width in the off shell H → ZZ region
July 5, 2017 Author: Gabriël Koole 10663746 Supervisors: Ivo van Vulpen Hella SnoekReport Bachelor Project Physics and Astronomy 15 EC
Conducted between April 3 and July 5, 2017
NIKHEF
UNIVERSITEIT VANAMSTERDAM
Abstract
The Higgs boson decay width (ΓH) provides information about the mean lifetime
of the Higgs boson and its couplings to other particles, yet is still unknown. Using simulated data, the invariant mass resolution in the ZZ → 4µ channel of the ATLAS detector at the Large Hadron Collider (LHC) in CERN is determined to be 1.7 ± 0.2 GeV for 100 < minv < 130GeV. Since the expected width based on the Standard
Model (SM) is 4.15 MeV for a 125 GeV Higgs boson, the ATLAS detector is not sen-sitive enough to directly measure the Higgs width. Due to quantum interference between the gluon processes, the number of expected events in the minv > 300GeV
region is influenced by the Higgs width. To quantify this, simulated data in which a ΓHfive times the SM width is implemented is compared to simulated data assuming
a SM Higgs width. The difference is a 5.6% (S = 0.60σ) increase in expected events for the data with the greater Higgs width. After reducing the quark background by applying a cut in the minimal angular separation (∆R) between a jet and a Z boson, the impact is enhanced to 8.7% (S = 0.93σ). In order for this impact to exceed the statistical uncertainty of√N, at least 131 events in the minv > 300GeV region of the
4µinvariant mass distribution are needed. For this the LHC has to gather 234 fb−1 of integrated luminosity, which CERN has set out to reach before 2023.
Samenvatting
De verwachte leeftijd van een Higgs boson is ontzettend klein: 1.56 · 10−22 s. Het doel van deze thesis is het bepalen van de breedte van de breedte van het Higgs boson (ΓH). Deze breedte, de vervalsbreedte genoemd, is namelijk een directe maat
voor de leeftijd van het Higgs boson. Op basis van het Standaard Model (SM) is de verwachte breedte van het Higgs boson bekend: 4.15 MeV. Mocht de breedte veel groter blijken te zijn, dan zou dat betekenen dat het Higgs bosonen naar meer deeltjes kan vervallen dan we nu kennen. Eerst is gekeken naar de invariante massa resolutie van de ATLAS detector voor het verval van Higgs bosonen naar twee Z bosonen die elk weer vervallen naar twee muonen. Op basis van gesimuleerde data bleek de resolutie 1.7 ± 0.2 GeV te zijn in het gebied rond 125 GeV, dus kan de breedte niet direct gemeten worden. Een mogelijke oplossing voor dit probleem is de quantum interferentie tussen het proces waarbij twee gluonen een Higgs deeltje vormen dat vervalt naar twee Z boson, en het proces waarbij twee gluonen direct twee Z bosonen produceren. De vervalsbreedte van het Higgs deeltje blijkt namelijk terug te komen in de interferentie termen. Het effect van een grotere Higgs boson breedte als gevolg van interferentie is bepaald door te kijken naar twee datasets waarin verschillende breedtes geïmplementeerd zijn. Het effect bleek een toename van 5.6 % in het verwachte aantal events bij een breedte die 5 keer groter is dan de SM Higgs breedte. Om dit effect significant te maken, moet de statistische fout kleiner worden dan 5.6 %. Daarvoor zijn minstens 319 specifieke events nodig. Dit gaat de Large Hadron Collider (LHC) naar verwachting nog minsten 10 jaar kosten, dus is er gekeken of we dit effect kunnen vergroten door de achtergrond te reduc-eren. Door bepaalde snedes uit te voeren in de gesimuleerde data is het effect ver-groot naar 8.7 %. Dit lijkt misschien niet veel, maar nu zijn ’slechts’ 131 specifieke events nodig, iets wat CERN waarschijnlijk gaat behalen voor 2023.
Contents
1 Introduction 1
2 The Higgs boson in the Standard Model 2
2.1 The Standard Model . . . 2
2.2 The Higgs Mechanism . . . 4
2.2.1 Gauge invariance . . . 4
2.2.2 Symmetry breaking. . . 4
2.3 The Higgs boson decay width . . . 6
2.3.1 The decay width of unstable particles . . . 6
2.3.2 The expected Higgs boson decay width . . . 7
2.4 Higgs production & decay . . . 8
2.4.1 The ZZ → 4µ channel . . . 8
2.4.2 The 4µ invariant mass distribution . . . 9
2.5 Interference between the gluon processes . . . 10
3 The ATLAS detector 11 3.1 Introduction . . . 11
3.2 The transverse momentum resolution of the ATLAS detector . . . 12
3.2.1 Measurement of the muon transverse momentum in the Muon Spectrometer . . . 12
3.2.2 The transverse momentum resolution for ZZ → 4µ events from simulated data . . . 12
3.3 The invariant mass resolution of the ATLAS detector . . . 14
3.3.1 Calculating the invariant mass for H → ZZ → 4µ events . . . . 14
3.3.2 The invariant mass resolution for ZZ → 4µ events from simu-lated data . . . 15
4 Impact of a larger width of a Higgs boson 17 4.1 Introduction . . . 17
4.2 The impact of ΓH on the invariant mass distribution of the four muons via quantum interference. . . 17
4.3 The invariant mass ratio for simulated data with ΓSMH and Γ5SMH in the gluon processes . . . 18
4.4 The influence of the Higgs width on the combined q ¯q → ZZand gg → H → ZZprocesses . . . 19
4.5 Statistical analysis on the impact of a greater Higgs boson width . . . . 21
5 Separating the gg → ZZ and q ¯q → ZZprocesses 22 5.1 Introduction . . . 22
5.2 The variables discriminating the gg → ZZ and q ¯q → ZZprocesses . . 22
5.3 Analysis of cuts on θZZ and ∆RjZ . . . 24
Chapter 1
Introduction
The Standard Model (SM) of particle physics is one the most celebrated theoretical frameworks that describes the way in which particles, the building blocks of mat-ter, interact. It contains three of the four fundamental forces as well as all known elementary particles and forms a basis from which we can pose predictions and con-duct experiments. In 2012 the CMS and ATLAS collaborations at CERN managed to detect the last unobserved particle in the SM: the Higgs boson. Although this dis-covery completes the observation of all particles in the SM, fundamental questions about the properties of the Higgs boson remain unanswered. One of the properties of the Higgs boson that is still unknown is its decay width (ΓH). The decay width
of a particle provides information about its mean lifetime and its couplings to other particles. Since the Higgs boson mass was determined in 2012, the expected decay width according to the SM can be calculated. The goal of this thesis is to test whether the Higgs decay width is in line with our expectations from the SM. Measuring the Higgs boson width could be used as a method to test the SM because a deviation from the expected decay width could be a consequence of the Higgs boson decaying to other exotic particles that do not (yet) fit within our current physical frameworks. The outline of this thesis is as follows. Chapter 2 describes the theoretical frame-work on which this thesis is based and discusses the specific goals and hypotheses of this thesis. In chapter 3 the experimental resolutions of the ATLAS detector will be determined from simulations to check whether or not it is sensitive enough to directly measure the Higgs decay width. In Chapter 4, the effect of the Higgs boson width in the high mass region is examined. Chapter 5 provides an analysis of sim-ulated data reducing background signals to improve sensitivity for the Higgs boson width in the high mass region. In Chapter 6 the concluding remarks are presented.
Chapter 2
The Higgs boson in the Standard
Model
This thesis is devoted to the search for the Higgs boson decay width. In this chapter the theoretical concepts on which this thesis is based are discussed. First, the Stan-dard Model and the role of the Higgs boson in the StanStan-dard Model are discussed. In section2.3and2.4 the decay width of unstable particles and the expected decay width of the Higgs boson are discussed, followed by a discussion of the production and decay of Higgs bosons in the Large Hadron Collider at CERN in the last section.
2.1
The Standard Model
As mentioned in the introduction, the SM describes three of the four fundamental interactions: the electromagnetic force, the weak force and the strong force. Each force is mediated by one or more gauge bosons (table 2.1). The electromagnetic force, mediated by photons, for example acts between atomic nuclei and electrons, while the strong force, mediated by gluons, binds neutrons and protons to form atomic nuclei. The weak force is the only fundamental force in the SM which is mediated by massive bosons: the W± and Z0 bosons, and its best known effect is
radioactive decay. The fourth fundamental force, gravity, is not described by the SM but is extremely weak compared to the other interactions, so is therefore not discussed here.
Interaction Mediator Spin / Parity
strong gluon, G 1−
electromagnetic photon, γ 1− weak W±, Z0 1−, 1+
TABLE2.1: The three fundamental interactions in the Standard Model and the corresponding boson mediators and the spin/parity of the
mediators. (Perkins,2000).
These forces mediate the interactions between the fundamental particles of mat-ter: fermions. Fermions are spin-1/2 particles are classified as leptons and quarks. The leptons and quarks are divided into three ’families’ that have different masses. The lightest family consists of the electron (e), the electron-neutrino (νe), the
up-quark (u) and the down-up-quark (d). These particles are stable and make up the vis-ible universe, whereas the particles of the second and the third family are unstable and will decay (Deigaard, I.,2016). The fundamental fermions and some of their quantum numbers are shown in table 2.2. The leptons interact through the elec-tromagnetic and weak forces, except for the neutrino’s which only interact via the
weak force since they carry no electric charge. The quarks also interact through the electromagnetic and weak forces as well as the strong force, because quarks carry colour-charge.
Particle Flavour Q/|e| I3
leptons e µ τ - 1 -1/2 νe νµ ντ 0 +1/2 quarks u c t +2/ 3 +1/2 d s b -1/ 3 -1/2
TABLE 2.2: The fermions in the Standard Model with their symbol, the ratio of their electric charge Q to the elementary charge e and the
third component of the weak isospin I3(Perkins,2000).
The interactions in the SM are based on local gauge symmetries in nature. The gauge bosons discussed above are represented mathematically by vector fields: gauge fields. The SM is a gauge theory in which the fermions interact via the exchange of these gauge fields (Pich,2012). The γ, W±and Z0 fields form the electroweak sector of the SM. In the next section, the consequences of imposing local gauge symmetry in the electroweak sector of the SM will be discussed, resulting in the Higgs mecha-nism: the spontaneous symmetry breaking of the electroweak symmetry group.
2.2
The Higgs Mechanism
Through interacting with the Higgs field, the particles in the Standard Model acquire mass. This is called the Higgs Mechanism, which was introduced to solve problems arising from local gauge symmetry in the electroweak sector of the SM. In this sec-tion the problems from imposing gauge invariance will be discussed, followed by the introduction of the Higgs mechanism as the solution for these problems.
2.2.1 Gauge invariance
Gauge invariance is a powerful tool to determine the dynamical forces among the fundamental constituents of matter (Pich,2012). It states that the Lagrangian of a system is invariant under local transformations. In electromagnetism for example, the physical electric and magnetic fields, E and B, are obtained from scalar and vec-tor potentials φ and A. Imposing gauge invariance means that the E and B fields are invariant under the gauge transformation:
Aµ→ A0µ= Aµ− ∂µχ (2.1)
where Aµ= (φ, −A)and ∂µ= (∂0, ∇)(Thompson,2013). In the Standard Model,
physicists assume a fundamental symmetry similar to the gauge invariance of elec-tromagnetism. This symmetry requires local gauge invariance, which states that the Lagrangian is invariant under local gauge transformations defined as:
ψ → ψ0 = eiα(x)ψ (2.2)
This invariance was achieved by the introduction of a new vector field Aµwhich
transforms specifically according to equation2.1. This vector field is interpreted as the field corresponding to a massless gauge boson (Thompson,2013). Since Aµ is
interpreted as a massless boson, the symmetry requirements in the SM, namely the local gauge invariance, make it impossible for gauge bosons to acquire mass. The weak force though is of short range and very weak at low energies, which implies that its mediating bosons, the W- and Z bosons, have large masses. The W- and Z gauge bosons have indeed been measured to have large masses, which is in clear contradiction with the symmetry requirements of the SM. A mechanism giving rise to the masses of W- and Z bosons while maintaining gauge symmetry will be dis-cussed next.
2.2.2 Symmetry breaking
The previous section described the mass problem that arises from local gauge sym-metry. The solution to this problem is the introduction of a new complex scalar field with a specific potential that keeps the Lagrangian gauge invariant, but breaks the symmetry of the vacuum (Van Vulpen,2013). As a result the W- and Z bosons in the SM acquire mass through this spontaneous symmetry breaking (Chatrchyan,2014). This mechanism is called the Higgs mechanism, or Brout-Englert-Higgs mechanism, and was proposed by Higgs (Higgs,1964) and Brout & Englert (Englert, F. & Brout, R.,1964) in 1964.
For the Lagrangian in the electroweak sector of the SM to be invariant under local gauge transformation, the derivatives must be replaced with corresponding covari-ant derivatives which include the new vector field (Aµ) discussed above, resulting
in a Lagrangian:
L = (Dµφ) · (Dµφ) − V (φ2) (2.3) The Higgs mechanism is the spontaneous symmetry breaking of this Lagrangian (2.3) due to introducing a complex scalar field with a potential:
V (φ) = µ2φ†φ + λ(φ†φ)2, (2.4) where µ represents the mass of the particle and λ is positive to ensure that the Lagrangian has an absolute minimum (Thompson, 2013). There are two possible shapes of the potential depending on the sign of µ2. These shapes are shown in figure2.1.
FIGURE2.1: The shape of the Higgs potential V(φ) in the case µ2> 0
(left), and µ2< 0 (right) (Barceló,2012).
The minimum of the potential is defined as the vacuum state. In the µ2> 0 case,
the potential has a single minimum at φ = 0 and the Lagrangian is symmetric. In the µ2 < 0 case however, there are infinitely many minima for the potential, so the vacuum state is degenerate. By choosing a physical vacuum state the symmetry of the Lagrangian is broken, but gauge invariance is respected.
The symmetry breaking of the Lagrangian produces a complex scalar field with four degrees of freedom (Chatrchyan,2014). Three degrees of freedom lead to the W- and Z bosons, while the fourth gives rise to a massive scalar field η. This scalar field is the Higgs field. In addition to this Higgs field, the symmetry breaking of the Lagrangian also gives a description of the gauge bosons having mass. Therefore, introducing a Higgs mechanism not only produces a Higgs particle, but also solves the problem of massless gauge bosons from local gauge symmetry.
2.3
The Higgs boson decay width
As discussed in the previous section, the spontaneous symmetry breaking in gauge theories could be achieved through the introduction of a scalar field (CMS collab.,
2012). This results in the W- and Z bosons acquiring mass and the prediction of a new scalar particle: the Higgs boson. The mass of the Higgs boson itself is a free variable which had to be experimentally determined. Once the Higgs mass is deter-mined, it is possible to determine the expected decay width based on the SM. In this section the decay width as a measure for the lifetime of a particle is briefly discussed, followed by a discussion of the measurement of the Higgs boson mass in 2012 and its corresponding expected decay width.
2.3.1 The decay width of unstable particles
In quantum mechanics, the energy-time uncertainty principle provides a theoreti-cal limit to the precision with which the pair of properties energy & (life)time of a particle can be known:
∆E∆t ≥ ¯h
2 (2.5)
This results in a significant theoretical uncertainty in the energy for particles with a short lifetime (unstable particles). Therefore measuring the energy, or invariant mass (which depends on the energy), of such a particle a large number of times provides a probability distribution, see figure2.2.
FIGURE2.2: The probability density function for a Breit-Wigner dis-tribution, using values for the Z boson mass and width as parameters
(Ocariz, J.,2014).
A probability distribution as the one shown in figure2.2is called a Breit-Wigner distribution. The decay width Γ of the particle is defined as twice the uncertainty in the energy, which corresponds to the actual width of the Breit-Wigner peak.
From there, it follows that: ∆E = Γ 2 = ¯ h 2τ ⇒ τ = ¯ h Γ, (2.6)
where the particle lifetime τ is taken as the uncertainty in time. The decay width of a particle thus provides a way to determine the lifetime of highly unstable par-ticles. In the next section the expected decay width of the Higgs boson will be dis-cussed.
2.3.2 The expected Higgs boson decay width
In 2012 the CMS and ATLAS collaborations at CERN managed to detect the Higgs boson and determine its mass: mH= 125.3 ± 0.4 (stat.)± 0.5 (syst.) GeV (CMS collab.,
2012, ATLAS collab.,2012). From there, the expected Higgs boson decay width ac-cording to the Standard Model (ΓSMH ) corresponding to this mass can be determined. The Higgs decay width as a function of the Higgs boson mass is displayed in figure
2.3.
FIGURE2.3: SM Higgs total width as a function of the Higgs-boson mass (Dittmaier,2011).
The expected total ΓSM
H for mH = 125.3GeV is 4.15 MeV (Dittmaier,2011),
cor-responding to a mean lifetime of 1.56 ·10−22s. As mentioned in the introduction, a deviation in the width of the Higgs boson (ΓH) could lead to new physics beyond
the Standard Model. If ΓH is found to be much larger than the expected value based
on the SM, it would be possible that the Higgs boson decays to more particles than the SM currently contains. To test this the width of the Higgs boson would have to be measured. This thesis is devoted to this search for the Higgs boson width.
2.4
Higgs production & decay
In the previous section the expected Higgs boson mean lifetime was determined to be 1.56 ·10−22s. The goal is to determine the mean lifetime of the Higgs boson exper-imentally to check whether or not it is in line with our expectations based on the SM. To do this, the Large Hadron Collider (LHC) in CERN produces Higgs bosons by let-ting protons with very high energies (√s= 7 TeV or 8 TeV) collide. From measuring various properties of the decay products of Higgs bosons, the ATLAS experiment at the LHC provides experimental data from which we can hopefully determine the Higgs boson width.
2.4.1 The ZZ → 4µ channel
The protons accelerated in the LHC collide in the beam pipe of the ATLAS detec-tor. In these collisions different processes can take place in which Higgs bosons are produced. These different processes contribute to the different Higgs production channels at the LHC. The dominant Higgs production channel is the gluon fusion channel (Baglio,2012). Here, two gluons from the colliding protons fuse to form a Higgs boson.
As discussed in the previous chapter, Higgs bosons live shortly before they decay to other particles. One possible decay mode is the Higgs decaying to two Z bosons: H → ZZ. The Branching Ratio (BR), which is the fraction of particles decaying to a specific decay mode, for the H → ZZ decay mode is 2.62% (Baglio,2012). An example of the production of a Higgs boson which decays to two Z bosons is shown in figure2.4 (right). There are two more contributions to the production of a pair of Z bosons, as shown in figure2.4: the quark background, q ¯q → ZZ(left), and the gluon continuum background, gg → ZZ (center).
FIGURE2.4: Lowest order contributions to the main ZZ production processes: (left) quark-initiated production, q ¯q → ZZ, (center) gg continuum background production, gg → ZZ, and (right) Higgs-mediated gg production, gg → H → ZZ, the signal. (CMS collab.,
2014).
The Z bosons then decay to a fermion-antifermion pair. The decay to pairs of electrons, muons and taus have a BR of about 10% (Salvucci, 2014). Despite the relatively low BR, the H → ZZ → 4l decay channel is called the ’golden channel’ because of the very clear signal. Therefore, this thesis focusses on the Higgs produc-tion and decay in the ’golden’ H → ZZ → 4l channel. We limit ourselves to the ZZ → 4µprocess, in which each of the two Z bosons decays to a pair of charged muons.
2.4.2 The 4µ invariant mass distribution
In section 2.3 the decay width of the Higgs boson (ΓH) was discussed. ΓH is the
width of the peak in the Breit-Wigner distribution for measuring the energy or in-variant mass of a particle a large number of times. The inin-variant mass (m4l)
distribu-tion of the muons in the ZZ → 4µ channel provides a such distribudistribu-tion. In figure2.5
the invariant mass distributions of the four leptons in the CMS and ATLAS experi-ments is shown. The peaks around 125 GeV represent the Higgs boson. The goal is to determine the width of these peaks. In order to do this, it is necessary is to check whether or not it is possible to directly determine the Higgs boson width from the invariant mass distribution of four-muon events.
(A) (CMS collab.,2013) (B) (ATLAS collab.,2012)
FIGURE2.5: The observed mass distribution of the four-lepton invari-ant mass, m4l. The results from CMS (A) are shown on the left and
the ATLAS results (B) are shown on the right.
In chapter3the invariant mass resolution of the ATLAS detector will be deter-mined from simulated data to see if it can directly measure the Higgs boson width. Spearman (2014), determined the invariant mass resolution of the ATLAS detector to be about 1-2 GeV for a four lepton Higgs event, and since the expected Higgs width (as shown in section2.3.2) is 4.15 MeV (Dittmaier,2011), our hypothesis is that the ATLAS resolution is not sensitive enough.
2.5
Interference between the gluon processes
In the previous section our hypothesis was discussed, stating that the invariant mass resolution of the ATLAS detector is expected not to be sensitive enough to directly measure the Higgs boson width. To bypass this resolution problem, another method has to be found to determine the Higgs boson width. In this section the impact of the Higgs boson width in the high mass region due to quantum interference between the gluon processes is discussed, which will be determined explicitly in chapter5.
The main contributions to the ZZ → 4µ channel were shown in figure2.4. The signal process (gg → H → ZZ) and the gluon continuum background (gg → ZZ) have the same initial- and final states. In quantum mechanics, processes that have the same initial- and final states interfere. When for example a system in an initial state |ψi is transited to a final state |ϕi via an intermediate state |ii, the probability of this transition is given by:
X i hψ|ii 2 hi|ϕi 2 + X ij;i6=j ψi∗ψjϕ∗jϕi (2.7)
in which the sum on the right represents the extra quantum interference terms. In our case, the production of four leptons from 2 gluons in the initial state (gg → 4l) is a superposition of several processes which are indistinguishable by their final state (Wolf,2015). The extra interference terms increase the probability of these transi-tions, resulting in an increase in expected events for the gluon processes. An increase in probability corresponds to a greater decay width, as a decay width is defined as the width of the peak of the Breit-Wigner probability distribution (see section2.3). A possible difference from the expected Higgs decay width ΓSMH could therefore be determined from the impact of the interference on the invariant mass distribution of the four muons. In chapter 4 the impact of a greater width of a Higgs boson width on the invariant mass distribution of the four muons is determined from simulated data.
Chapter 3
The ATLAS detector
3.1
Introduction
In this chapter the momentum resolution and invariant mass resolution will be de-termined based on simulated data in order see if the ATLAS detector is sensitive enough to directly measure the Higgs boson width. The ATLAS detector is shown in figure3.1. The protons collide in the beam pipe in the center of the detector. The calorimeters shown in the figure measure the energy a particle loses by ’absorbing’ particles. Calorimeters can stop most particles, except muons and neutrinos, because the muons are too massive and the neutrinos don’t interact through electromagnetic or hadronic interactions. Since the muons are not stopped by the calorimeters, they eventually enter the muon chambers where their momenta will be measured.
FIGURE3.1: A schematic view of the ATLAS detector (Shank,2009).
The invariant mass of the four muons is not measured directly but derived from their measured momenta (and mass). In the next section the experimental uncer-tainty that comes with measuring the momenta of the muons will be discussed, fol-lowed by the momentum resolution of the ATLAS detector based on simulated data. In section3.3the invariant mass resolution of the four muon invariant mass will be determined from simulated data.
3.2
The transverse momentum resolution of the ATLAS
de-tector
3.2.1 Measurement of the muon transverse momentum in the Muon Spec-trometer
In the ATLAS experiment, the transverse momentum PT of charged particles, like
muon, is measured in the muon chambers of the Muon Spectrometer. The trans-verse momentum is the momentum in plane perpendicular to the beam pipe. In these muon chambers the trajectories of charged muons are curved by a strong mag-netic field.By analyzing the degree of curvature, the PT can be determined, see figure 3.2. Sagitta (s) is a measure for the distance between the curved trajectory and the straight line the muon would follow if there was no magnetic field (B). The trans-verse momentum is calculated from B and s: PT = BL
2
8s , where L is the straight line
segment between the outer red points in the figure.
FIGURE3.2: Illustration of the muon transverse momentum measure-ment (Chevallier,2008).
Muons with very high momenta are less affected by the magnetic field. There-fore the distance s for high-PT muons is very small, making it difficult to precisely
measure their curvature. Because of this, we expect an increase in the experimental error for high-PT muons and thus a worse PT resolution as PT increases.
3.2.2 The transverse momentum resolution for ZZ → 4µ events from sim-ulated data
In this section the transverse momentum resolution (σPT) of the ATLAS detector is studied using simulated Monte Carlo (MC) data. This is done by determining the relative difference between the simulated reconstructed data and the simulated truth data. The difference between these two datasets is that the truth data assumes a perfect detector, while in the reconstructed data the experimental uncertainties (dis-cussed in section3.2.1) have been implemented. By comparing the two, the expected
experimental resolution of the detector can be determined. For the transverse mo-mentum, we define the relative difference between the reconstructed data and the truth data to be:
∆PT = PTreco− Ptruth T Ptruth T . (3.1)
Next, the ∆PT is plotted and a gaussian fit is applied. An example is shown if
figure3.3. The momentum resolution σPT is defined to be the standard deviation of the ∆PT-distribution.
FIGURE3.3: ∆PT between the truth and reconstructed PT for (2nd)
muons with 100 < PT < 140GeV. The red line shows the gaussian fit
applied.
This procedure was done for all four muons in every simulated event. From there, σPT was determined for 5 different PT regions, as shown in table3.1.
region PT σPT 1 0-20 2.85± 0.01 2 20-60 2.87 ± 0.02 3 60-100 2.93 ± 0.04 4 100-140 2.92± 0.06 5 140-200 3.13± 0.09
TABLE3.1: The different transverse momentum regions in GeV and their resolutions and errors in %
By plotting these resolutions (figure3.4) versus the transverse momentum, it be-comes clear that the transverse momentum resolution tends to increase when PT is
FIGURE3.4: The transverse momentum resolution as a function of the maximum Ptruth
T for 5 different momentum regions. The horizontal
error bars represent the width of these regions.
3.3
The invariant mass resolution of the ATLAS detector
In the previous section the transverse momentum resolution of the ATLAS detec-tor was determined based on simulated data. From the measured momenta of the muons the invariant mass of the muons can be determined. In this section the calcu-lation of the invariant mass from the momenta of the muons is discussed, followed by the invariant mass resolution determined from simulated data.
3.3.1 Calculating the invariant mass for H → ZZ → 4µ events
The invariant mass is defined by the energy-momentum relation. For a four-muon system, the invariant mass is:
m24µ= (XEµ)2− kX ~Pµk2, (3.2)
where Eµand ~Pµrepresent the energy and momentum of the individual muons.
The energy of the muons is approximately equal to their momenta. This approxi-mation is valid, because the muon mass (∼ 105 MeV) is negligible compared to the momenta of the muons (∼ 100 GeV). In section3.2.1the measurement of the PT of
the muons was discussed. Defining the z-axis to be the beam pipe axis, the trans-verse momentum is equal top(Px)2+ (Py)2. In order to complete the momentum
three-vector in equation3.2, the z component of the momentum is determined from the transverse momentum and the pseudorapidity η, which is defined as:
η = − ln (tan (θ
where θ is the angle between the particle’s path and the z axis. From equation3.2
it is clear that four-muon systems with high-PT muons have high invariant masses.
Thus the larger the momenta of the muons, the larger the invariant mass of the four-muon system. Combining this with the increase in uncertainty for measuring the PT
of the muons with higher PT discussed in section3.2.2, we expect the invariant mass
resolution of the ATLAS detector to be worse for 4µ-systems with a higher invariant mass.
3.3.2 The invariant mass resolution for ZZ → 4µ events from simulated data
In this section the invariant mass resolution of the ATLAS detector in the Z → 4µ channel is determined based on simulated Monte Carlo (MC) data from CERN. The invariant mass for every simulated 4µ event was calculated as discussed in section
3.3.1. Next, the method used in section3.2.2to determine the momentum resolution is applied on the invariant mass of the four muons in the simulated events. The relative difference between the simulated reconstructed data and the simulated truth data is defined as:
∆minv =
mrecoinv − mtruth inv
mtruthinv . (3.4)
Figure3.5shows the ∆minvdistribution over the total invariant mass region (0 −
800GeV). The red line shows the gaussian fit applied. The invariant resolution σminv is defined to be the standard deviation of the ∆minv-distribution.
FIGURE3.5: minv over the total invariant mass distribution (0 − 800
GeV). The red line shows the gaussian fit applied (σminv = 1.92% ±
0.07%).
The invariant mass resolution over the total invariant mass range for a four-muon event, determined from simulated data is about 2% (see figure 3.5), which corresponds to a mass difference of ∼ 2.4 GeV for an on shell Higgs boson (mSM
Higgs=
125.6GeV). This resolution was determined from the ∆minvdistribution over the
to-tal invariant mass range provided by the data: from 0 to 800 GeV. In order to be more precise, the invariant mass resolution is determined for different mass regions. The total invariant mass range (0 - 800 GeV) was divided in 10 mass regions for each of which the resolution was determined, as shown in table3.2.
region minv σminv 1 0-80 1.90 ± 0.51 2 80-100 1.86 ± 0.02 3 100-130 1.94 ± 0.04 4 130-200 1.92 ± 0.02 5 200-250 1.88 ± 0.01 6 250-300 1.90 ± 0.02 7 300-400 2.00 ± 0.02 8 400-500 2.18 ± 0.04 9 500-600 2.36 ± 0.06 10 600-800 2.36 ± 0.06
TABLE3.2: The different invariant mass regions in GeV and their res-olutions and errors in %.
The invariant mass resolutions and errors for the different mass regions are plot-ted versus the four-muon invariant mass in figure3.6.
FIGURE3.6: The invariant mass resolution depending on mtruth inv for
10 different mass regions. The horizontal error bars represent the width of these regions.
Figure 3.6 shows that the the invariant mass resolution of the detector differs from about 1.8 % to 2.4 %, depending on the invariant mass. The resolution tends to increase when the invariant mass of the muons increases. A resolution of around 2% corresponds to invariant mass resolution of about 2.4 GeV, which is a lot larger than the expected width of 4.15 MeV. Therefore, as expected, the ATLAS detector is not sensitive enough to directly measure the Higgs boson width. Because of this, a dif-ferent method to determine the Higgs width will be discussed in the next chapters.
Chapter 4
Impact of a larger width of a Higgs
boson
4.1
Introduction
Since the invariant mass resolution was determined not to be good enough to di-rectly measure the Higgs boson width, an indirect method to determine the width is proposed in this chapter. As discussed in section2.5, due to quantum interference between the gg → ZZ → 4µ and gg → H → ZZ → 4µ processes, a greater ΓH
has an impact on the invariant mass distribution of the four muons. In this chapter this interference will be be analyzed and the impact of choosing a Higgs width fives times the expected width (ΓSM
H ) on the invariant mass of the muons will be
deter-mined based on simulated data. In section4.2the impact of interference is discussed and in section4.3this impact on the invariant mass distributions of the gluon pro-cesses is made explicit by plotting the invariant mass ratio for simulated datasets with different Higgs bosons widths. Section 4.4 discusses the impact of a greater Higgs width on the total signal, including the quark background, and in section4.5
statistical analysis is done to determine whether we can measure this impact.
4.2
The impact of Γ
Hon the invariant mass distribution of
the four muons via quantum interference
For this analysis four Monte Carlo datasets are used. The first dataset consists of Monte Carlo events for the gg → H → ZZ signal and the gg → ZZ background. The second dataset contains the events coming from the interference between the gluon processes. The third dataset consists of the gluon signal, background and interfer-ence but here a greater Higgs width is implemented. The fourth dataset consists of the quark initiated background events.
In figure4.1 the first and second dataset were used to plot the invariant mass distributions of the gg → ZZ and the gg → H → ZZ processes based on MC data as a function of the invariant mass. From figure4.1it is clear that in the high mass region (minv > 300 GeV), the distribution of the gg → H → ZZ process (in which
the quantum interference is included) has a slightly higher resonance than the gg → ZZ process. This impact is represented by the red area on top of the gg → ZZ background (grey). As discussed in section2.5, this corresponds to a BW distribution with a greater width. Thus from determining the impact of interference between the gluon processes in the high mass region, it could be possible to determine the Higgs boson width. To quantify this impact, the ratio between the third dataset and the combined first and second datasets will be determined in the next section.
FIGURE4.1: The resonance distributions of the gg → ZZ background (grey) and the gg → ZZ background + gg → H → ZZ interference (red) processes as a function of the invariant mass of the four muons.
4.3
The invariant mass ratio for simulated data with Γ
SMHand
Γ
5SMHin the gluon processes
The invariant mass distribution of the four muons in the high mass region (minv >
300 GeV) is influenced by the presence of the Higgs boson intermediate state due to quantum interference, as explained in the previous section. In this section the impact of a greater width of a Higgs boson ΓH is determined using simulated data. The first
and second dataset combined, in both of which a SM Higgs width is assumed, are compared with the dataset where a Higgs width that is five times the expected SM width is implemented. By plotting the ratio between the invariant mass of these datasets versus the invariant mass of the muons, the influence of a greater Higgs width becomes apparent (figure4.2).
FIGURE4.2: The invariant mass ratio between MC data with ΓH =
5 × ΓSM
For minv> 300 GeV, the ratio Minv5SM/MinvSMis greater than 1. In this region the
in-variant mass data assuming ΓH = 5 × ΓSMH SM value is thus larger than the invariant
mass assuming ΓH = ΓSMH . For the further analysis in this thesis, we focus on this
region, because influence of a greater Higgs width on the invariant mass becomes apparent. The increase in invariant mass in this region is 32.7%. This corresponds to 32.7% more expected events for the gluon processes in the high mass region for Γ5SMH compared to the number of expected events for ΓSM
H . Unfortunately the quark
process is the dominant contributor to this channel, but does not interfere with the gluon fusion Higgs signal. In the next section the quark background will be taken into account to determine the impact of a Higgs width five times the SM Higgs width on the total signal.
4.4
The influence of the Higgs width on the combined q ¯
q →
ZZ
and gg → H → ZZ processes
For high masses, i.e. minv > 300GeV, the Higgs boson width influences the gg →
H → ZZprocess due to quantum interference. In the previous section the influence of a Higgs boson width greater than the SM width was shown by plotting the ratio between the invariant mass distributions for ΓSM
H and Γ5SMH . In our channel, the
q ¯q → ZZbackground also contributes to the invariant mass distribution of the four muons, but does not interfere with the Higgs signal from gluon fusion. It is therefore imperative to determine how much of the measured signal comes from the gluon processes and how much the quark background contributes to the signal. In this section the numbers of expected events are determined for each process. After this the impact of Γ5SM
H determined in the previous section is applied on the total signal
in order to understand how much ΓH would influence the measurements.
In 2013, the CMS Collaboration determined the expected numbers of events per process for the ZZ → 4l channel in their published analysis. These expectations and the measured data are shown in figure4.3.
FIGURE4.3: The distribution of the four-lepton invariant mass in in the range 100 < m4l< 800GeV (CMS collab.,2014).
In our analysis, specific weights in the MC datasets were applied to ensure that the number expected events for the gg and q ¯q processes would match the values CMS determined in their published analysis. The influence of a greater Higgs boson width on the gg → H → ZZ process in the high mass region was determined by plotting the ratio between the invariant masses of the sample with ΓSMH and the sample with Γ5SMH . Based on this ratio (figure4.2) and the expected mass distribution (figure4.3) the numbers of expected events are determined for the gluon processes with ΓH = Γ5SMH . The results are shown in table4.1.
Process Expected Events Pecentage
q ¯q → ZZ 79.4 83 %
gg → H → ZZ(ΓSMH ) 16.5 17 % gg → H → ZZ (Γ5SM
H ) 21.9 22 %
TABLE4.1: The expected number of events in the ZZ → 4µ channel for minv> 300GeV.
The quark initiated background contributes to 83% of the total signal. Therefore, the increase in expected gluon events of 32.7% determined in section4.2corresponds to an increase of 5.6%, or 5.4 events, in expected events for the total signal. To quan-tify the influence of a Higgs boson width that is fives times the SM Higgs boson width on the invariant mass distribution, we define the significance of the impact (S0) to be the following signal over background ratio:
S0 = signal √ background = 5.4 √ 79.4 = 0.60σ (4.1)
In the next section, we determine whether or not the LHC gathered enough data to measure the discussed effect with statistical significance, or how long it would take the LHC to reach the needed amount of data.
4.5
Statistical analysis on the impact of a greater Higgs boson
width
In the previous section, the impact of a Higgs boson width fives times the SM Higgs boson width was determined to be an increase of 5.6% in expected events for minv
> 300 GeV. In this section the amount of data needed to measure this impact with a statistical significance is determined, along with a n indication as to how long it will take the LHC to achieve this.
The statistical uncertainty that comes with measuring (large numbers) of events is defined as:
∆N = √
N , (4.2)
where N is the number of events.To be able to measure an effect of 5.6 %, the statistical uncertainty on the number of measured events has to be smaller than 5.6%. The minimum number of events the detector must measure in order to achieve a significant result is calculated as follows:
√
N ≤ 5.6% ⇒ N ≥ ( 1
0.0562) ≥ 319. (4.3)
In 2011 and 2012, CMS measured about 14 events in the 4l channel for minv > 300
GeV, at an integrated luminosity of 19.7 fb−1(8 TeV) + 5.1 fb−1(7 TeV) (CMS collab.,
2014). The integrated luminosity is defined as:
Lint= σ · N, (4.4)
where σ represents the cross section and N denotes the number of events. A cross section is defined as the fraction of events that is the result of a specific process or group of processes. The integrated luminosity is a measure for the total number of events observed. The LHC measured 14 events with a combined integrated lu-minosity of 24.8 fb−1 and there are 319 events needed to measure the impact of a greater Higgs boson width. Therefore the integrated luminosity needed to achieve statistical significance is ∼565 fb−1.
On their website, CERN,2016published their goal to reach an integrated lumi-nosity of 300 fb−1 by 2023. Since we need an integrated luminosity of 565 fb−1 to measure the impact a greater Higgs width, our expectation is that it will not be pos-sible to determine the Higgs width just by acquiring more data in the next 10 years. For this reason it is useful to search for a method to separate the q ¯qand gg processes in order to achieve a greater sensibility for the Higgs width in the high mass region, which would reduce the integrated luminosity that is needed. In the next chapter an approach is discussed reducing that number of events that are needed by applying cuts in the data.
Chapter 5
Separating the gg → ZZ and
q
q → ZZ
¯
processes
5.1
Introduction
In the previous chapter the impact of a Higgs width 5×ΓSM
H on the invariant mass
distribution of the four muons was determined to be an 5.6% increase in expected events for minvabove 300 GeV, corresponding to an impact significance of S0 = 0.60
σ. In order to achieve statistical significance at least 319 events will have to be ob-served in the 4µ channel in this region. As discussed, it will take the LHC years to reach an integrated luminosity large enough for this number of events. The goal in this chapter is to reduce the number of background events in order to achieve a greater statistical significance. The approach is to apply cuts to variables discrimi-nating the quark- from the gluon processes. Section5.2will discuss the variables that separate the gluon signal from the quark background and in section5.3the applied cuts and results will be presented.
5.2
The variables discriminating the gg → ZZ and q ¯
q → ZZ
processes
In their published analysis, the CMS collaboration discriminated the gluon fusion signal from the quark background by applying cuts in the angles between the decay products of the Higgs boson (CMS collab.,2014). Based on this approach, this thesis focusses on angles between these decay products and jets. In particular, the angle between the two Z bosons (θZZ) and the minimal angular distance between a jet and
a Z boson (∆RjZ) are examined.
In the proton collisions in the beam pipe of the ATLAS detector, quarks and glu-ons form jets. Quarks carry color charge, and in a collision these quarks fragment. Each fragment carries away some color charge, but in quantum chromodynamics only colorless states are allowed. Therefore these fragments create other objects to remain colorless. These compositions of fragmented quarks or gluons are called jets. For a further discussion on the production of jets in quantum chromodynamics, the reader is referred to Andersson, 1983. In the ATLAS detector, these jets are mea-sured to determine the properties of the original quarks. Figure5.1shows an event display of a four-muon event in the ATLAS detector. While the red lines represent the muons, the yellow tracks are other tracks. The yellow spikes indicate jets.
FIGURE 5.1: An event display containing four muons, displayed
as red lines. Other tracks are shown in yellow. Retrieved from http://atlasexperiment.org/photos/event-displays.html.
AT-LAS Experiment ©2016 CERN.
In this analysis, the minimal angular separation between a jet and a Z boson is used to separate the quark process from the gluon processes. The angular (or geometrical) separation ∆R between two objects is defined as follows:
∆R =p(∆η)2+ (∆φ)2, (5.1)
in which η was defined in section3.3.1and φ is the transverse angle between two objects. In our case, defining the beam axis as the z axis, η is a measure for the angle between a Z boson and a jet in the yz-plane and φ is the angle between a Z boson and a jet in the xy-plane. ∆RjZ is
5.3
Analysis of cuts on θ
ZZand ∆R
jZAs discussed in the previous section, the angle between the two Z bosons (θZZ) and
the minimal angular distance between a jet and a Z boson (∆RjZ) are examined to
discriminate between the gluon signal from the quark background. In this section the applied cuts are discussed along with the analysis to determine to optimal signal to background ratio.
Figure5.2shows the distributions for θZZ and ∆RjZ from simulated data. The
goal is to achieve the optimal signal over background ratio. To do this, cuts in de data are applied on the variables shown in the figure.
(A) (B)
FIGURE5.2: The distributions for θZZ(A) and ∆RjZ(B) for the gluon
processes (green) and the quark background (blue).
To determine exactly where to cut, the relative efficiencies were calculated for every angle between the Z bosons (0 < θZZ < π) and minimal angular separation
(0 < min ∆RjZ < 4.1). The efficiency (ε) is the number of signal or background
events that are not removed by the cut. In figure 5.3 the efficiency for the gluon processes (εgg) versus the efficiency for the quark background (εqq) are shown.
FIGURE5.3: The efficiencies as a fraction of the total number of events
for the gluon processes (εgg) versus the quark background (εqq) for
From the efficiencies as fractions of the total number of simulated events (the efficiency fraction) and the number of expected events, the signal over background ratio can be calculated for every cut to determine the optimal cut. The number of expected events, discussed in section 4.4. For the dataset assuming a SM Higgs width 16.5 gluon events were expected in the minv > 300 GeV region, and for the
dataset were a greater Higgs width (ΓH = 5 × ΓSMH ) was implemented 21.9 events
were expected. Thus the impact of a greater Higgs width is 21.9 - 16.5 = 5.4 ’extra’ events in the minv > 300 GeV region. The number of expected events for the quark
background is 79.4 events. The significance of a cut is calculated by multiplying the number expected events with the efficiency fraction as shown in equation5.2.
S = √ signal background =
εgg· 5.4
pεqq· 79.4 (5.2)
The cuts found to maximally enhance the signal over background ratio and their corresponding significances are shown in table5.1.
θZZ ∆RjZ
> 1.3
< 2.4 < 1.3 0.58 σ 0.93 σ
TABLE5.1: The applied cuts, in radians, and their corresponding sig-nal over background ratios.
From table 5.1 we conclude that the cut applied on θZZ actually decreases the
signal over background ratio: from S0 = 0.60 σ to S = 0.58 σ. This is due to fact that
even though more background than signal events are removed, still a lot of signal events are dismissed. Since the significance is calculated by dividing the number of signal events by the square root of the background events, the significance can still be lower than expected. The cut on ∆RjZhowever, increases the significance to S = 0.93
σ. This corresponds to an 8.7 % increase in expected events. As discussed in section
4.4the number of events needed to achieve statistical significance for an impact of 5.6 % was 319. After applying the cut on ∆RjZ, the same calculation results in achieving
statistical significance when only 131 events are measured, which corresponds to an integrated luminosity of 234 fb−1. As mentioned in section4.4, CERN has set out to reach 300 fb−1by 2023, thus by applying this cut we expect to be able to measure the impact of a greater Higgs boson with by 2023.
Chapter 6
Conclusion
The goal in this thesis is determine the Higgs boson decay width, which is a measure for its mean lifetime. If the Higgs boson width would turn out to be much larger than the expected value of 4.15 MeV (mH = 125 GeV) based on the SM, it would be
possible that the Higgs boson decays to more other particles than the SM currently contains.
First, the invariant mass resolution of the ATLAS detector in the ZZ → 4µ chan-nel was determined based on simulated data to check if it would be possible to directly measure the Higgs boson width. The invariant mass resolution was deter-mined to be 1.7 ± 0.2 GeV for 100 < minv < 130 GeV. Therefore we conclude that is
the resolution is not sensitive enough to directly measure the Higgs boson width. A solution for this problem was found by examining the impact of the Higgs boson width in the minv > 300 GeV region, which is a consequence of the quantum
interference between the gluon processes. Using simulated data, the ratio was deter-mined between the invariant mass of the four muons for a dataset with a SM Higgs boson width and a dataset where a Higgs boson width was implemented that is five times larger than the SM Higgs boson width. This ratio was plotted versus the in-variant mass of the muons which resulted in a 32.7 % increase for the inin-variant mass distribution assuming a greater Higgs width. After this, the quark background was taken into account. The impact of a greater Higgs width on the total signal was deter-mined to be 5.6 % (0.60 σ). The number of events that is needed to achieve statistical significance for a 5.6 % impact is 319. It was discussed that the LHC would have to reach an integrated luminosity of 565 fb−1 to achieve statistical significance, which would take at least 10 years based on the published luminosity goals by CERN.
To reduce the number of events needed to measure the impact of a greater Higgs boson width, the quark background had to be reduced. This was done by applying cuts in the angle between the two Z bosons (θZZ) and the minimal angular distance
between a jet and a Z boson (∆RjZ). The cut in θZZ turned out to be useless since
it lowered the signal over background ratio to 0.58 σ. The cut in ∆RjZ however did
increase the impact we want to measure to a significance of 0.93 σ. This corresponds to an impact of 8.3 %. Therefore applying this cut reduced the number of events needed from 319 to 131. This number of events will be achieved when the LHC reaches an integrated luminosity of 234 fb−1. Since CERN announced its goal to reach an integrated luminosity of 300 fb−1by 2023, it will then be able to determine the impact of a Higgs boson width 5 × the SM Higgs boson width to check if the Higgs boson width is 5 times larger than expected or not.
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