.025 -0.0073180

750

0.40 230.239 0.34624990.50 147.355 0.35902770.70 75.186 0.25466661.40 18.820 0.07754442.00 9.261 0.0383016

scalar H

500

0.40 80.559 0.41419000.50 51.559 0.32867000.70 26.309 0.20686001.40 6.594 0.06305402.00 3.259 0.03285205.00 0.901 0.00491309.00 0.744 0.0016100

750

0.40 189.642 0.17593330.50 121.373 0.15692770.64 74.083 0.11746661.40 15.506 0.03145882.00 7.637 0.0162188

9

retrieve the relation (5) for the spin correlation between the axes a and b.

C(a, b) = −9⟨cos θa+ cos θb−

⟩(5)

Integrating one of the angles in equation (4) gives the single-differential cross section (6).

1

σ

dσ

d cos θa=

1

2

(1 +Ba cos θa+

)(6)

From equation (6) one can retrieve the relation:

Ba = 3 〈cos θa〉 (7)

All the observables are based on cos θ where, to define the different θ angles (anglesbetween the direction of the momentum of the decayed lepton and an axis) the followingbasis is chosen using three orthogonal spin quantization axes:

• The helicity axis (k) is defined as the top quark direction in the tt rest frame

• The transverse axis (n) is defined to be transverse to the production plane createdby the top quark direction and the beam axis

• The r-axis (r) is an axis orthogonal to the other two axis

Figure 6: Illustrative drawing of the chosen basis for the top quark decay product.

With this definition of the axes the autors of [9] define a set of observables summarizedin Table 2. Each one of the observables is sensitive to one coefficient of the spin density

10

matrix.

Table 2: The top spin observables, their definitions and their expectation value.

Name Expectation value ObservableHelicity polarization Bk cos θk±

Transverse polarization Bn cos θn±R polarization Br cos θr±

Helicity correlation C(k, k) cos θk+ cos θk−Tranverse correlation C(n, n) cos θn+ cos θn−

R correlation C(r, r) cos θr+ cos θr−R-Hel Sum C(r, k) + C(k, r) cos θr+ cos θk− + cos θk+ cos θr−R-Hel Diff C(r, k)− C(k, r) cos θr+ cosk−− cos θk+ cos θr−

Trans-Hel Sum C(n, k) + C(k, n) cos θn+ cos θk− + cos θk+ cos θn−Trans-Hel Diff C(n, k)− C(k, n) cos θn+ cos θk− − cos θk+ cos θn−Trans-R Sum C(n, r) + C(r, n) cos θn+ cos θr− + cos θr+ cos θn−Trans R-Diff C(n, r)− C(r, n) cos θn+ cos θr− − cos θr+ cos θn−

Those observables are not correlated so they are a great tool to test the validity of theSM and to search for theories BSM. In this report we use this observables to study thecompatibility between the data and the Two-Higgs-Doublet models (2HDM).

2.4 Chi-squared test with correlations between the bins

In the analysis of the results, we will need to compare the simulated data from the2HDM with the simulated data form the SM and the real data from ATLAS detector.The χ2 test is used to compare simulated data and the models. The χ2 test is given by:

χ2 =n∑

j=1

[f(Bj)− ft(Bj)]2

σ2 [ft(Bj)](8)

where ft(Bj) is the theoretical frequency for Bj observed value, f(Bj) is the expectedfrequency and σ2 [ft(Bj)] is the variance associated to the Bj value.

In the case the comparison is made between simulations and the ATLAS measurements,the correlations between the different bins is taken into account. Considering this in theχ2 test we have to use the covariance matrix defined as:

11

Vij = σiσjCij (9)

where Cij is the correlation matrix and σi is the error associated with bin i.

With this matrix we can calculate the χ2 using [16].

χ2 = ∆TV −1∆ (10)

where V −1 is the inverse of the covariance matrix, and ∆ is:

∆i = Ndatai −Nmodeli (11)

3 Results and discussion

In this report we compare the behaviour of the spin observables defined in the SM [9]and the different 2HDM models of [15] with the measurements performed by ATLAScollaboration in [10]. The purpose of this comparison is trying to find any deviationbetween the data and the 2HDM in order to find new physics BSM or to discard someof the 2HDM, limiting the possible values of their free parameters.

For constructing the observables we use the MC simulations of the Table 1 and the SM,we reconstructed the dileptonic decay of the tt system and the spin quantization axesdefined in section 2.2. With this information, we calculated the 15 spin correlation andpolarization observables for each event.

3.1 Compatibility between the SM and the 2HDM

First of all, we compare the behaviour of this observables between the SM and the dif-ferent 2HDM to check if, with enough accuracy, we could distinguish them. An exampleof this comparison for the 15 observables is shown in Figures 7, 8 and 9. In Table 3 isshown a compilation of the probability of coincidence using the χ2 test between the SMand each of the 2HDM that we study.

In results shown in Table 3 we can observe that, for all the 2HDM, there are someobservables (like the correlations) that are incompatible with the SM for each 2HDM.Other observables show incompatibilities just for some of them (like the polarizations).If enough accuracy is reached in the measured data, it would be possible to distinguishbetween the SM and the 2HDM with the corresponding parameters. To compare thecompatible observables we should increase the amount of MC data until we can distin-guish the two models and then, we would compare with the data.

12

)+k θ

d(co

sσd σ1

0

0.2

0.4

0.6

0.8

1

A = 500GeV

SM

= 0.50 (p = 0.914074)βtan

= 5.00 (p = 3.66743e-06)βtan

+kθcos

1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.90.920.940.960.98

11.021.041.061.08

1.1

) -k θd(

cosσd

σ1

0

0.2

0.4

0.6

0.8

1

A = 500GeV

SM

= 0.50 (p = 0.389757)βtan

= 5.00 (p = 0.304519)βtan

-kθcos

1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.90.920.940.960.98

11.021.041.061.08

1.1

)+n θ

d(co

sσd σ1

0

0.2

0.4

0.6

0.8

1

A = 500GeV

SM

= 0.50 (p = 0.110986)βtan

= 5.00 (p = 0.00267402)βtan

+nθcos

1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.90.920.940.960.98

11.021.041.061.08

1.1

) -n θd(

cosσd

σ1

0

0.2

0.4

0.6

0.8

1

A = 500GeV

SM

= 0.50 (p = 0.73015)βtan

= 5.00 (p = 0.0172627)βtan

-nθcos

1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.90.920.940.960.98

11.021.041.061.08

1.1

)+r θ

d(co

sσd σ1

0

0.2

0.4

0.6

0.8

1A = 500GeV

SM

= 0.50 (p = 0.400127)βtan

= 5.00 (p = 0.0480682)βtan

+rθcos

1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.90.920.940.960.98

11.021.041.061.08

1.1

) -r θd(

cosσd

σ1

0

0.2

0.4

0.6

0.8

1

A = 500GeV

SM

= 0.50 (p = 0.111816)βtan

= 5.00 (p = 0.0147907)βtan

-rθcos

1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.90.920.940.960.98

11.021.041.061.08

1.1

Figure 7: Comparison between SM and two 2HDM MC simulations for the observablescos θk± , cos θn± and cos θr±. Those 2HDM are for tan β = 0.50 and tan β = 5.00corresponding to models with a pseudoscalar Higgs boson A of mass 500 GeV.

) -k θ c

os+k θ

d(co

sσd

σ1

0

0.5

1

1.5

2

2.5 A = 500GeV

SM

= 0.50 (p = 0)βtan

= 5.00 (p = 1.5008e-86)βtan

-kθ cos+

kθcos1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.50.60.70.80.9

11.11.21.31.41.5

) -n θ c

os+n θ

d(co

sσd

σ1

0

0.5

1

1.5

2

2.5A = 500GeV

SM

= 0.50 (p = 5.24765e-30)βtan

= 5.00 (p = 6.64868e-13)βtan

-nθ cos+

nθcos1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.50.60.70.80.9

11.11.21.31.41.5

) -r θ c

os+r θ

d(co

sσd

σ1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

A = 500GeV

SM

= 0.50 (p = 7.69759e-238)βtan

= 5.00 (p = 1.63257e-120)βtan

-rθ cos+

rθcos1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.50.60.70.80.9

11.11.21.31.41.5

Figure 8: Comparison between SM and two 2HDM MC simulations for the observablescos θk+ cos θk− , cos θn+ cos θn− and cos θr+ cos θr−. Those 2HDM are for tan β = 0.50and tan β = 5.00 corresponding to models with a pseudoscalar Higgs boson Aof mass 500 GeV.

14

) -n θ c

os+k θ

+ c

os-k θ

cos

+n θd(

cos

σd σ1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

A = 500GeV

SM

= 0.50 (p = 0.714004)βtan

= 5.00 (p = 0.648582)βtan

-nθ cos+

kθ + cos-kθ cos+

nθcos1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.90.920.940.960.98

11.021.041.061.08

1.1

) -n θ c

os+k θ

- c

os-k θ

cos

+n θd(

cos

σd σ1

0

0.2

0.4

0.6

0.8

1

1.2

1.4A = 500GeV

SM

= 0.50 (p = 0.604323)βtan

= 5.00 (p = 0.269678)βtan

-nθ cos+

kθ - cos-kθ cos+

nθcos1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.90.920.940.960.98

11.021.041.061.08

1.1

) -n θ c

os+r θ

+ c

os-r θ

cos

+n θd(

cos

σd σ1

0

0.2

0.4

0.6

0.8

1

1.2

1.4A = 500GeV

SM

= 0.50 (p = 5.58828e-16)βtan

= 5.00 (p = 3.32149e-16)βtan

-nθ cos+

rθ + cos-rθ cos+

nθcos1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.50.60.70.80.9

11.11.21.31.41.5

) -n θ c

os+r θ

- c

os-r θ

cos

+n θd(

cos

σd σ1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

A = 500GeV

SM

= 0.50 (p = 0.241301)βtan

= 5.00 (p = 3.84483e-06)βtan

-nθ cos+

rθ - cos-rθ cos+

nθcos1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.90.920.940.960.98

11.021.041.061.08

1.1

) -r θ c

os+k θ

+ c

os-k θ

cos

+r θd(

cos

σd σ1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

A = 500GeV

SM

= 0.50 (p = 0.236073)βtan

= 5.00 (p = 0.135133)βtan

-rθ cos+

kθ + cos-kθ cos+

rθcos1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.90.920.940.960.98

11.021.041.061.08

1.1

) -r θ c

os+k θ

- c

os-k θ

cos

+r θd(

cos

σd σ1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6A = 500GeV

SM

= 0.50 (p = 0.773254)βtan

= 5.00 (p = 0.0908534)βtan

-rθ cos+

kθ - cos-kθ cos+

rθcos1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

SM

Mod

el

0.90.920.940.960.98

11.021.041.061.08

1.1

Figure 9: Comparison between SM and two 2HDM MC simulations for the observ-ables cos θr+ cos θk− + cos θk+ cos θr− , cos θr+ cosk−− cos θk+ cos θr− , cos θn+ cos θk− +cos θk+ cos θn− , cos θn+ cos θk− − cos θk+ cos θn− , cos θn+ cos θr− + cos θr+ cos θn− andcos θn+ cos θr− − cos θr+ cos θn−. Those 2HDM are for tan β = 0.50 and tan β =5.00 corresponding to models with a pseudoscalar Higgs boson A of mass500 GeV.

3.2 Compatibility between the ATLAS data and the differentmodels

Once we know the observables for which we can distinguish each model from SM, wecompare the MC simulations with the measured data from ATLAS [10]. An example ofthis comparison for some of the observables is shown in Figure 10. In those plots we cansee that some observables have more discrepancy between the 2HDM and the data thanothers. For example, the observables cos θk+ and cos θn+ cos θr−+cos θr+ cos θn− do not let usexclude this model because, in the first case, the behaviour is really similar and, in thesecond, the error bars are too big. However, the observable cos θr+ cos θr− show a greatdiscrepancy between the model and the measurement. With a more detailed analysis,we could exclude this model.

Performing these comparisons for more 2HDM and observables we have found severalplots which show sensitivity between the SM, the 2HDM distributions and the data (e.g.Figure 11).

In Table 4 is shown a compilation of the probability of coincidence using the χ2 testwithout considering correlations between the ATLAS data and different models (all the2HDM that we study and the SM). In this table we can see that, the more sensitiveobservables are the correlation cos θk+ cos θk− , cos θn+ cos θn− and cos θr+ cos θr−.

In Table 5 is shown the same compilation of the probability of coincidence but, thistime, using the χ2 test taking into account the correlations (as we studied in section2.4). Comparing these tables (with and without correlation) we can see that, in general,the correlation between the bins decrease the probability of coincidence.

Although a more detailed analysis has to be performed, we have several evidences ofmodels that we could exclude that the usual method described in section 2.2 could not(e.g. Figure 12).

16

Figure 10: Example of plots for each kind of observable comparing the SM, one 2HDMwith mA = 500 GeV and tan β = 0.50 and the ATLAS data. The probabilityof coincidence have been calculated using the χ2 test considering correlations(as shown in section 2.4).

17

) -r θ c

os+r θ

d(co

sσd

σ1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

A = 750GeV

SM (p = 0.136261)

= 1.40 (p = 3.49351e-29)βtan

data

-rθ cos+

rθcos1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

data

Mod

el

0.5

1

1.5

2

2.5

) -k θ c

os+k θ

d(co

sσd

σ1

0

0.5

1

1.5

2

2.5 H = 500GeV

SM (p = 0.016533)

= 0.70 (p = 4.80935e-53)βtan

data

-kθ cos+

kθcos1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

data

Mod

el

0.5

1

1.5

2

2.5

) -n θ c

os+n θ

d(co

sσd

σ1

0

0.5

1

1.5

2

2.5H = 750GeV

SM (p = 0.000252426)

= 0.40 (p = 4.16711e-98)βtan

data

-nθ cos+

nθcos1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

data

Mod

el

0.5

1

1.5

2

2.5

Figure 11: Comparison between different 2HDM and the ATLAS data for some polar-ization observables.

18

) -r θ c

os+r θ

d(co

sσd

σ1

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

A = 750GeV

SM (p = 0.136261)

= 0.70 (p = 1.14877e-28)βtan

data

-rθ cos+

rθcos1− 0.8− 0.6− 0.4− 0.2− 0 0.2 0.4 0.6 0.8 1

data

Mod

el

0.5

1

1.5

2

2.5

Figure 12: Left: comparison between the ATLAS data and the 2HDM with mA =750 GeV and tan β = 0.70 for the observable cos θr+ cos θr−. Right: exclu-sion plot from [15] for the pseudoescalar A.

4 Conclusions

Many theories have been proposed to solve the limitations of the Standard Model. Thetechniques used for this finality are diverse. In many of them, the top quark plays animportant role due to its great mass which might mean that he would play a specialrole with BSM particles. If supermassive particles exist, they would probably decayto top quark (or to tt pair). In this project, we have worked with a simple extensionof the SM Higgs, the 2HDM. This model proposes five Higgs boson and two of themcontribute to the production of tt pairs via the Feynman diagram of Figure 1. We havealso seen that the authors of [9] tried to use the invariant mass of tt pair to find thisparticles but, the interference between Feynman diagrams caused the measurements tobe less sensitive, reason for which we were able to exclude only a few values of the freemodel parameters. This difficulty in finding particles has encouraged to study othersproperties of top quark, in our case, the polarization and the spin correlation of the ttpair. In [15] the authors used a set of observables, described in Section 2.2, and theycompared with the SM without observing any significative discrepancy. In this work, wehave compared the behaviour of these observables in different 2HDM, seeing that we canalways find some observable which differs with SM and allows us to distinguish it fromSM. Then, we performed the same comparison in [9], but, in this case, we compared theATLAS data with the results obtained from reconstructing the observables for the MCsimulations of 2HDM.

The results we obtained from doing these comparisons are very promising, since we ob-served significative discrepancies between measured values and the predicted by lots of

19

2HDM. The different preliminay statistical analysis we have performed point out that,in general, the correlations are the observables which are most sensitive because theirmeasurements have relatively small associated errors. If we examine the results providedby the χ2 test, without considering the correlations, we see that the biggest discrepan-cies we can find in the observable cos θn+ cos θn− for all 2HDM with the scalar H. Also, weobserve a significative discrepancy in the observable cos θk− in the model with mA = 500y tan β = 9.00.

Performing a more complete statistical test (χ2 with correlations), as we showed in Sec-tion 2.4, we noted some results with a higher discrepancy between 2HDM and data. Thisis because, in general, the correlations tended to move the data away from the modelsprediction. The biggest discrepancies are still observed in the observables related withthe correlations ( cos θk+ cos θk−, cos θn+ cos θn−, cos θr+ cos θr−).

This is the first attempt to interpret the measurement of the top spin observables toconstrain new physics models. Results seem very promising but are still very preliminary.More studies are needed to understand the sensitivity of the observables and optimizethe interpretation. For example, we have consider that the correlation affects at all theerror bar of the data but, in fact, it does not affect to the modeling uncertainty.This could lead to very interesting results in terms of interpretation of precise top quarkproperties.

20

Tab

le3:

Pro

bab

ilit

yof

coin

ciden

ceb

etw

een

the

MC

dat

aob

tain

edusi

ng

the

SM

and

the

diff

eren

t2H

DM

[15]

for

the

15ob

serv

able

sdefi

ned

in[9

].T

he

com

par

ison

hav

eb

een

per

form

edusi

ng

theχ

2te

st.

Pro

bab

ilit

ies

under

10−

10

(incl

usi

ve)

hav

eb

een

consi

der

edto

be

zero

.

Mas

sA

[GeV

]50

075

0XX

XXX

XXX

XXXX

Obse

rvab

les

tanβ

0.40

0.50

0.68

1.40

2.00

5.00

9.00

0.40

0.50

0.70

1.40

2.00

cosθk +

0.54

70.

914

0.00

253

0.00

335

0.04

163.

67·1

0−6

04.

48·1

0−5

0.00

0121

2.95·1

0−7

1.29·1

0−5

1.69·1

0−9

cosθk −

0.42

00.

390

0.93

20.

0001

880.

0363

0.30

50

7.90·1

0−9

1.31·1

0−5

0.00

0181

4.60·1

0−9

7.03·1

0−8

cosθn +

0.06

720.

111

0.90

10.

765

0.22

60.

0026

70

0.07

360.

0143

0.00

0277

0.00

0211

0.00

0239

cosθn −

0.73

10.

730

0.29

30.

0884

0.63

00.

0173

00.

0237

0.02

000.

556

0.00

294

0.00

0175

cosθr +

0.85

00.

400

0.13

40.

8253

0.18

90.

0481

00.

0067

60.

082

0.01

610.

0001

220.

0051

1co

sθr −

0.88

80.

112

0.84

50.

0068

50.

0443

0.01

480

0.00

0816

0.00

0363

0.22

60.

0595

0.01

00co

sθk +

cosθk −

00

00

00

00

00

00

cosθn +

cosθn −

00

00

00

00

00

00

cosθr +

cosθr −

00

00

00

00

00

00

cosθr +

cosθk −

+co

sθk +

cosθr −

0.39

60.

236

0.75

30.

764

0.91

70.

135

00.

0133

0.00

0211

0.17

50.

0264

0.01

49co

sθr +

cosk −−

cosθk +

cosθr −

0.76

90.

773

0.50

30.

227

0.10

60.

0909

00.

0007

200.

0770

1.73·1

0−5

0.21

30.

0001

25co

sθn +

cosθk −

+co

sθk +

cosθn −

0.94

20.

714

0.22

50.

0721

0.19

20.

649

00.

0084

20.

0052

70.

0004

240.

0067

80.

0457

cosθn +

cosθk −−

cosθk +

cosθn −

0.11

50.

604

0.87

70.

676

0.10

30.

270

00.

0036

30.

514

0.01

542.

96·1

0−6

0.09

07co

sθn +

cosθr −

+co

sθr +

cosθn −

1.46·1

0−6

04.

38·1

0−7

1.60·1

0−8

00

00

00

00

cosθn +

cosθr −−

cosθr +

cosθn −

0.81

10.

241

0.27

10.

0499

0.00

942

3.84·1

0−6

09.

24·1

0−7

0.00

0603

1.23·1

0−8

00

Mas

sH

[GeV

]50

075

0XX

XXX

XXX

XXXX

Ob

serv

able

sta

nβ

0.40

0.50

0.68

1.40

2.00

5.00

9.00

0.40

0.50

0.64

1.40

2.00

cosθk +

1.29·1

0−5

0.00

0146

0.00

723

8.22·1

0−7

0.00

338

0.00

101

0.44

30.

0097

80.

425

0.39

20.

2667

0.07

50co

sθk −

9.93·1

0−5

0.04

750.

0969

2.29·1

0−6

0.03

570.

0095

60.

0321

0.12

90.

744

0.08

050.

692

0.57

0co

sθn +

0.01

200.

429

0.08

700.

0224

0.24

40.

0178

0.01

450.

495

0.38

50.

237

0.98

30.

0058

3co

sθn −

0.12

40.

276

0.24

30.

206

0.32

50.

194

0.18

60.

920

0.27

90.

0112

0.25

90.

0622

cosθr +

0.38

60.

676

0.02

590.

0950

0.12

60.

150

0.80

20.

462

0.48

60.

618

0.28

60.

615

cosθr −

0.01

650.

268

0.09

980.

039

0.93

50.

673

0.17

20.

107

0.11

20.

960

0.23

60.

646

cosθk +

cosθk −

00

00

00

00

00

00

cosθn +

cosθn −

00

00

00

00

00

00

cosθr +

cosθr −

00

00

00

00

00

00

cosθr +

cosθk −

+co

sθk +

cosθr −

0.03

150.

145

0.64

20.

0307

0.47

80.

327

0.18

30.

0093

90.

100

0.32

20.

0019

00.

0490

cosθr +

cosk −−

cosθk +

cosθr −

3.26·1

0−5

4.39·1

0−7

0.00

146

1.16·1

0−7

1.00·1

0−6

5.41·1

0−9

8.41·1

0−9

0.13

80.

0318

0.32

39.

82·1

0−5

0.02

22co

sθn +

cosθk −

+co

sθk +

cosθn −

0.00

695

0.07

164.

41·1

0−6

3.61·1

0−6

0.00

0202

710.

0007

320.

0001

280.

574

0.77

20.

213

0.12

53.

81·1

0−5

cosθn +

cosθk −−

cosθk +

cosθn −

0.33

00.

0025

10.

176

0.00

562

0.08

400.

371

0.72

30.

274

0.38

40.

478

0.79

30.

405

cosθn +

cosθr −

+co

sθr +

cosθn −

0.00

0269

6.81·1

0−5

0.00

584

0.44

40.

577

0.03

431.

14·1

0−10

00

00

0co

sθn +

cosθr −−

cosθr +

cosθn −

6.03·1

0−5

0.20

60.

0005

376.

76·1

0−5

0.05

190.

0275

0.00

399

0.47

60.

130

0.49

60.

807

0.56

1

21

Tab

le4:

Pro

bab

ilit

yof

coin

ciden

ceb

etw

een

the

mea

sure

ddat

afr

omA

TL

AS

det

ecto

r[1

0]an

dth

eM

Cdat

afr

omth

ediff

eren

tm

odel

s(S

Man

d2H

DM

[15]

)fo

rth

e15

obse

rvab

les

defi

ned

in[9

].T

he

com

par

ison

hav

eb

een

per

form

edusi

ng

aχ

2

test

.P

robab

ilit

ies

under

10−

10

hav

eb

een

consi

der

edto

be

zero

.

Mas

sA

[GeV

]50

075

0XX

XXX

XXX

XXXX

Obse

rvab

les

tanβ

SM

0.40

0.50

0.68

1.40

2.00

5.00

9.00

0.40

0.50

0.70

1.40

2.00

cosθk +

0.88

70.

856

0.85

10.

729

0.94

10.

939

0.68

60.

038

0.79

00.

738

0.69

30.

719

0.50

3co

sθk −

0.66

50.

817

0.67

90.

629

0.48

30.

514

0.61

06.

14·1

0−3

0.38

90.

309

0.53

70.

359

0.35

1co

sθn +

0.97

00.

969

0.93

60.

959

0.95

50.

921

0.72

80.

533

0.93

20.

872

0.80

30.

800

0.79

6co

sθn −

0.88

80.

887

0.85

10.

813

0.70

10.

789

0.57

80.

034

0.64

70.

604

0.84

10.

530

0.45

3co

sθr +

0.40

10.

361

0.38

00.

430

0.36

10.

447

0.24

30.

177

0.32

40.

292

0.25

90.

296

0.33

2co

sθr −

0.90

90.

941

0.97

10.

939

0.83

20.

875

0.84

10.

594

0.94

00.

863

0.90

70.

898

0.84

2co

sθk +

cosθk −

0.62

20.

175

0.15

80.

139

0.17

50.

165

0.24

70.

147

0.21

80.

221

0.20

50.

204

0.23

7co

sθn +

cosθn −

0.56

20.

328

0.21

30.

144

0.02

80.

0309

0.35

70.

455

0.37

80.

312

0.20

20.

237

0.35

0co

sθr +

cosθr −

0.87

60.

155

0.13

60.

130

0.13

00.

092

0.12

90.

611

0.23

80.

154

0.19

40.

169

0.20

2co

sθr +

cosθk −

+co

sθk +

cosθr −

0.64

60.

695

0.72

20.

647

0.68

10.

676

0.73

30.

650.

679

0.73

40.

729

0.69

60.

718

cosθr +

cosk −−

cosθk +

cosθr −

0.94

60.

947

0.94

40.

942

0.94

70.

915

0.94

00.

862

0.92

70.

929

0.91

40.

925

0.91

5co

sθn +

cosθk −

+co

sθk +

cosθn −

0.86

00.

873

0.85

30.

824

0.85

20.

818

0.83

60.

580

0.77

50.

804

0.72

30.

792

0.77

0co

sθn +

cosθk −−

cosθk +

cosθn −

0.99

50.

995

0.99

00.

993

0.99

70.

997

0.99

50.

965

0.99

90.

994

0.99

90.

995

0.99

7co

sθn +

cosθr −

+co

sθr +

cosθn −

0.98

00.

875

0.75

00.

872

0.86

00.

868

0.62

10.

0006

110.

381

0.47

40.

419

0.38

90.

307

cosθn +

cosθr −−

cosθr +

cosθn −

0.80

50.

890

0.78

80.

804

0.76

10.

779

0.82

60.

146

0.75

50.

730

0.54

20.

688

0.69

1

Mas

sH

[GeV

]50

075

0XX

XXX

XXX

XXXX

Ob

serv

able

sta

nβ

0.40

0.50

0.68

1.40

2.00

5.00

9.00

0.40

0.50

0.64

1.40

2.00

cosθk +

0.71

80.

860

0.80

30.

803

0.82

70.

826

0.86

40.

878

0.96

80.

895

0.93

90.

951

cosθk −

0.69

80.

608

0.80

50.

765

0.83

30.

817

0.84

40.

761

0.71

50.

665

0.69

40.

789

cosθn +

0.91

70.

980

0.92

10.

875

0.94

10.

989

0.88

40.

940

0.95

10.

926

0.97

20.

822

cosθn −

0.95

70.

977

0.96

70.

887

0.87

70.

968

0.82

90.

933

0.78

50.

601

0.95

00.

743

cosθr +

0.45

90.

384

0.33

60.

389

0.48

50.

533

0.45

30.

389

0.32

40.

370

0.27

30.

494

cosθr −

0.84

40.

834

0.89

20.

872

0.92

50.

935

0.88

60.

842

0.89

80.

928

0.81

70.

878

cosθk +

cosθk −

0.07

50.

079

0.10

90.

065

0.10

10.

098

0.10

60.

157

0.18

70.

160

0.18

20.

149

cosθn +

cosθn −

7.51·1

0−7

1.24·1

0−7

3.00·1

0−8

7.91·1

0−9

02.

903·

10−

90

2.99·1

0−6

1.24·1

0−6

4.59·1

0−7

2.38·1

0−7

3.40·1

0−7

cosθr +

cosθr −

0.61

30.

579

0.53

80.

483

0.48

90.

447

0.37

70.

716

0.69

70.

712

0.59

20.

617

cosθr +

cosθk −

+co

sθk +

cosθr −

0.60

50.

640

0.67

90.

621

0.69

60.

682

0.54

50.

763

0.71

90.

654

0.73

40.

728

cosθr +

cosk −−

cosθk +

cosθr −

0.94

30.

927

0.95

70.

912

0.95

60.

936

0.95

20.

959

0.93

70.

937

0.94

30.

924

cosθn +

cosθk −

+co

sθk +

cosθn −

0.90

30.

866

0.91

10.

908

0.89

10.

896

0.91

80.

843

0.86

20.

881

0.91

10.

941

cosθn +

cosθk −−

cosθk +

cosθn −

0.99

50.

991

0.98

60.

954

0.99

50.

999

0.99

50.

998

0.99

80.

996

0.99

80.

990

cosθn +

cosθr −

+co

sθr +

cosθn −

0.92

90.

907

0.95

00.

984

0.98

00.

996

0.98

20.

383

0.63

30.

668

0.75

70.

696

cosθn +

cosθr −−

cosθr +

cosθn −

0.71

30.

788

0.74

90.

723

0.90

10.

792

0.83

30.

875

0.75

20.

855

0.79

00.

826

22

Tab

le5:

Pro

bab

ilit

yof

coin

ciden

ceb

etw

een

the

mea

sure

ddat

afr

omA

TL

AS

det

ecto

r[1

0]an

dth

eM

Cdat

afr

omth

ediff

eren

tm

odel

s(S

Man

d2H

DM

[15]

)fo

rth

e15

obse

rvab

les

defi

ned

in[9

].T

he

com

par

ison

hav

eb

een

per

form

edusi

ng

aχ

2

test

wit

hco

rrel

atio

n.

Pro

bab

ilit

ies

under

10−

10

hav

eb

een

consi

der

edto

be

zero

.

Mas

sA

[GeV

]50

075

0XX

XXX

XXX

XXXX

Obse

rvab

les

tanβ

SM

0.40

0.50

0.68

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508

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726

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501

0.43

30.

379

0.37

10.

149

cosθk −

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50.

356

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60.

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310.

135

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770.

0317

cosθn +

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40.

953

0.39

30.

756

0.90

00.

616

0.47

20.

227

0.84

10.

684

0.59

80.

626

0.45

7co

sθn −

0.56

50.

665

0.55

90.

381

0.33

90.

334

0.29

86.

23·1

0−5

0.10

40.

0686

0.45

70.

116

0.02

30co

sθr +

0.29

80.

240

0.27

10.

295

0.21

20.

334

0.15

50.

0392

0.07

800.

184

0.11

20.

208

0.19

9co

sθr −

0.61

80.

746

0.92

90.

753

0.42

10.

638

0.29

80.

173

0.58

70.

628

0.72

860.

536

0.54

7co

sθk +

cosθk −

0.01

650

00

00

02.

39·1

0−5

00

00

0co

sθn +

cosθn −

0.00

0252

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00

00

00

00

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0co

sθr +

cosθr −

0.13

60

00

00

00

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00

0co

sθr +

cosθk −

+co

sθk +

cosθr −

0.05

590.

0385

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60.

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560.

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720.

0679

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60.

0561

cosθr +

cosk −−

cosθk +

cosθr −

0.67

50.

685

0.66

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613

0.70

90.

554

0.68

20.

427

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6220

0.52

10.

644

0.70

3co

sθn +

cosθk −

+co

sθk +

cosθn −

0.29

20.

281

0.21

10.

217

0.19

90.

178

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10.

0136

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40.

142

0.09

970.

120

0.12

5co

sθn +

cosθk −−

cosθk +

cosθn −

0.95

90.

814

0.90

30.

892

0.99

30.

9996

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80.

536

0.99

70.

881

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90.

995

0.99

7co

sθn +

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+co

sθr +

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0.68

30.

295

0.10

00.

227

0.25

00.

181

0.01

70

0.00

0286

0.00

211

0.00

0763

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0377

2.31·1

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cosθn +

cosθr −−

cosθr +

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0.80

50.

837

0.82

70.

808

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60.

7901

0.44

00.

0005

750.

674

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80.

403

0.41

30.

447

Mas

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[GeV

]50

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0XX

XXX

XXX

XXXX

Obse

rvab

les

tanβ

0.40

0.50

0.68

1.40

2.00

5.00

9.00

0.40

0.50

0.64

1.40

2.00

cosθk +

0.25

00.

579

0.24

50.

456

0.30

60.

469

0.39

60.

714

0.77

90.

640

0.66

20.

830

cosθk −

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430.

0242

0.30

80.

102

0.24

20.

166

0.27

00.

359

0.19

20.

207

0.18

30.

291

cosθn +

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30.

958

0.61

20.

908

0.81

20.

921

0.89

10.

735

0.51

10.

434

0.85

20.

262

cosθn −

0.71

20.

913

0.79

50.

376

0.36

70.

920

0.24

00.

716

0.40

80.

240

0.80

90.

362

cosθr +

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10.

324

0.22

00.

212

0.40

50.

330

0.34

70.

312

0.16

60.

298

0.11

60.

402

cosθr −

0.47

80.

519

0.60

80.

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0.61

70.

659

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20.

307

0.79

10.

688

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20.

422

cosθk +

cosθk −

00

00

00

00

00

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cosθn +

cosθn −

00

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00

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cosθr +

cosθr −

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580.

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1.78·1

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0.05

520.

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3co

sθr +

cosθk −

+co

sθk +

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190.

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820.

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0961

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160.

178

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490.

131

cosθr +

cosk −−

cosθk +

cosθr −

0.39

30.

317

0.49

10.

285

0.35

20.

200

0.31

00.

614

0.52

10.

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0.42

70.

510

cosθn +

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+co

sθk +

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0.46

30.

297

0.50

90.

532

0.51

20.

489

0.43

10.

336

0.35

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415

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474

cosθn +

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cosθk +

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80.

627

0.75

50.

399

0.90

70.

994

0.98

90.

980

0.99

00.

997

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812

cosθn +

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445

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578

0.82

10.

553

0.76

20.

0003

290.

0087

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0060

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91co

sθn +

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cosθr +

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0.33

90.

658

0.44

70.

364

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516

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843

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50.

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90.

860

23

References

[1] Particle Data Group. Review of particle physics. Chinese physics C, 40(10):100001,2016.

[2] Roger Felipe Naranjo Garcia. Measurements of top-quark properties at 8 TeV usingthe ATLAS detector at the LHC. PhD thesis, Universitat Wuppertal, Fakultat furMathematik und Naturwissenschaften Physik Dissertationen, 2017.

[3] Adrian Irles Quiles. Determination of the top-quark pole mass using tt + 1 − jetevents with the ATLAS detector at the LHC. PhD thesis, University of Valencia,2014.

[4] A. Aguilar et al. Evidence for neutrino oscillations from the observation of ν¯ eappearance in a ν¯ µ beam. Physical Review D, 64(11):112007, 2001.

[5] Stephen P. Martin. A supersymmetry primer. Adv. Ser. Direct. High Energy Phys,21(515):1–153, 2010.

[6] Howard Georgi and Sheldon L. Glashow. Unity of all elementary-particle forces.Physical Review Letters, 32(8):438, 1974.

[7] Rabindra N. Mohapatra and Goran Senjanovic. Neutrino masses and mixings ingauge models with spontaneous parity violation. Physical Review D, 23(1):165,1981.

[8] CDF Collaboration. Evidence for a mass dependent forward-backward asymmetryin top quark pair production. Physical Review D, 83(11):112003, 2011.

[9] Werner Bernreuther, Dennis Heisler, and Zong-Guo Si. A set of top quark spincorrelation and polarization observables for the LHC: Standard Model predictionsand new physics contributions. Journal of High Energy Physics, 2015(12):26, 2015.

[10] ATLAS Collaboration. Measurements of top quark spin observables in tt eventsusing dilepton final states in

√s = 8 tev pp collisions with the ATLAS detector.

arXiv preprint arXiv:1612.07004, 2016.

[11] F. Abe et al. Observation of top quark production in p p collisions with the ColliderDetector at Fermilab. Physical review letters, 74(14):2626, 1995.

[12] CDF Collaboration. Observation of the top quark. Physical Review Letters,74(14):2632, 1995.

[13] Taesoo Song and Hamza Berrehrah. Hadronization time of heavy quarks in nuclearmatter. Physical Review C, 94(3):034901, 2016.

[14] G. Branco et al. Theory and phenomenology of two-higgs-doublet models, phys.rept. 516 (2012) 1–102. arXiv preprint arXiv:1106.0034, 136.

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[15] ATLAS collaboration. Search for heavy Higgs bosons a/h decaying to a topquark pair in pp collisions at

√s=8 tev with the ATLAS detector. arXiv preprint

arXiv:1707.06025, 2017.

[16] DESY. Dealing with systematics for chi-square and for log likelihood goodness offit statistics. http://www.desy.de/~blobel/banff.pdf, 2006.

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