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Summer Research Fellowship Programme of India's Science Academies

Resonant double Higgs production in the Z'-2HDM model with bb_+γγ as the final state, using MadGraph

Shreyas Shukla

National Institute of Technology Calicut, NIT Campus P.O., Kozhikode 673601, Kerala

Dr. Jyothsna Rani Komaragiri

Indian Institute of Science, Bangalore 560012, Karnataka

Abstract

With the discovery of the Standard Model Higgs Boson (h) in 2012, there have been continued studies to understand the couplings of h with fermions, massive vector bosons (Z, W+, W-), massless bosons (photons, gluons) and with itself. The cross-section of the Standard Model di-Higgs production process is very low and hence, difficult to detect. It is still an open question how Higgs couples to itself to be a massive particle. We therefore look at Beyond the Standard Model (BSM) double Higgs production to understand the self-coupling which predicts an enhanced cross-section. The Z'-2HDM model is an extention of the 2HDM (2 Higgs Doublet Model) model which predicts that there are 5 types of Higgs - h, H0, H+, H- and A0. The Z'-2HDM was meant for Dark Matter(DM) searches: ppZ'A0hXX_bb_ (where, X and X_ are DM candidates), but there was an idea that we could turn the missing transverse energy (MET) signature due to dark matter into Standard Model final states (bb_ or γγ). This project focuses on the resonant process: ppZ'A0h→bb_γγ which is a Next to Leading Order process (NLO). The decay of Higgs to bb~ has the highest branching ratio (BR) but also a high backgroud which is a big challenge. On the other hand, Higgs to γγ has a low BR but is a clean signal (low background). Thus, these two decay modes of Higgs are used together. This process has been simulated using MadGraph5 v2.6.5 and Pythia8 ( for h to γγ decay) for A0 masses 300 GeV, 400 GeV and 500 GeV, and Z' masses 450 GeV, 500 GeV, 600 GeV, 800 GeV, 1000 GeV and 1200 GeV. Plots to study the kinematics of the resonance particle (Z'), the two higgs - h and A0, and all the final state particles have been made and the possibility of resonant double Higgs (A0 and h in this case) production using the Z'-2HDM model has been studied. A comparison of these plots has also been made with the kinematics of the SM double-higgs production process.

Keywords: Beyond the Standard Model (BSM), MET, branching ratio, pT, eta, phi

Abbreviations

Abbreviations
SMStandard Model
BSMBeyond Standard Model
DMDark Matter 
2HDM 2 Higgs Doublet Model
METMissing transverse energy
BRBranching Ratio
MG5MadGraph 5
MCMonte Carlo 
LHELes Houches Event
LHCLarge Hadron Collider
NLONext to Leading Order
BEHBrout-Englert-Higgs

INTRODUCTION

The Standard Model

The universe is described by four fundamental forces - strong force, weak force, electromagnetic force and gravitational force. The first three are described by the Standard Model and the gravitational force by the General Theory of Relativity. SM also contains information about the fundamental particles which are the building blocks of the universe and their interactions. It explains most of the phenomena in the visible universe with a high level of accuracy. A picture which summarises the Standard Model is shown below (​Fig 1)​.

Standard_Model_of_Elementary_Particles.png.png
    Particles of the Standard Model

    Inspite of predicting the visible universe with good accuracy, the SM falls short on a numbers of aspects. Firstly, the Standard Model fails to incorporate the gravitational force (hierarchy problem) and thus, we need a more unified theory which incorporates gravity. It is known from astronomical observations that nearly 95% of the universe consists of dark matter and dark energy, but the SM is unable to explain this. Thirdly, SM does not satisfactorily explain the reason behind the observed masses of particles. Another shortcoming is that it cannot explain neutrino oscillations and the origin of neutrino mass. We need a more comprehensive theory which includes these various aspects, and thus we turn to Beyond Standard Models. In the context of this project, we look at BSM due to an aspect called cross-section which is low in SM for double Higgs production process. This is discussed in the adjoining paragraph.

    Double-higgs production

    The Higgs Boson was the last missing piece in the Standard Model until it was discovered in 2012 at the LHC. The Higgs boson is the quantum particle associated with the Higgs field which is described by the Brout-Englert-Higgs (BEH) mechanism, just as the photon is the quantum particle associated with electromagnetic field. The Higgs field is an all-pervasive, non-zero field which gives mass to the elementary particles by their interaction with it​​ [1] [2] (​​Fig 2​​) . The mass of the Higgs boson was measured to be 125 GeV/c2. This implies that the Higgs boson should derive its mass by self-coupling (interacting with itself). Since then there have been continued efforts to understand the mechanism of self-coupling.

    The ATLAS collaboration has searched for Higgs boson pairs (HH) in the dataset collected in 2015 and 2016 using various decay channels. The most sensitive of these involve one Higgs boson decaying into a pair of b-quarks and the other decaying into either another pair of b-quarks (HH→bbbb), two tau-leptons (HH→bbττ) or two photons (HH→bbγγ). These three searches were recently statistically combined and, as a result, the production rate of HH pairs could be excluded beyond 6.7 times the Standard Model prediction, at a 95% confidence level​[3]​.

    New physics could be indicated by a Higgs self-coupling which differs from the Standard Model prediction by a factor κλ. This would affect the production rate and the kinematic distributions of the Higgs boson pairs and, as such, is an excellent probe for new physics. The recent statistical combination of the HH searches in ATLAS constrains the value of κλ to be between –5.0 and +12.1, at a 95% confidence level (see figure). It is the world’s most stringent constraint on the anomalous Higgs self-coupling to date​​[3]​​.

    Higgs potential.png
      An illustration of the Higgs potential, V(ϕϕ) =μ2ϕ) + λ(ϕϕ)2

      Z'-2 Higgs Doublet Model [4]

      The Z'-2HDM model is an extension of the 2HDM (2 Higgs Doublet Model) model. This model predicts that there are 5 types of higgs - h, H0, H+, H- and A0. The h is the SM Higgs, H+ and H- are the charged Higgs bosons, and H0 and A0 are the pseudoscalar (particles with spin 0 and odd parity) Higgs. It was primarily meant for DM searches in which one (or more) particle of the SM is produced and detected in the collider, recoiling against some missing transverse energy (MET) associated with the DM. The DM couples to the SM through a new mediator (Z' gauge boson) that can be produced on-shell. The resonance Z' then decays to a Higgs plus an intermediate state which decays to a DM pair. Since a SM state decaying to DM is highly constrained, we consider a two-Higgs doublet extension (instead of just one Higgs) to the standard model with Z'h A0, where A0 is a heavy pseudoscalar with a large branching ratio to dark matter (​Fig 3​).

      Dark matter production in Z'-2HDM.png
        Production mechanism for dark matter plus Higgs through a new Z' coupled to a two Higgs doublet model, where the new pseudoscalar A0 decays primarily to the dark matter.

        There was an idea that we could turn the missing transverse energy (MET) signature due to dark matter into Standard Model final states (bb_ or γγ). This idea is used in this project to understand the possibility of resonant double Higgs production using the process: ppZ'A0 hbb_ γγ (where, A0 decays to bb_ and h to ​γγ).

        OBJECTIVES OF THE PROJECT

        To study the resonant double Higgs production process using the Z'-2HDM model by studying the basic kinematic distributions of all the final state particles. This is a preliminary study which would aid in the measurement of the Higgs self-coupling that is still not observed experimentally. Also, to determine if the analysis for the SM double-Higgs production process is applicable to this model . Observing and measuring this self-coupling would be the ultimate validation of the theory of mass generation. Thus, to simulate the double Higgs production process using Monte Carlo event generators- MadGraph and Pythia (for h to γγ decay) and analyse the produced data using ROOT.

        Scope

        In this project, the process: ppZ'A0 hbb_ γγ has been generated using the Z'-2HDM model at center of mass energy, s=13 TeV, which was the center of mass energy for the proton-proton collisions of the Large Hadron Collider for Run 2. About 10,000 events have been produced for all of the processes using the Monte Carlo event generator, MadGraph. While generating the process, the mass of SM higgs (h) was fixed to 125 GeV, and varied the masses of A0 as [300, 400, 500] GeV and Z' as [450, 500, 600, 800, 1000, 1200] GeV. Also, the decay widths of A0 and Z' have been set to 1% of their masses. All the events generated are at the generator level and hence, no cuts have been applied to take into account the detector specifications. LHAPDF6 was used as the parton distribution function (pdf) in this process.

        Any deviation of the self-coupling from Standard Model predictions, i.e validation of BSM scenarios (Z'-2HDM in this case) would open a window on new physics which we are not able to observe as yet.

        SOME BASIC CONCEPTS AND DEFINITIONS

        Branching fraction or ratio (BR)

        The branching fraction of a decay mode is the fraction of particles which decay by that particular decay mode with respect to the total number of particles which decay [5]. In fact, it is the probability that a particle would decay through a particular decay mode. It is equal to the ratio of the partial decay constant to the overall decay constant.

        For example, the b-channel branching ratio for a Standard Model Higgs (H) of mass= 125 GeV, Br(Hbb_)≈0.577 ​[6]​, and the diphoton branching ratio is only Br(H→γγ)≈2.28×10−3. This means that the Higgs boson decays to bottom-antibottom quark pair (bb_) 57.7% of the time. ​

        Feynman diagrams

        Feynman diagram is a graphical method of representing the interactions of elementary particles. It is a two-dimensional representation in which one axis, usually the horizontal axis, is chosen to represent time, while the second (vertical) axis represents space. Straight lines are used to depict fermions (matter particles) and wavy lines are used for bosons (force carriers) (​Fig 4​). The basic interaction appears on a Feynman diagram as a “vertex”—i.e., a junction of three lines. Each vertex must conserve charge, baryon number and lepton number.

        Components of Feynman diagram.png
          Components of a Feynman diagram

          In the figure below (​Fig 5​) two incoming electrons (e) interact with each other through a photon (γ) and scatter off each other. From this diagram, we cannot say whether the ewhich is below emitted the photon and the e which is above absorbed the photon or vice-versa.

          Feynman diagram-Moller scattering.png
            Feynman diagram for interaction between two electrons (e) through a photon (γ) called Møller scattering

            One interesting feature of Feynman diagrams is that antiparticles are represented as ordinary matter particles moving backward in time. For example, in another typical interaction (​Fig 6​), an electron collides with its antiparticle, a positron (e+), and both are annihilated. A photon is created by the collision, and it subsequently forms two new particles in space: a muon (μ) and its antiparticle, an antimuon (μ+). In the diagram of this interaction, both antiparticles (e+ and μ+) are represented as moving backward in time (towards the past). This interaction is also called Bhabha scattering.

            Feynman diagram-electron positron annihilation.png
               Feynman diagram of the annihilation of an electron (e) by a positron (e+)

              Another example of Feynman diagram is depicted below (​Fig 7​). In this diagram, a neutron decays into a proton emitting an electron and an electron antineutrino in the process. A neutron consists of two down quarks and an up quark. A proton consists of two up quarks and a down quark. The decay can also be visualised as the decay of a down quark into an up quark.

              Feynman diagram-beta decay.png
                Feynman diagram for beta decay

                Decay width (Γ)

                Particle lifetime, τ, is the time taken for the sample to reduce to 1/e of original sample. The total decay width of the particle can thuse be defined as:

                Γ=1τ

                It is the probability per unit time that a given particle will decay. Since the dimension of Γ is the inverse of time, in the system of natural units, it has the same dimension as mass (or energy). When the mass of an elementary particle is measured, the total rate shows up as the irreducible “width” of the shape of the distribution. Hence the name decay width.

                Coupling

                ​Particles which interact with each other are said to be coupled. This interaction is caused by one of the fundamental forces, whose strengths are usually given by a dimensionless coupling constant. In quantum electrodynamics, this value is known as the fine-structure constant α, approximately equal to 1/137. For quantum chromodynamics, the constant changes with respect to the distance between the particles. This phenomenon is known as asymptotic freedom. Forces which have a coupling constant greater than 1 are said to be "strongly coupled" while those with constants less than 1 are said to be "weakly coupled" [7] .

                Higgs decay

                Higgs boson having a mass of 125 GeV/c2 has a mean lifetime of about 1.6×10−22 s, decaying almost instantly. Since it interacts with all the massive elementary particles of the SM, the Higgs boson has many different processes through which it can decay. Each of these possible processes has its own probability, expressed as the branching ratio.

                Here are some of the decay modes:

                Decay to photons (H→𝛾𝛾)

                • Only a small fraction of the Higgs boson produced decays into 2 photons. The branching fraction for this mode is approximately 2.28 x 10-3 for a Higgs of mass 125 GeV/c2.
                • This decay is rare because the Higgs cannot interact directly with the two photons because the photon is massless.
                • However, the decay can still happen because of an exchange of intermediate particles (​Fig 8​).
                Higgs Decay-1.png
                  Feynman diagram for the decay of Higgs boson to 2 photons (𝛾𝛾) through exchange of intermediate particles like W bosons and top quarks (t).

                  Decay to tau leptons (H→𝜏+𝜏-)

                  • 𝜏-leptons decay before being detected.
                  • 𝜏-leptons can decay in 3 ways:
                    • e- + neutrinos
                    • 𝜇- + neutrinos
                    • Hadronically - in this decay, there can be one or three charged hadrons which will be reconstructed as tracks in the detector and there might also be some neutral pions which are reconstructed as energy deposits in the calorimeters.
                  • The probability of  H→𝜏+𝜏- is much larger than that of the decay to photons or Z-bosons.
                  • This mode helps us to understand the mechanism which allows the Higgs boson to give mass to the fermions.
                  Higgs Decay-2.png
                    Feynman diagram for the decay of Higgs boson to 𝜏-leptons

                    Decay to Z-bosons (H→ZZ)

                    • The two Z-bosons decay to various particles such as e-e+, 𝜇-𝜇+ (​Fig 10​).
                    • This decay mode happens once in about 10,000 decay of Higgs.
                    • It is a clean channel because there are not many backgrounds.
                    • Looking at the angles between the directions of the electrons and muons, it was found that the Higgs boson has no spin.
                    Higgs Decay-3.png
                      Feynman diagram for the decay of Higgs to a pair of Z-bosons which in turn decays to either e- or 𝜇- and their corresponding anti-particle.

                      Decay to bottom quarks (Hbb_)

                      • Higgs decays to bottom-quarks ~58% of the time (BR~0.577 for H-mass =125 GeV/c2)
                      • Yet, it is difficult to observe these because of the large background.
                      Higgs Decay-4.png
                        Vector boson fusion production of Higgs which decays to bb_

                        Decay to W-bosons (H→W+W-)

                        • W-bosons are unstable particles which decay into hadrons or leptons. For example, they may decay into electrons or muons and their corresponding neutrinos.
                        Higgs Decay-5.png
                          Feynman diagram for the decay of Higgs to W-bosons and their subsequent decay to leptons and neutrinos.

                          The branching fraction of the various decay modes of the Standard Model Higgs as a function of its mass has been depicted in the plot below (​Fig 13​):

                          Higgs Decay-6.png
                            The decay branching ratios of the SM Higgs boson as a function of its mass

                            Kinematic variables

                            Transverse momentum (pT)

                            pT is the transverse momentum of a particle, i.e. momentum of the particle along a plane perpendicular to the direction of the beams. The figure below shows it graphically (​Fig 14​).

                            Transverse momentum.png
                              Graphical representation of transverse momentum

                              Thetha (θ) here is the polar angle (0 along the beamline) and 'p' is the momentum of the particle.

                              Rapidity (y) and Pseudorapidity (η)

                              They are used instead of polar angle (θ) in hadron collider experiments because the Centre-of-Momentum frame (frame in which net momentum is zero) of the interacting particles is boosted in the lab at hadron colliders. Rapidity is defined as:

                              y=12lnE+pzE-pz=tanh-1pzE

                              The really neat feature of this variable is that a Lorentz transformation gives: y − tanh−1β, the derivative of which (wrt y) is the same as the derivative of y itself. So, the shape of the rapidity distribution is Lorentz invariant.

                              In the limit p >> m (high energy particles), pseudo-rapidity, η, can be defined as:

                              η-ln(tan θ2)y

                              Azimuthal angle (ϕ)

                              It is the angle made by the projection of the momentum onto the X-Y plane with the X-axis. The figure below explains η and ϕ ().

                              Eta graph.png
                                Pseudorapidityηis a geometric quantity. It is a function of polar angle θ that goes from ∞ to −∞ as θ goes from 0 to π. Azimuthal angle φ goes around the beam.​[8]

                                Invariant mass

                                Invariant mass, m, is defined as:

                                m2c4=(E)2-(p)2c2

                                where, E and p are the energy and momentum respectively of the particle in the lab frame. It is a Lorentz invariant quantity. It becomes equal to the rest mass in the CM frame.

                                Cross-section

                                Cross section describes the likelihood of two particles interacting under certain conditions. Those conditions include, for example, the number of particles in the beam, the angle at which they hit the target, and what the target is made of.

                                Cross sections come in many varieties. They can help describe what happens when a particle hits a nucleus. In elastic reactions, particles bounce off one another but maintain their identities, like two ricocheting billiard balls. In inelastic reactions, one or more particleshatters apart, like a billiard ball struck by a bullet. In a resonance state, short-lived virtual particles appear. These measurements of one or more aspects of the interaction are called differential cross sections, while summaries of all of these reactions put together are called total cross sections. ​Speak physics: What is a cross section?, et al​ `

                                Cross section is independent of the intensity and focus of the particle beams, so cross section numbers measured at one accelerator can be directly compared with numbers measured at another, regardless of how powerful the accelerators are. Arrows are arrows, no matter how many of them are fired into the sky. Cross section

                                METHODOLOGY

                                Event Generation using MadGraph5_aMC@NLO

                                MadGraph is a Monte Carlo (MC) event generator for collider studies, nowadays widely used to simulate events at the LHC. Monte Carlo event generators are essential components of almost all experimental analyses and are also widely used by theorists and experiments to make predictions and preparations for future experiments ​[9]​. MadGraph5_aMC@NLO is a framework that aims at providing all the elements necessary for SM and BSM phenomenology, such as the computations of cross sections, the generation of hard events and their matching with event generators, and the use of a variety of tools relevant to event manipulation and analysis. The result of the MadGraph simulation is a LHE (Les Houches Event) file which is a universally accepted format to store events' data.

                                For this project, MadGraph v2.6.5 has been used. All the processes have been simulated with a center of mass energy, s=13 TeV, which was the center of mass energy for the proton-proton collisions of the LHC for Run 2. About 10,000 events have been produced in all the processes using MadGraph. Note that all the events generated are at the generator level and hence, no cuts have been applied to take into account the detector specifications.

                                The steps followed for event generation are as follows:

                                • First, the model file 'Zp2HDM' is added to the 'models' folder in 'MG5_aMC_v2_6_5' directory.
                                • Next,the following set of commands are executed in the MadGraph terminal:

                                >import model Zp2HDM

                                >generate p p > zp > a0 h, (a0 > b b~)

                                >output mywork/pp_zp_a0h_bb_292600_scan

                                >launch

                                >0

                                To change the parameters of the process, the follwing commands are executed after launch command:

                                >set param_card mass 5  4.8

                                >set param_card mass 32 scan:[800,1000,1200]

                                >set param_card mass 26 300

                                >set param_card mass 27 300

                                >set param_card mass 28 scan:[300,500]

                                >set param_card ZPINPUTS 1 1.0

                                >set param_card ZPINPUTS 2 0.8

                                >set param_card DECAY 32 10

                                >set param_card DECAY 28 5

                                LHAPDF6 was used as the parton distribution function (pdf) in this process. Thus, in run_card.dat, the following changes were made:

                                        lhapdf    = pdlabel     ! PDF set

                                292600= lhaid ! if pdlabel=lhapdf, this is the lhapdf number

                                Launching the above process by pressing '0' produces 6 LHE files corresponding to the variations in the masses of A0 and Zp.

                                • In a similar way, 3 other LHE files are produced by setting the masses of A0 (PDGID: 28 ​[10]​) and Zp (PDGID: 32​[10]​), and their decay widths as:

                                >set param_card mass 32 scan:[450,500,600]

                                >set param_card mass 28 300

                                >set param_card DECAY 32 5

                                >set param_card DECAY 28 3

                                Another LHE file was produced by setting the masses of A0 (PDGID: 28) and Zp (PDGID: 32) as:

                                >set param_card mass 32 600

                                >set param_card mass 28 400

                                >set param_card DECAY 32 6

                                >set param_card DECAY 28 4

                                Note that all the values entered for mass and decay width are in GeV.

                                • The Feynman diagrams for the process is depicted below (​Fig 16​):
                                imgonline-com-ua-twotoone-GQHhT5yChF.jpg
                                  Feynman diagrams for the MadGraph generated process
                                  • Note: A0 and a0, Zp and zp have been used interchangeably in this project.

                                  SM Higgs decay using Pythia8

                                  Pythia is another such software for the generation of high energy collisional events. The final file obtained after Pythia hadronisation is an ntuple ROOT file which has a tree structure. ROOT file as the output speeds up post process analysis such as analysing the kinematics (pT, η, ϕ, invariant mass) of the various particles. We use Pythia primarily to decay SM Higgs (h) to two photons (γγ) which was previously left undecayed in the MadGraph simulation.

                                  Event data analysis using ROOT

                                  The ROOT version v6.16.00 has been used for this project. To read data from the ntuple ROOT file and to plot histograms of kinematic variables (pT, η, ϕ, invariant mass) of all final state particles, a0, h and resonance particle (zp), PyROOT has been used with Python 3 as the interface.

                                  To plot the histograms, the following algorithm has been used:

                                  • Read the ntuple ROOT file with the help of TChain() and Add() functions.
                                  • Read the number of entries in the ROOT file using GetEntries() and loop over all the entries.
                                    • Read all the branches of the tree and store them in variables using __getattr__().
                                    • Identify the correct particle with its PDG ID and mom PDG ID.
                                      • Read the transverse momentum (pT), pseudorapidity (η), azimuthal angle (ϕ) and mass of this particle.
                                      • Store these in a TLorentzVector() variable using SetptEtaPhiM() function.
                                    • Create histograms for the kinematic variables using TH1F() having proper bin sizes and fill these with the values using Fill(), Pt(), Eta(), Phi() and M() functions.
                                  • Draw the histogram using the Draw() function and save it in '.root' and '.png' format

                                  The values of kinematic variables of h, a0 and zp have been found by reconstructing the four-momentum of γγ, bb~ and bb~γγ respectively.

                                  RESULTS AND DISCUSSION

                                  Cross-sections of the process

                                  The cross-sections of all the runs (obtained by varying the masses of A0 and Zp) for the MadGraph generated process: ppzp→a0(bb~) h have been summarised in ​Sec. A. Cross-section of runs​ of APPENDICES. The plot of the same can be found below (​Fig 17​):

                                  Combined_cross_section_2D.png
                                    Cross-sections

                                    From the plot, it can be seen that there is no general trend and the cross-section is highest for the run corresponding to a0 and zp masses-300 GeV and 600 GeV respectively. It can also be noted that the cross-section corresponding to a0 and zp masses-400 GeV and 600 GeV respectively cannot be seen in the plot. This is because the cross-section of this run is about 6.200600e-06 pb which is very low compared to the other runs. Thus, the kinematic plots for the process corresponding to this run have not been plotted.

                                    Plots of kinematic variables

                                    Process: ppZp→A0 h→bb~ γγ.

                                    Plots of kinematics variables (pT, η, ϕ) for all final state particles (b, b~ and γ's) have been made. pT, η, ϕ and invariant mass plots have been made for A0 and h, and invariant mass plot for resonance Zp. The plots have been made in such a way that the mass of a0 is kept constant and the mass of zp is varied. All plots have been made with y-axis as number of events and normalized to 1 .

                                    Plots for mA0=300 GeV as constant

                                    Combined_A0_mass_a0300_2.png
                                      Invariant mass of A0
                                      Combined_h_mass_a0300_2.png
                                        Invariant mass of h
                                        Combined_zp_mass_a0300_2.png
                                          Invariant mass of Zp

                                          From these plots (​​​ Fig 18-20​), it can be seen that there are resonance peaks at mbb~=300 GeV, mγγ=125 GeV and mγγbb~=[450,500,600,800,1000,1200] GeV which correspond to the invariant masses of A0, h and Zp for this process.

                                          Combined_b_pt_a0300_2.png
                                          Transverse momentum (pT) of bottom-quark
                                            Combined_bbar_pt_a0300_2.png
                                            Transverse momentum (pT) of anti-bottom quark
                                              Transverse momentum (pT) of bottom-quarks
                                              • The distribution of pT of b and b~ (​​​ Fig 21a & 21b​) are skewed right. Many b and b~ particles have momentum about 100 GeV. Also, the right skewness of the distributions decreases with the increasing mass of Zp.
                                              • The maximum value of pT for b (​Fig 21a​​​) is about 400 GeV for mZp=450 GeV and it increases with increase in Zp mass, having a value of 840 GeV for mZp=1200 GeV.
                                              • The maximum value of pT for b~ (​​​​Fig 21b​​) is about 320 GeV for mZp=450 GeV and it increases with increase in Zp mass, having a value of 760 GeV for mZp=1200 GeV.
                                              • The distributions tend to spread out (maximum pT increases) with increase in Zp mass. This is because the extra mass of Zp (invariant mass of Zp - inavariant mass of its daughter particles) get converted into energy of its daughter particles and hence, particles (b and b~) get a boost in energy (or momentum) with increase in Zp mass since the extra mass increases.
                                              Combined_a1_pt_a0300_2.png
                                              Transverse momentum (pT) of photon γ1
                                                Combined_a2_pt_a0300_2.png
                                                Transverse momentum (pT) of photon γ2
                                                  Transverse momentum (pT) of photons
                                                  • The distribution of pT of γ1 and γ2 (​​​​ Fig 22a & 22b​​) are skewed right. Many γ1 and γ2 particles have momentum about 100 GeV. Also, the right skewness of the distributions decreases with the increasing mass of Zp.
                                                  • The maximum value of pT for γ1 (​​​​​Fig 22a​) is about 200 GeV for mZp=450 GeV and it increases with increase in Zp mass, having a value of 720 GeV for mZp=1200 GeV.
                                                  • The maximum value of pT for γ2 (​Fig 22b​​​​) is about 240 GeV for mZp=450 GeV and it increases with increase in Zp mass, having a value of 800 GeV for mZp=1200 GeV.
                                                  • The distributions tend to spread out (maximum pT increases) with increase in Zp mass. This is because the extra mass of Zp (invariant mass of Zp - inavariant mass of its daughter particles) get converted into energy of its daughter particles and hence, particles (γ1 and γ2) get a boost in energy (or momentum) with increase in Zp mass since the extra mass increases.
                                                  Combined_A0_pt_a0300_2.png
                                                  Transverse momentum of A0
                                                    Combined_h_pt_a0300_2.png
                                                    Transverse momentum of h
                                                      Transverse momentum of A0 and h 
                                                      • The distribution of pT of A0 and h (​​​​​ Fig 23a & 23b​) are skewed right. The right skewness of the distributions decreases with the increasing mass of Zp.
                                                      • The mode of the distribution for mZp=450 GeV is about 80 GeV for both A0 and h. This value increases to about 560 GeV for mZp=1200 GeV.
                                                      • The maximum value of pT for A0 (​Fig 23a​) and h (​Fig 23b​​) is about 360 GeV and 240 GeV respectively for mZp=450 GeV and it increases with increase in Zp mass, having a value of 900 GeV for mZp=1200 GeV for both the particles.
                                                      • The reason for the spread in the distributions, increase in mode value and increase in maximum pT value is the same as that for b or γ.
                                                      Combined_b_eta_a0300_2.png
                                                      η of bottom-quark
                                                        Combined_bbar_eta_a0300_2.png
                                                        η of anti-bottom quark
                                                          Pseudorapidity (η) of bottom-quarks
                                                          • η is a central property of a particle, i.e. it is symmetrically distributed about 0. As the pT of the particle increases, the particle beam starts approching the perpendicular direction to the proton beam. Hence, θ approches 900 and η->0.
                                                          • Most of the particles (b and b~) are at η=0 (​​ Fig 24a & 24b​). The number of particle at η=0 increases with increase in Zp mass since the pT of these particles increases as observed from the pT graphs (​ Fig 21a & 21b)​.
                                                          • The range of η for both particles decreases from [-6,6] for mZp=450 GeV to [-4.5,4.5] for mZp=1200 GeV.
                                                          Combined_a1_eta_a0300_2.png
                                                          Pseudorapidity (η) of γ1
                                                            Combined_a2_eta_a0300_2.png
                                                            Pseudorapidity (η) of  γ2
                                                              Pseudorapidity (η) of photons
                                                              • Most of the particles (γ1 and γ2) are at η=0 (​​​ Fig 25a & 25b​). The number of particle at η=0 increases with increase in Zp mass since the pT of these particles increases as observed from the pT graphs (​​ Fig 22a & 22b​)​.
                                                              • The range of η for both particles decreases from [-6,6] for mZp=450 GeV to [-4,4] for mZp=1200 GeV.
                                                              Combined_A0_eta_a0300_2.png
                                                              Pseudorapidity (η) of A0
                                                                Combined_h_eta_a0300_2.png
                                                                Pseudorapidity (η) of h
                                                                  Pseudorapidity (η) of A0 and h
                                                                  • Most of the particles (A0 and h) are at η=0 (​​​​ Fig 26a & 26b​). The number of particle at η=0 increases with increase in Zp mass since the pT of these particles increases as observed from the pT graphs (​​​ Fig 23a & 23b​)​.
                                                                  • The range of η for both particles decreases from [-6,6] for mZp=450 GeV to [-4,4] for mZp=1200 GeV.
                                                                  Combined_b_phi_a0300_2.png
                                                                  Azimuthal angle (ϕ) of b
                                                                    Combined_bbar_phi_a0300_2.png
                                                                    Azimuthal angle (ϕ) of b~
                                                                      Combined_a1_phi_a0300_2.png
                                                                      Azimuthal angle (ϕ) of γ1
                                                                        Combined_a1_phi_a0300_2.png
                                                                        Azimuthal angle (ϕ) of γ2
                                                                          Plots of Azimuthal angle (ϕ)
                                                                          • The azimuthal angle (ϕ) is a central property of the particle, i.e. it is symmetrically distributed about 0. All the particles are equally distributed among all values of ϕ (-π to π).
                                                                          • Since ϕ-distribution for all the particles remains the same, we will not analyse the ϕ-plots henceforth.

                                                                          Plots for mA0=500 GeV as constant

                                                                          Combined_A0_mass_a0300_2.png
                                                                            Invariant mass of A0
                                                                            Combined_h_mass_a0500.png
                                                                              Inavriant mass of h
                                                                              Combined_zp_mass_a0500.png
                                                                                Invariant mass of Zp

                                                                                From these plots (​​​​ Fig 28-30​), it can be seen that there are resonance peaks at mbb~=500 GeV, mγγ=125 GeV and mγγbb~=[800,1000,1200] GeV which correspond to the invariant masses of A0, h and Zp for this process.

                                                                                Combined_b_pt_a0500.png
                                                                                Transverse momentum (pT) of bottom-quark
                                                                                  Combined_bbar_pt_a0500.png
                                                                                  Transverse momentum (pT) of anti-bottom quark
                                                                                    Transverse momentum (pT) of bottom-quarks
                                                                                    • The distribution of pT of b and b~ (​ Fig 31a & 31b​​) are skewed right. Many b and b~ particles have momentum about 200 GeV. Also, the right skewness of the distributions decreases with the increasing mass of Zp.
                                                                                    • The maximum value of pT for b (​​Fig 31a​​​​​) is about 750 GeV for mZp=800 GeV and it increases with increase in Zp mass, having a value of 1000 GeV for mZp=1200 GeV.
                                                                                    • The maximum value of pT for b~ (​​​​​Fig 31b​​) is about 750 GeV for mZp=800 GeV and it increases with increase in Zp mass, having a value of 1050 GeV for mZp=1200 GeV.
                                                                                    • The distributions tend to spread out (maximum pT increases) with increase in Zp mass. The reason is same as that mentioned previously for b-particles.
                                                                                    Combined_a1_pt_a0500.png
                                                                                    Transverse momentum (pT) of photon γ1
                                                                                      Combined_a2_pt_a0500.png
                                                                                      Transverse momentum (pT) of photon γ2
                                                                                        Transverse momentum (pT) of photons
                                                                                        • The distribution of pT of γ1 and γ2 (​​​​​ Fig 32a & 32b​) are skewed right. Many γ1 and γ2 particles have momentum about 50 GeV. Also, the right skewness of the distributions decreases with the increasing mass of Zp.
                                                                                        • The maximum value of pT for γ1 (​​​​​​​Fig 32a​​) is about 500 GeV for mZp=800 GeV and it increases with increase in Zp mass, having a value of 800 GeV for mZp=1200 GeV.
                                                                                        • The maximum value of pT for γ2 (​ Fig 32 b​​) is about 500 GeV for mZp=800 GeV and it increases with increase in Zp mass, having a value of 850 GeV for mZp=1200 GeV.
                                                                                        • The distributions tend to spread out (maximum pT increases) with increase in Zp mass. The reason for this is same as that mention previously for photons.
                                                                                        Combined_A0_pt_a0500.png
                                                                                        Transverse momentum of A0
                                                                                          Combined_h_pt_a0500.png
                                                                                          Transverse momentum of h
                                                                                            Transverse momentum of A0  and h
                                                                                            • The distribution of pT of A0 and h (​​​​​​ Fig 33a & 33b​) are skewed right. The right skewness of the distributions decreases with the increasing mass of Zp.
                                                                                            • The mode of the distribution for mZp=800 GeV is about 200 GeV for both A0 and h. This value increases to about 500 GeV for mZp=1200 GeV.
                                                                                            • The maximum value of pT for A0 (​​Fig 33a​​) and h (​​Fig 33b​​) is about 850 GeV for mZp=800 GeV and it increases with increase in Zp mass, having a value of 1100 GeV for mZp=1200 GeV for both the particles.
                                                                                            • The reason for the spread in the distributions, increase in mode value and increase in maximum pT value is the same as that for b or γ.
                                                                                            Combined_b_eta_a0500.png
                                                                                            η of bottom-quark
                                                                                              Combined_bbar_eta_a0500.png
                                                                                              η of anti-bottom quark
                                                                                                Pseudorapidity (η) of bottom-quarks
                                                                                                • η is a central property of a particle, i.e. it is symmetrically distributed about 0. As the pT of the particle increases, the particle beam starts approching the perpendicular direction to the proton beam. Hence, θ approches 900 and η->0.
                                                                                                • Most of the particles (b and b~) are at η=0 (​​​ Fig 34a & 34b​). The number of particle at η=0 increases with increase in Zp mass since the pT of these particles increases as observed from the pT graphs (​​ Fig 31a & 31b​)​.
                                                                                                • The range of η for both particles decreases from [-6,6] for mZp=800 GeV to [-5,5] for mZp=1200 GeV.
                                                                                                Combined_a1_eta_a0500.png
                                                                                                Pseudorapidity (η) of γ1
                                                                                                  Combined_a2_eta_a0500.png
                                                                                                  Pseudorapidity (η) of γ2
                                                                                                    Pseudorapidity (η) of photons
                                                                                                    • Most of the particles (γ1 and γ2) are at η=0 (​​​​ Fig 35a & 35b​). The number of particle at η=0 increases with increase in Zp mass since the pT of these particles increases as observed from the pT graphs (​​​ Fig 32a & 32b​)​.
                                                                                                    • The range of η for both particles decreases from [-5,5] for mZp=800 GeV to [-4.5,4.5] for mZp=1200 GeV.
                                                                                                    Combined_A0_eta_a0500.png
                                                                                                    Pseudorapidity (η) of A0
                                                                                                      Combined_h_eta_a0500.png
                                                                                                      Pseudorapidity (η) of h
                                                                                                        Pseudorapidity (η) of A0 and h
                                                                                                        • Most of the particles (A0 and h) are at η=0 (​​​​​ Fig 36a & 36b​). The number of particle at η=0 increases with increase in Zp mass since the pT of these particles increases as observed from the pT graphs (​​​​ Fig 33a & 33b​)​.
                                                                                                        • The range of η for A0 decreases from [-6,6] for mZp=800 GeV to [-4.5,4.5] for mZp=1200 GeV.
                                                                                                        • The range of η for A0 decreases from [-6,6] for mZp=800 GeV to [-4.5,4.5] for mZp=1200 GeV.

                                                                                                        CONCLUSIONS AND RECOMMENDATIONS

                                                                                                        • Through this project, an understanding of the basic concepts involved in experimental particle physics was obtained.
                                                                                                        • Next, the tools for event generation at generator level like MadGraph and Pythia, and for analysis of produced data like PyROOT was familiarzed. As the project included analysis of large amount of data, it gave an idea of how such data is analysed at the various experimental particle physics facilities.
                                                                                                        • The event generators were used to produce the process: ppZ'A0h→bb_γγ in the Z'-2HDM model for mA0=[300, 400, 500] GeV and mZp=[450, 500, 600, 800, 1000, 1200] GeV.
                                                                                                        • The analysis included producing plots of kinematic variables (pT, η, ϕ) for all final state particles, A0 and h using PyROOT.
                                                                                                        • For the processes in which mA0=300 GeV and mZp=[450,500,600], the final state particles (b, b~ and γ's) are less boosted and we feel that the analysis used for the SM double Higgs production can be used for these too.
                                                                                                        • This project is just the first step in the path towards analysing real collisional data to find double Higgs production as predicted by the Z'-2HDM model and would be helpful for any further studies on this topic. Validation of BSM scenarios (Z'-2HDM in this case) would open a window on new physics which has not been observed as yet.

                                                                                                        ACKNOWLEDGEMENTS

                                                                                                        First and foremost, I would to express my sincere gratitude to my guide, Dr. Jyothsna Rani Komaragiri for her constant guidance and support throughout the duration of the project. This project truly gave me an overview of the field of Experimental Particle Physics and I am grateful to have got the opportunity to work on simulations of real life particle cross-sections. For this, I would like to thank the Indian Academy of Sciences, Bengaluru for accepting my candidature for the Summer Research Fellowship Programme 2019 and providing me this wonderful opportunity.

                                                                                                        This project would not have been possible without the help of the PhD students of the Experimental Particle Physics Group, Centre for High Energy Physics (IISc Bangalore) namely, Ms. Lata Panwar, Mr. Deepak Kumar and Mr. Praveen Chandra Tiwari. Last but not the least, I would to thank my fellow interns, Mithanshu Thakore and Shilpi Jain for making this internship a cherishable experience.

                                                                                                        APPENDICES

                                                                                                        A. Cross-section of runs

                                                                                                        The table below summarizes the cross-section of all the runs along with the masses and decay widths of a0 and h:

                                                                                                        Summary of all the runs of the generated process
                                                                                                         Runs Mass of a0[GeV] Decay width of a0[GeV]Mass of zp[GeV]  Decay width of zp[GeV]Cross-section[pb] 
                                                                                                        1300 3 450 5 9.464500e-04 
                                                                                                        23003 500 5 2.859700e-03 
                                                                                                        3300 3 6005 4.555700e-03 
                                                                                                        44004600 6 6.200600e-06
                                                                                                        5300 5 800 10 1.136500e-03 
                                                                                                        6 300 5 1000 10 7.397500e-04 
                                                                                                        7300 5 1200 10 4.637300e-04 
                                                                                                        8500 5 800 10 5.596300e-04 
                                                                                                         9500 5 1000 10 6.562700e-04 
                                                                                                         10500 5 1200 10 5.167000e-04 

                                                                                                        References

                                                                                                        • Englert, F. and Brout, R. (1964). Broken Symmetry and the Mass of Gauge Vector Mesons. 13,

                                                                                                        • Higgs, Peter W. (1964). Broken Symmetries and the Masses of Gauge Bosons. 13,

                                                                                                        • ATLAS Collaboration, ATLAS searches for double Higgs production, https://atlas.cern/updates/physics-briefing/atlas-searches-double-higgs-production

                                                                                                        • Berlin, Asher and Lin, Tongyan and Wang, Lian-Tao (2014). Mono-Higgs detection of dark matter at the LHC. 2014,

                                                                                                        • IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "branching fraction".

                                                                                                        • LHC Higgs Cross Section Working Group collaboration, S. Heinemeyer et al.,Handbook of LHC Higgs cross sections: 3. Higgs properties, arXiv:1307.1347.

                                                                                                        • Griffiths, David (2010). Elementary Particle Physics-Second, Revised Edition. Wiley-VCH. ISBN 978-3-527-40601-2

                                                                                                        • Matthew D. Schwartz, TASI Lectures on Collider Physics, arXiv:1709.04533v1 [hep-ph] 13 Sep 2017

                                                                                                        • Speak physics: What is a cross section?, Symmetry Magazine, https://www.symmetrymagazine.org/article/speak-physics-what-is-a-cross-section

                                                                                                        • Cross section, Fermi Lab, http://www.fnal.gov/pub/today/archive/archive_2013/today13-03-01.html

                                                                                                        • Michael H. Seymour and Marilyn Marx, “Monte Carlo Event Generators”, Lectures given at 69th Scottish Universities Summer School in Physics (SUSSP 69), St. Andrews, 19th August - 1st September 2012, https://arxiv.org/abs/1304.6677

                                                                                                        • Monte Carlo Particle Numbering Scheme, http://pdg.lbl.gov/2018/reviews/rpp2018-rev-monte-carlo-numbering.pdf

                                                                                                        Source

                                                                                                        • Fig 1: https://en.wikipedia.org/wiki/Standard_Model
                                                                                                        • Fig 2: https://arxiv.org/pdf/1312.5672.pdf
                                                                                                        • Fig 3: https://link.springer.com/content/pdf/10.1007%2FJHEP06%282014%29078.pdf
                                                                                                        • Fig 4: http://www.lppp.lancs.ac.uk/higgs/pop-ups/feynman.html
                                                                                                        • Fig 6: http://inspirehep.net/record/1087931/plots
                                                                                                        • Fig 7: http://www.lppp.lancs.ac.uk/higgs/pop-ups/feynman.html
                                                                                                        • Fig 13: http://cds.cern.ch/record/1155823/plots
                                                                                                        • Fig 15: https://arxiv.org/pdf/1709.04533.pdf
                                                                                                        More
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