# Separating the process gg HH b b from irreducible background at the LHC 2020-06-08آ Separating...

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### Transcript of Separating the process gg HH b b from irreducible background at the LHC 2020-06-08آ Separating...

Separating the process gg → HH → bb̄γγ from irreducible background at the LHC

Martijn Pronk

Student ID: 10191739

July 6, 2014

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Verslag van Bachelorproject Natuur- en Sterrenkunde, omvang 15 EC,

uitgevoerd tussen 03-04-2014 en 27-06-2014

Naam begeleider: Magdalena Slawinska, Nikhef

Tweede beoordelaar: Stan Bentvelsen, Nikhef & UvA

Faculteit Natuurkunde, Wiskunde en Informatica, Universiteit van Amsterdam

Abstract

We rederive the Higgs mechanism for the U(1) unitary group and find a value of λ3H ≈ 190 GeV for the strength of the triple Higgs coupling. We study the channels for double Higgs

production and the decay of the Higgs boson at the LHC at 14 TeV centre of mass energy.

For a Higgs boson mass of 125 GeV we choose the channel gg → HH → bb̄γγ that has a cross section of 4.27 ∗ 10−2 fb. We start our analysis of the signal and irreducible b̄

¯ γγ background

processes from LO matrix elements and included the effect of Initial State Radiation (ISR),

Final State Radiation (FSR) and hadronisation on the variables ∆R(γ, γ) and min(∆R(γ, b))

We investigate the cuts proposed by an earlier ATLAS study [1]. Our analysis is based on

Monte Carlo simulations. We use MadGraph5 aMC@NLO for generating gg → HH matrix elements and Pythia 8 for Higgs decay, ISR, FSR and hadronisation. We calculate numbers

of events as expected at a luminosity of L = 3000fb−1. We find that the proposed cuts give a

S/ √ B-ratio of 4.22, but our optimized values for these cuts improve the S/

√ B-ratio to 4.69.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Theory of the Higgs boson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1 Higgs mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Higgs boson production . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Higgs boson decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Di-Higgs kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4 bb̄γγ final state and irreducible background . . . . . . . . . . . . . . . . . . . 16

4.1 Hard process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2 Initial state radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.1 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.2 Isolated photon selection . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.3 Tagging b-quarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

6 Conclusion & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3

4

1 Introduction

The Higgs mechanism was introduced in 1964 to explain why gauge bosons have mass. Con-

sequently however, the theory predicted a new scalar boson, its interactions with itself (triple

and quadruple Higgs coupling) and with massive fermions and bosons. In 2012 the announce-

ment was made by ATLAS (A Toroidal LHC Apparatus) & CMS(Compact Muon Solenoid)

experiments, both working at the LHC (Large Hadron Collider) that a particle has been dis-

covered which was probably the Higgs boson [2, 3]. If this new particle truly is the Standard

Model Higgs boson, then according to the theory, also the triple and quadruple Higgs coupling

exist, with values predicted by the theory. Therefore the search for these interactions is a

good way to test the Higgs mechanism in the Standard Model.

In this bachelor thesis a study has been made on measuring the Higgs pair production,

which is important for measuring the triple Higgs coupling. In the first part of section 2 the

Higgs mechanism is described for simplicity as a U(1) symmetry group. This captures the

essence of the Higgs mechanism, although the unification of the electromagnetic interaction

and the weak interaction is a U(1)×SU(2)L symmetry group. The second part of the section 2 will describe the Higgs boson pair production, and the third part its decay modes. In these

last two sections we explain the choice of experimental signature.

In section 3 then we investigate the kinematics of the Higgs pair production with some

typical variables of the process, such as the transverse momentum and the separation angle.

A good understanding of the kinematics is necessary for separating the Higgs production and

decay from the background processes, which are discussed in section 4, along with kinematic

cuts. In section 4 we follow earlier studies at ATLAS [1] and analyse the hard process signal

and irreducible background processes. This is followed by including initial state radiation

(ISR). In section 5 we will make a more realistic approach and we will take final state radiation

(FSR) and hadronisation into account. We conclude with section 6 in which we will summarize

our findings and discuss them.

Note that in this writing we will take c = 1, so masses and momenta are measured in

GeV.

5

2 Theory of the Higgs boson

2.1 Higgs mechanism

In quantum field theory particles are described by excitations of a quantum field which can

be expressed in terms of the Lagrangian density [4]. This Lagrangian density we will just call

the Lagrangian. Using the principle of least action, the Euler-Lagrange equation for fields φi

becomes

∂µ

( ∂L

∂(∂µφi)

) − ∂L ∂φi

= 0 (1)

According to Noether’s theorem a symmetry of the Lagrangian corresponds to a conserved

quantity. In field theory this quantity is a conserved current. For example if we transform

the Lagrangian for the free Dirac field

L = iψ̄γµ∂µψ −mψ̄ψ (2)

under the global U(1) phase transformation

ψ → ψ′ = eiθψ ψ̄ → ψ̄′ = e−iθψ̄ (3)

we get

L → L′ = i(e−iθψ̄)γµ∂µ(eiθψ)−me−iθψ̄eiθψ

= i(e−iθeiθ)ψ̄γµ∂µψ −m(e−iθeiθ)ψ̄ψ

= iψ̄γµ∂µψ −mψ̄ψ = L (4)

so the Dirac Lagrangian is invariant under this transformation and we have the corresponding

current

jµ = ψ̄γµψ (5)

which is conserved, according to the continuity equation.

If we now consider a scalar field φ with the so called ’Higgs’-Lagrangian [4]

L = (∂µφ)∗(∂µφ)− V (φ)

V (φ) = µ2φ∗φ+ λ(φ∗φ)2 (6)

where φ is a complex scalar field of the form

φ = 1√ 2

(φ1 + iφ2) (7)

6

Φ V HΦL

Figure 1: λ < 0

Φ

V HΦL

Figure 2: λ > 0, µ2 < 0

Φ

V HΦL

Figure 3: λ > 0, µ2 > 0

We fill in equation (7) into equation (6) and get

L = 1 2

(∂µφ1) ∗(∂µφ1) +

1

2 (∂µφ2)

∗(∂µφ2)− 1

2 µ2(φ21 + φ

2 2)−

1

4 λ(φ21 + φ

2 2)

2 (8)

For the potential (density) V (φ) to have a stable minimum, λ > 0, but µ2 can be both positive

or negative, as can be seen in figure 1,2 and 3 (for a simplified two dimensional potential).

We find the extrema by calculating ∂∂φ1V (φ1, φ2) = 0 and ∂ ∂φ1

V (φ1, φ2) = 0.

∂

∂φ1 V (φ1, φ2) = µ

2φ1 + λ(φ 2 1 + φ

2 2)φ1 = 0 (9)

∂

∂φ2 V (φ1, φ2) = µ

2φ2 + λ(φ 2 1 + φ

2 2)φ2 = 0 (10)

For µ2 ≥ 0 the minimum of the potential occurs when both φ1 and φ2 are zero and the vacuum state corresponds to the fields being zero, but when µ2 < 0, then the extremum at

φ1 = φ2 = 0 is a local maximum instead of a global minimum, and the potential now has

minima for all values of the fields which satisfy

φ21 + φ 2 2 = −µ2

λ ≡ v2 (11)

with v being the vacuum expectation value. We will show in the following that v 6= 0 is a necessary condition under which the Higgs boson can generate the masses of the W and Z

boson. There is an infinite amount of possible vacuum states, but because there is only one

actual vacuum state, the system has to ’choose’ one of the vacuum states, a process known as

spontaneous symmetry breaking. Without loss of generality, we can choose the vacuum state

to be the state at which φ2 = 0 and φ1 = v. Because we want to expand the field about the

vacuum state we define φ1(x) ≡ η(x) + v and φ2(x) = ξ(x) and thus φ = 1√2(η + v + iξ). ξ describes the excitation along the minima and η the excitation perpendicular to the minima.

The essential difference between the two fields is that ξ is expanded around zero, while η is

7

Figure 4: The minima of the potential satisfy φ21 + φ 2 2 = v

2, which is the equation for a circle

with radius v.

expanded around v, which is a non-zero value. Substituting this in equation (6) we get

L(η, ξ) = 1 2

(∂µ(η + v + iξ)∗(∂µ(η + v + iξ)− 1

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