Finding the Higgs boson via Vector Boson Fusion in …...de Higgs-boson gevonden met een...

16
Finding the Higgs boson via Vector Boson Fusion in the WW*‘ν‘ν decay channel with the ATLAS detector at s= 13 TeV with a misidentified jet Maarten Hammer 10525319 July 5, 2017 Report Bachelor Project Physics and Astronomy, size 15 EC Conducted between 10-4-2017 and 10-7-2017 Supervisors: Lydia Brenner Msc & Carsten Burgard Ph.D. Second Assessor : dr. Ivo van Vulpen Research institute: Nikhef Wordcount : 3949 Abstract Analysis of the VBF Higgs production in the decay mode H WW * ‘μ‘μ. In the case where only one jet has been identified. The data is collected with ATLAS detector in the LHC at a luminosity of 36fb -1 recorded at s = 13 TeV. Higgs boson mass is assumed to be 125 GeV. The data is analysed in three distinct cases. The first case assured as little simulated signal loss as possible and resulted in a 2.2(0.7)σ significance. The second case had aimed for a high signal over background ratio disregarding signal conservation and resulted in a signal over background rate of 0.20 with a significance of 1.7(0.5)σ. In the last case a balance was obtained between between VBF signal conservation and signal over background ratio. The last scenario resulted in a significance of 1.9(0.5)σ and signal over background ration of 0.09.

Transcript of Finding the Higgs boson via Vector Boson Fusion in …...de Higgs-boson gevonden met een...

Page 1: Finding the Higgs boson via Vector Boson Fusion in …...de Higgs-boson gevonden met een statistische signi cantie van 2.3˙, dit komt neer op een zekerheid van ongeveer 95%. 2 Contents

Finding the Higgs boson via Vector Boson Fusion in the

WW*→ `ν`ν decay channel with the ATLAS detector at√

s =

13 TeV with a misidentified jet

Maarten Hammer

10525319

July 5, 2017

Report Bachelor Project Physics and Astronomy, size 15 EC

Conducted between 10-4-2017 and 10-7-2017

Supervisors: Lydia Brenner Msc & Carsten Burgard Ph.D.

Second Assessor : dr. Ivo van Vulpen

Research institute: Nikhef

Wordcount : 3949

Abstract

Analysis of the VBF Higgs production in the decay mode H → WW ∗ → `µ`µ. In the

case where only one jet has been identified. The data is collected with ATLAS detector in

the LHC at a luminosity of 36fb−1 recorded at√s = 13 TeV. Higgs boson mass is assumed

to be 125 GeV. The data is analysed in three distinct cases. The first case assured as little

simulated signal loss as possible and resulted in a 2.2(0.7)σ significance. The second case had

aimed for a high signal over background ratio disregarding signal conservation and resulted

in a signal over background rate of 0.20 with a significance of 1.7(0.5)σ. In the last case a

balance was obtained between between VBF signal conservation and signal over background

ratio. The last scenario resulted in a significance of 1.9(0.5)σ and signal over background

ration of 0.09.

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Populair wetenschappelijke samenvatting

Het Higgs-boson is in 2012 door de wetenschappers van de ATLAS en CMS samenwerk-

ingsverbanden bevestigd. Ze hebben dit deeltje ontdekt door in de Large Hadron Collider

in Geneve protonen met zeer hoge snelheden te laten botsen. Bij deze botsing vervallen de

deeltjes in de protonen op verschillende manieren naar andere deeltjes. Door deze verval-

processen te modelleren kunnen voorspellingen worden gedaan over deze vervalkettingen.

Deze voorspellingen zijn vergeleken met de data die de ATLAS en CMS detectors meten en

hieruit is geconcludeerd dat het Higgs-boson een massa heeft van 125 GeV. Dit onderzoek

hebben ze gedaan door naar veel verschillende vervalprocessen te kijken en de resultaten

samen te voegen in een groot onderzoek.

In mijn onderzoek heb ik gekeken of ik in een specifieke vervalketting de Higgs kon vin-

den. Ik heb gekeken naar het geval dat de protonen W- of Z-deeltjes uitstralen die fuseren

in het Higgs deeltje. Dit noemt men Vector Boson Fusion omdat W- en Z-deeltjes vector

bosonen zijn en deze deeltjes fuseren in een Higgs-boson. Het Higgs-boson heeft een korte

levensduur, en vervalt voor het gedetecteerd kan worden. Het Higgs-boson kan alleen wor-

den gezien door zijn vervalproducten te bekijken. Ik heb gekeken naar het vervalprocess

waarbij het Higgs-boson naar twee W-deeltjes vervalt. Die dan weer vervallen in elektronen,

muonen en neutrinos.

Bij deze vervalketting zijn er vier deeltjes meetbaar door de ATLAS detector, twee jets

(deeltjes van de protonen) en twee geladen leptonen (een muon en een elektron). De neu-

trinos zijn niet meetbaar door de detector. Neutrinos zijn wel te reconstrueren door te

kijken waar de detector energie en impuls mist. De detector meet niet altijd alle deeltjes

die meetbaar zijn, en gevallen waar een deel van de data mist wordt meestal weggegooid. Ik

kijk wel naar deze data. Mijn onderzoek kijkt naar de data waar een jet mist of verkeerd is

geidentificeerd.

Bij de botsingen in de LHC wordt veel meer gemaakt dan alleen het signaal waar ik

naar kijk. Andere vervalketens kunnen dezelfde eindproducten hebben als het signaal waar

ik naar kijk (een jet, twee geladen leptonen en missende energie). Deze andere vervalketens

zijn achtergrond data voor mijn onderzoek naar het Higgs-boson. Door de reacties te mod-

elleren kan er een voorspelling worden gemaakt hoe deze andere vervalprocessen zich gedra-

gen. Door in deze voorspellingen te kijken waar deze achtergrond groter is dan het signaal

(VBF Higgs-bosonen) en deze achtergrond weg te knippen blijft er een kleine dataset over

waar veel signaal in zit relatief tot de achtergrond. Deze kleine dataset wordt de signaal

regio genoemd.

Deze selectie criteria heb ik daarna ook op de gemeten data toegepast van de ATLAS

detector. Door de gemeten data en de gesimuleerde data te vergelijken met elkaar heb ik

de Higgs-boson gevonden met een statistische significantie van 2.3σ, dit komt neer op een

zekerheid van ongeveer 95%.

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Contents

1 Introduction 4

2 Theory 5

2.1 Vector Boson Fusion Higgs boson production to W-Boson pair decay . . . . . 5

2.2 Data simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Data gathering in the ATLAS detector . . . . . . . . . . . . . . . . . . . . . . 6

2.4 Significance determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 VBF Analysis 8

3.1 Preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.2 Background rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.3 Event selection example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Results 12

5 Conclusion 14

6 Discussion 14

7 Acknowledgements 15

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1 Introduction

For the discovery of the Standard Model (SM) Higgs boson in 2012 by ATLAS [3] and CMS

[6], various production modes and decay channels have been used to reach a 5σ significance

for the discovery of the Higgs boson with a mass of 125 GeV. The analysis of the particle

has continued with higher center-of-mass energy to rediscover the Higgs boson in each in-

dividual production mode. In Vector Boson Fusion (VBF) this 5σ significance has not yet

been achieved.

In this report the VBF produced Higgs boson is analysed in the WW → `ν`ν decay

channel. In the case of a clean signal, the ATLAS detector can detect two quark jets, two

charged leptons and missing energy. The analysis has already been done in the clean signal

scenario and has resulted in a 1.9σ signal significance [5]. An analysis on data sets with

missing information has not been done yet.

The scenario where one jet has been misidentified is discussed in this report. In this

scenario the most effective event selection variables are unusable as they rely on data from

both jets. To reduce the background in this dataset a different approach has to be applied.

A set of 14 variables has been created to make an event selection on. Three of these variables

have been defined for this analysis specifically.

The analysis has been performed at a center-of-mass energy of√s =13 TeV with a 36

fb−1 luminosity using the ATLAS detector at the LHC. Due to large Drell-Yan background

of Z→ ee/µµ only states with opposite flavour and opposite sign have been considered. All

other Higgs boson production modes have been considered as background in this analysis

and a Higgs boson mass has been assumed of mH = 125 GeV.

Section 2 explains the production mode and decay channels of the SM VBF Higgs boson

as well as the data production. Section 3 explains three distinct selection processes used to

find the Higgs boson in this mode. In Section 4 the results are displayed and in 5 they are

presented. Finally, these results and future improvements to this analysis are discussed in

Section 6.

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2 Theory

2.1 Vector Boson Fusion Higgs boson production to W-Boson pair

decay

Vector Boson Fusion (VBF) is one of four dominant production modes of the Higgs boson

in the LHC [4]. The other three dominant production modes are gluon-gluon fusion (ggF);

associated production with a vector boson (VH) and with a top-pair (ttH). The distinct

difference between VBF and other Higgs boson production modes is that the quark jet is

not consumed in the reaction. In VBF two quarks produce vector bosons (W bosons or Z

bosons) which fuse into other particles. One of the possible results is a Higgs boson.

The lifetime of the Higgs boson is around 10−22seconds [7], which has the effect that the

ATLAS detector can only measure the decay products. The Higgs boson has five dominant

decay channels in the ATLAS detector [3]. The Higgs boson decay into a W boson pair is

discussed here. The full VBF Higgs boson → WW → `µ`µ production chain is displayed in

Fig. 1. Other decay channels of the Higgs boson are the H→bb, H →ZZ and H→ ττ .

Figure 1: The Feynman diagram describing the VBF Higgs boson production if it decays in two

W bosons who then decay into a two lepton-neutrino pairs [8].

2.2 Data simulation

The dataset used in this analysis consists of two parts, a simulation with truth information

and observed data by the ATLAS detector. The simulated dataset is generated by Monte

Carlo (MC) generators at√s = 13 TeV with an intensity of 36 fb−1. The data is simulated

to contain ggF and VBF Higgs bosons at 125 GeV. ttH and bbH Higgs boson production

modes have been neglected because of their small cross section. The VH associated produc-

tion modes have been neglected due to the small cross section in the Nlep = 2 region. The

ggF Higgs boson production mode is considered as a background for this analysis.

The simulation is accurate to next-to-leading order in all signal channels as well as ac-

curate in next-to-next-to-leading order in ggF Higgs boson production. The background

signals analysed are events with two W bosons (WW events); non-Higgs boson VBF events;

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single top-quark production events; W+jet production events; Z+jet production events as

well as other events with two bosons (other VV events) this includes Wγ, Wγ∗, WZ and

ZZ events. Further explanation on the background simulation, including the MC generators

used, can be found in Ref. [5].

2.3 Data gathering in the ATLAS detector

The observed data is measured by the ATLAS detector. A Toroidal LHC ApparatuS (AT-

LAS) is one of seven detectors in the Large Hadron Collider (LHC). The ATLAS detector is

a forward-backward symmetric cylindrical particle detector [2] and covers close to 4π solid

angle. It detects according to the coordinate system explained in Fig. 2.

The ATLAS detector consist of an inner tracking detector to determine the charge and

momentum of charged particles by tracking their movement through a strong magnetic field.

Around the inner detector hadronic and electromagnetic calorimeters determine the energy

of particles. In the outer shell large muon spectrometers determine the momenta and charge

of muons, which move through all other parts of the detector unhindered. Neutrinos are not

detectable by the ATLAS detector, but using the momentum and energy imbalance across

the 4π solid angle EmissT and pmissT can be determined which contains information about the

neutrinos [10].

Figure 2: The ATLAS detector uses a right-handed coordinate system with its origin at the

collision point in the beam pipe. The z-axis follows the beam pipe, the x-axis is directed to the

center of the LHC, the y-axis is points upward. The φ angle is measured with respect to the

x-axis. The θ angle is measured with respect to the z-axis. The pseudorapidity η is defined as

η = - ln tan(θ/2) [12].

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2.4 Significance determination

With the final dataset the significance σobserved of the signal can be determined by the

normal Poisson significance given in Equations 1 and 2 [1]. This is under the assumption

NS << NB [1].

S1 =NS√NB

(1)

S2 =NS√

NS +NB(2)

If NS and NB are of the same order of magnitude Eq. 3 should be used instead [1].

2 ∗ S12 = 2 ∗ (√Ns +NB −

√NB) (3)

In these equations the NS is defined as NData −NB = NS for the observed significance

σobs. NB is defined to be the simulated background (Section 2.2) and NData is defined to be

the observed data by the ATLAS detector (Section 2.3). To calculated expected significance

σexp, NS is set as the amount of simulated VBF events.

VBF signal strength is defined as µ [5]:

µV BF =σobsσexp

(4)

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3 VBF Analysis

Event selection processes have been applied to MC simulated data obtained in Section 2.2

and the observed data obtained in Section 2.3. The analysis is split in two parts. The

first part is preselection to get a dataset conforming with the channel selection VBF Higgs

boson→WW→ `ν`ν. The second part are arbitrary event selections made to reject as much

background as possible.

The background rejection selection criteria have been done in three distinct scenarios. In

the first scenario the criteria were applied such that as much signal is preserved as possible.

In the second scenario the criteria were applied very restrictively, aiming for a high signal to

background ratio. In the third scenario the criteria were balanced such that the final signal

region never drops below 3 simulated VBF events in the MC dataset. The final signal regions

(SR) have been named relaxed signal region, restrained signal region and semi-restrained

signal region. In Table 1 the cuts are shown in order of application to the final dataset with

respect to each signal region.

3.1 Preselection

To get a VBF Higgs boson→WW→ `ν`ν compatible event selection, a basic preselection

has been applied. Final state leptons are required to have a different flavour and different

charge. The most energetic lepton is classified as the leading lepton and is required to have

a pT > 22 GeV the other lepton is considered the sub-leading lepton and is required to have

a pT > 15 GeV. To reduce low-mass resonances, the invariant dilepton mass is limited at

m`` > 10GeV . To get events with one missing or misidentified jet Njet = 1 is set. Finally

a Nb−jet = 0 cut and a Z → ττ veto is applied to exclude top and Z-background from the

data. The Z → ττ veto eliminates most Z → ττ background by requiring the invariant ττ

mass (mττ ) to be away from the Z boson resonance [11].

3.2 Background rejection

After the preselection, the background rejection event selection is applied in the form of

data cuts. An overview of these cuts is displayed in Table 1. The restrained and semi-

restrained signal regions miss cuts because of the dependence of cuts. A harsh cut on

∆R`` =√

(∆φ``)2 + (∆η``)2, makes a cut on ∆φ`` or ∆η`` less effective or obsolete. In the

next paragraph each cut will be clarified in chronological order of application in the last

run. The order of application of the cuts has been changed repeatedly to check dependence

of cuts on each other.

The first applied cut is on the missing transverse energy EmissT caused by the immea-

surable neutrinos. This cut reduces mostly W+jet background which also produces neu-

trinos. The next cut is on the vectorial sum of the transverse mass of the two leptons

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√(m`0

T )2 + (m`1T )2, this cut reduces the heavier decay products from the background. After

that a cut is made on the vectorial sum of the transverse momentum of the two leptons p``T .

This is a cut that reduces the relative strength of the WW and tt background. After this a

cut is applied on the transverse mass of the leading lepton m`0T . This cut has a similar effect

as the cut on the vectorial sum of the two transverse masses of the lepton described above,

which is why it is left out.

Next up are the cuts on the angles between the two leptons. The first cut in this cate-

gory is the ∆R`` =√

(∆φ``)2 + (∆η``)2 cut. This cut combines the azimuthal separation

∆φ`` and the rapidity separation ∆η``. These angles between the leptons are a result of the

H→WW split in the decay mode. For signal events these angles tend to be small. After the

cut on ∆R`` fine tuning cuts can be applied on ∆φ`` and ∆η``, but in the more restricted

scenarios this does not improve the data.

After the cuts on the separation of the two leptons a new set of cuts is defined. These

cuts are inspired by the outside lepton veto. The outside lepton veto requires the final state

leptons to exist in the rapidity gap spanned by the two jets in the final state [9]. As this

analysis only considers single jet events, this veto is not possible. To simulate the correla-

tion between the two jet system and the two lepton system three new variables have been

declared and cut on. ∆η``,jet compares the rapidity separation between the combined two

lepton system and the jet. ∆φ``,jet compares the azimuthal separation between the com-

bined two lepton system and the jet. ∆R``,jet =√

(∆φ``,jet)2 + (∆η``,jet)2 is a dependent

variable on the combination of the two. Te only link between the two lepton system and the

jet system is the VBF Higgs boson, so any correlation between the two systems is caused

by the Higgs boson.

Three final cuts have been applied. The cut on invariant mass of the dilepton system

m`` reduces WW and tt background. In VBF Higgs boson production the jet prefers to

move along the beam pipe and thus the rapidity ηjet is often higher than in scenarios where

non VBF events occur. A final cut is applied in the strict region to the momentum of the

leading lepton p`0T which reduces the W boson and ggF Higgs boson events at cost of large

signal strength.

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Condition Relaxed SR Restrained SR Semi-Restrained SR

Preselection Two isolated leptons with different flavour and opposite sign

p`0T > 22 GeV, p`1T > 15 GeV

M llT > 10 GeV

Njets = 1

Nb−jets = 0

Z → ττ − veto

Background EmissT < 100 GeV < 150 GeV -

rejection√

(m`0T )2 + (m`1

T )2 < 140 GeV < 120 GeV < 100 GeV

p``T > 60 GeV > 60 GeV > 60 GeV

m`0T < 110 GeV < 110 GeV -

∆R`` < 2.1 < 1.0 < 1.0

∆φ`` < 2.0 - -

∆η`` < 1.3 < 0.4 -

∆R``,jet > 3.1 > 3.2 > 2.9

∆η``,jet > 1.7 > 2.1 > 2.1

∆φ``,jet > 1.5 > 2.55 > 2.55

m`` < 60 GeV - -

|ηjet| > 1.5 > 1.1 > 1.7

p`0T - > 60 GeV -

Table 1: Event selection criteria used in each of the three signal regions of the VBF analysis,

definitions of the variables are given in the text (Section 3.1 and 3.2).

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3.3 Event selection example

In this subsection two examples have been given on event selection. All criteria have been

applied manually, which leaves the exact positions open for discussion. To determine where

to cut, the simulated data has been displayed as a minimalistic plot. This plot only shows

the background and the signal without specifying the breakdown of the contributions of

the background. In this minimalistic plots the signal (shown as a thick blue line) has been

re-scaled to be of the same order of magnitude as the background (shown as a thin line,

with hashed statistical deviation displayed).

The Fig. 3 and 4 display two scenarios in which the cuts have been made. Fig. 3 is an

example of a cut that allows for arbitrary tightness. If the goal is to preserve as much signal

as possible the cut is placed at 2.1, while a more restraining scenario could place it at 1.0.

In the second example (Fig. 4) the final cut has been placed around 3.0 in all three signal

regions as it is either very effective, or not effective at all.

(a) R`` distribution after the m`0T cut in

the relaxed SR.

(b) R`` distribution after the R`` cut in

the relaxed SR.

Figure 3: Example of a cut on ∆R``, VBF (MC) events have been scaled by 200, corresponds

with the ∆R`` event selection criteria in the relaxed signal region.

(a) R``,jet distribution after the ∆η``,jet

cut in the relaxed SR.

(b) R``,jet distribution after the ∆R``,jet

cut in the relaxed SR.

Figure 4: Example of a cut on ∆R``,jet, VBF (MC) events have been scaled by 90, corresponds

with the ∆R``,jet event selection criteria in the relaxed signal region.

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4 Results

The event selection criteria defined in Table 1 and Sections 3.1 & 3.2 have been applied

to the MC simulated data and the observed data from the ATLAS detector. These event

selections resulted in three signal regions. The breakdown of final state contributions of the

background and signal is shown in Table 2 In the relaxed signal region MC data expects

8 VBF Higgs boson events with a signal over background of 0.05. In the restrained signal

region a signal over background ratio of 0.20 is expected with 1.5 VBF Higgs boson events.

In the semi-restrained signal region a balance of the two is found with 3 VBF Higgs boson

events with a signal over background ratio of 0.09.

Category Relaxed SR Restrained SR Semi-restrained SR

VBF Higgs bosons 8.17 ± 0.24 1.46 ± 0.10 3.07 ± 0.16

Other Higgs bosons 33.8 ± 33.83 3.30 ± 0.42 8.84 ± 0.62

WW 46.17 ± 1.72 1.46 ± 0.29 5.13 ± 0.59

Other VV 12.12 ± 2.96 0 ± 0 4.32 ± 1.93

Top-quark 44.52± 3.61 1.80 ± 0.61 6.72 ± 1.32

W+Jets 22.30 ± 14.3 0.93 ± 1.08 6.80 ± 4.77

Z+Jets 6.36 ± 2.93 0 ± 0 1.75 ± 1.6

Total background 165.3 ± 15.0 7.4 ± 1.2 33.6 ± 5.3

Observed Data 197 14 46

Table 2: MC and Data yields for each signal region defined in Section 3. The total background

can differ slightly from the sum of the contributions due to rounding. Other Higgs boson have

been considered background in this analysis.

An overview of the mT =√

(E``T + EmissT )2 − |p``T EmissT |2 with E``T =√|p``T |2 +m2

`` dis-

tributions of the final signal regions is given in Figures 5a, 5b and 5c.

Using Eq. 2 the observed and expected significance have been determined of the signal

regions and using Eq. 4 the signal strength is determined. The signal strength and signifi-

cance of each signal region is summarised in Table 3.

The 120-140 mT bin in Fig. 5a has been analysed individually on significance and signal

strength. This subset of the relaxed signal region shows a higher observed significance than

the total signal region. As result the signal strength is also stronger in this bin.

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(a) Relaxed SR (b) Restrained SR

(c) Semi-restrained SR

Figure 5: mT distribution in the final state of the signal regions. MC data is displayed as

bars with contribution breakdown as displayed in the legend. The hatched band shows the

statistical uncertainty of the MC data. Data is shown as black crosses. The thick blue line is

the expected MC VBF Higgs boson signal. The difference between data and MC background

is used as observed VBF Higgs boson signal.

Signal Region Significance(expected) Signal Strength

Relaxed 2.3(0.6)σ 3.9µ

Restrained 1.7(0.5)σ 3.4µ

Semi-restrained 1.9(0.5)σ 3.8µ

Best single bin 2.6(0.5)σ 5.0µ

Table 3: Significance in all signal regions calculated using Eq. 2. The best single bin significance

is calculated using the 120-140 mT bin of the relaxed cut shown in Fig. 5a.

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5 Conclusion

Event selection processes have been applied to data collected by the ATLAS detector to

search for the VBF Higgs boson → WW → `ν`ν signal among the background. Three sets

of event selection criteria have been applied to the data to form three signal regions. The

observed (expected) signal significance of the mH = 125 GeV VBF Higgs boson is 2.3(0.6)σ

for the relaxed signal region; 1.7(0.5)σ for the restrained signal region; and 1.9(0.5)σ for

the semi-restrained signal region. A single bin analysis has also been performed to find

a 2.6(0.5)σ significance in one bin of the final state mT distribution in the relaxed signal

region. The signal strength of the data is found to be 3.9µ for the relaxed signal region;

3.4µ for the restrained signal region and 3.8µ for the semi-restrained signal region.

6 Discussion

The Higgs boson was discovered with 5.0σ significance in 2012 by ATLAS using multiple

production modes and decay channels. The VBF Higgs boson has already been analysed

in the H → WW → `ν`ν decay channel, but it has never been done with a missing jet.

Previous SM VBF Higgs boson analysis has resulted in a 1.9σ significance [5]. The data and

event selection provided in this report could help the search for the Higgs boson in the VBF

production mode to reach the 5σ. Finding a signal in the mH =125 GeV standard model

Higgs boson is expected for this analysis and complies with a SM Higgs boson prediction.

Many improvements can be made to the analysis done in this report. One of which is

to search for a selection process that can be applied to reduce ggF produced Higgs bosons

from the data. The ggF Higgs boson is between 20 and 40 % of the background in the

final signal regions in the VBF Higgs boson analysis. Even though ggF Higgs bosons are

not background for Higgs boson analysis, a veto on this production mode could be useful in

VBF Higgs boson production analysis specifically.

Because the event selection cuts have been applied by hand, they are probably not the

most effective or efficient. To resolve this problem an automated multivariate analysis could

be applied around the most significant selection cuts found in this analysis. This analysis

compares the data simultaneously over all variables and searches for ideal event selection.

The final signal region in a multivariate analysis will have higher signal to background ratio

than a cut-based analysis. The variables to train this multivariate analysis on would be a

subset of φ``, η``, R``, φ``,jet, η``,jet, R``,jet, EmissT , m`0

T , m`1T , p``t , m`` and ηjet.

Another method to increase the significance of this research is to collect more data. In

this analysis the signal region with relaxed cuts has resulted in the highest significance. This

significance of a signal depends on amount of signal and the signal over background ratio.

In the more restrained signal regions the benefit of higher signal over background ratio does

not surpass the disadvantage a lower signal count brings which results in lower significance.

For future analyses done on higher luminosity the more restraining signal regions might

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prove to be more effective.

In this analysis observed signal has been defined as NData − NB = NS . As result the

signal strength µ is high. This could indicate that some background is missing in the analysis

and the real significance should be lower. To test if the background is as stated, control

regions should be added to the analysis. A control region is, like a signal region, a subset

of your data. But in a control region the MC data is compared to the observed data to

compare the accuracy of your MC data. These subsets are taken in regions with good

predictions of the background. In Section 3.1 a cut is made using a Z→ ττ veto. This

veto is so effective because the Z→ ττ is a predictable background. By inverting the veto

you create a control region with a very strong Z→ ττ signal. If the MC data and observed

data vary greatly in this control region the background prediction is incorrect. To prove the

background prediction is correct, multiple control regions have to be checked.

7 Acknowledgements

I would like to thank my supervisors Lydia Brenner and Carsten Burgard for answering all

questions that came up. You have been the most supportive and excitable supervisors I

have ever been able to work with. I would also like to thank Ivo van Vulpen for taking the

time to read my thesis as second assessor.

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