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Phenomenological Studies on Composite Higgs Models

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Phenomenological Studies on Composite Higgs Models Phenomenological Studies on Composite Higgs Models Hesham El Faham Department of Physics and Astronomy Uppsala University A thesis submitted for the degree of Master of Science in Physics Uppsala, Sweden 2018 This thesis is dedicated to My parents, Adel El Faham and Ola Barakat. A special dedication to my mother whom without her support, this work, and future others, would have never been possible. Acknowledgements I am thankful.. to Gunnar Ingelman, who believed that I can do particle theory regardless of my Engineering background. The fuel of my persistence towards accomplishing anything during my master's studies came from knowing that Gunnar was al- ways there1. To my supervisor Rikard Enberg, who taught me a lot of physics in the last two years, and who had recently taught me that you can actually have a non-physics chat with a senior scientist while cycling your way to have dinner2. To Stefan Leupold, for all the fruitful conversations we had during the last two years, and for the advice he happily provided whenever I asked for it. To Gabriele Ferretti, for the great support he dispensed during my master's project work, and for his previous work (among others) that had inspired this work. To all the chats I had with my friend Thomas Mathisen which almost all of the time lead to the realization that we have done a terrible mistake in the model implementation. Well! We eventually (and apparently) got it right. To all the support I received from my good old friends in Egypt. To my sister and my brother, Reham and Mostafa. And finally, To my par- ents, whom their support is non-writable that I had already dedicated the `whole thing' to them. 1I can explain these two sentence about Gunnar in a whole book. 2If you studied in Egypt, you will be considered as a very lucky individual if you managed to see your supervisor. Abstract Composite Higgs Models (CHMs) are formulated in terms of strongly coupled theories. They often predict fermionic top partners with a mass around the TeV scale. Going beyond minimality enriches the spectrum of the theory with additional hypothetical scalars that significantly change the phenomenology. In this thesis, we explore an SO(6)=SO(5) CHM with an additional pseudo-scalar custodial singlet. The latter has anomalous couplings to the Standard Model vector bosons. We study the phenomenology of the singlet, including bounds from the available ATLAS and CMS searches in the relevant channels with di-boson and fermionic final states. We used HiggsBounds tool to test the model theoretical predictions against the current exclusion limits. The study is performed at the 8 and 13 TeV experiments at the LHC. We present a model parameter space from which the bounds on the (most sensitive) signal cross sections of the hypothetical singlet can be easily extracted. Contents 1 Svensk sammanfattninge 1 2 Introduction 2 3 The Standard Model (SM) 4 3.1 An overview of the SM interactions . 4 3.1.1 Quantum Chromo-Dynamics (QCD) . 5 3.1.1.1 Asymptotic freedom . 7 3.1.2 The Electro-Weak (EW) theory . 8 3.2 Electro-Weak Symmetry Breaking (EWSB) . 9 3.3 Mass generation: The Higgs mechanism . 12 4 Introduction to Higgs compositeness 14 4.1 SM as an effective theory . 14 4.2 Hierarchy problem of the Higgs boson mass . 15 4.3 Dimensional transmutation . 16 4.4 Higgs as NGB: Group theory aspects . 17 4.5 Construct a Composite Higgs Model (CHM) . 18 4.6 Our model: The M1 model . 24 5 Method and phenomenology 26 p 5.1 At s =8TeV ................................. 31 p 5.2 At s =13TeV ................................. 35 6 Outlook and discussion 37 A The explicit M1 38 B Implications of the CCWZ construction 41 C HiggsBounds ‘effective couplings' approach 44 i Bibliography 47 ii List of Figures 3.1 Feynman diagrams of the SM vertices involving gauge bosons (left), and a cartoon illustrating the interactions of the SM (right). Both figures are courtesy of Wikipedia. .............................. 5 3.2 Feynman diagrams for the Higgs bosons (dashed lines) quartic and cubic self-coupling (left), and its coupling to gauge bosons (right), both at tree-level. 13 4.1 Feynman diagrams for the Higgs boson coupling to the top quark (left), and a typical quartic self-coupling diagram (left), at one-loop level. 16 5.1 The production cross section of η in gluon fusion mode . 26 5.2 The branching fraction, BFVV , for all possible decay channels (apart from ZZ) of η, at a fixed mass of η, Mη= 500 GeV. 28 5.3 The branching fraction, BFVV , in a 3D model parameter space (Cb ∼ 0) where the particular final state, VV , is shown above each plot. The intuition that red, yellow, and blue colors indicate the branching fractions from highest to lowest, respectively, is true. The branching fractions numerical values are irrelevant since our argument here is qualitative. 30 5.4 The branching fraction, BFVV , in a 3D model parameter space (Cτ ∼ 0) where the particular final state, VV , is shown above each plot. 31 5.5 Bounds on the production cross section times the branching ratio, by ATLAS and CMS 8 TeV searches, on the most sensitive decay channels of a neutral psuedoscalar, η, as a function of its mass, Mη. 32 5.6 The branching fraction to ττ final state, BFττ=gg, as a function of Mη and the coupling Cτ (left). CMS experimental constraints, from 8 TeV searches, on the production cross section times BR(η ! Zγ) (right). 33 iii 5.7 Combined Bounds from ATLAS and CMS 8 TeV searches on production cross section times branching ratio of η to bosons. Contour lines are (σ8 × BR)b in pb. The regions to the the side of the red line (and the corners) are dominated by γγ decays. While, regions above and below the blue dashed line are dominated by Zγ decays. 34 5.8 Lowest-order Feynman diagrams for the production of a neutral MSSM Higgs boson via gluon fusion (left), and b-associated production (right). 35 5.9 ATLAS experimental constraints on the production cross section times the branching ratio at 13 TeV searches[4], of a neutral psuedoscalar, η, decaying to Zγ, as a function of its mass (left). Bounds on the production cross section times branching ratio of η to bosons. Contour lines are (σ8 × BR)b in pb (right). 36 iv Chapter 1 Svensk sammanfattninge De fundamentala krafterna ¨arde mest grundl¨aggande v¨axelverkningar som vi k¨annertill. Det finns fyra fundamentala v¨axelverkningar: gravitationell och elektromagnetisk, som ger krafter med l˚angr¨ackvidd, samt stark och svag v¨axelverkan, som ger krafter p˚aden sub- atom¨araniv˚an.F¨orutomgravitationen s˚akan den teori som kallas Standardmodellen (SM) beskriva de ¨ovrigatre fundamentala interaktionerna. Trots att SM ¨aren konsistent teori s˚a ¨arden inte komplett, och en utvidgning ¨arn¨odv¨andigf¨oratt kunna beskriva vissa fenomen som SM inte kan beskriva. SM beskriver alla elementarpartiklar som vi k¨annertill ¨ans˚a l¨ange. En av dessa ¨arden s˚akallade Higgsbosonen. Denna partikel ¨arinblandad i att ge de andra elementarpartiklarna sina massor. Higgsbosonens egenskaper i SM kan m¨atasoch observeras vid Large Hadron Collider (LHC). LHC ¨arv¨arldensmest kraftfulla partikelkolliderare, byggd av European Organiza- tion for Nuclear Research (CERN) i Gen`eve i Schweiz. Inuti acceleratorn cirkulerar tv˚a partikelstr˚alarmed mycket h¨ogenergi (mestadels protonstr˚alar),n¨araljusets hastighet, in- nan de krockas samman. Flera sofistikerade detektorer har byggts f¨oratt detektera dessa kollisioner, och studera och m¨atade olika fundamentala v¨axelverkningar som f¨orekommer. Flera utvidgningar av SM kan f¨or¨andraHiggsbosonens egenskaper. Att observera och m¨atas˚adanaf¨or¨andringarskulle kunna bekr¨aftaeller begr¨ansaolika scenarier f¨orfysik bortom SM och utesluta andra. Ett av dessa scenarier ¨ars˚akallade sammansatta Higgs- modeller (Composite Higgs Models, CHM). Dessa modeller tar Higgsbosonen som en sam- mansatt partikel, dvs den ¨arinte en elementarpartikel utan ¨arsammansatt av andra mer fundamentala partiklar. CHM:er har m˚angafria parametrar som bildar det s˚akallade pa- rameterrummet. I detta arbete har vi studerat en specifik modell som ¨arinspirerad av detta scenario f¨oren sammansatt Higgsboson. Vi har d¨arf¨ordefinierat ett parameterrum f¨ormodellen, d¨arvi har uteslutit vissa regioner med hj¨alpav relevanta data fr˚anLHC- experimentet. 1 Chapter 2 Introduction The philosophical concept of \Atomism", namely that all matter must be built up of more fundamental constituents, was originated way back in the early times. `Atomism' was first developed by ancient Greek philosophers in the 6th century BC and it had proposed the idea that everything is made of indivisible small fundamental constituents called `atoms'. In modern fundamental physics, atoms are already so big, they are built up of even more fundamental constituents than protons and neutrons, these `tiny' constituents are called elementary particles. Elementary particles that we know of are made of no other parti- cles, they have no sub-structure and they are, so far, considered to be the fundamental constituents of the matter in our world. How nature behaves at the `very small' scale of elementary particles is best described by Quantum Mechanics (QM). The quantum mechanical behaviour of subatomic particles1 is far beyond the classical intuition that we develop from our everyday experience. In par- ticle physics, it is of a major interest to study how subatomic particles interact together. Therefore, Einstein's theory of Special Relativity (SR) plays a substantial role in our under- standing of the behaviour of the subatomic (or fundamental) interactions2. Combining QM and SR together gave birth to Quantum Field Theory (QFT).
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