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Left-Right Symmetric Model Left-Right Symmetric Model ± Putting lower bounds on the mass of the heavy, charged WR gauge boson Melissa Harris 940609-1885 [email protected] A thesis presented for the degree of MSc: Master in Physics Supervised by Rikard Enberg, Andreas Ekstedt and Johan L¨ofgren Theoretical High Energy Physics Uppsala University Sweden Abstract In this project I have studied the left-right symmetric model (LRSM) as a candidate beyond standard model theory of particle physics. The most common version of the theory, called the minimal LRSM, has been studied and tested extensively for several decades. I have therefore modified this minimal LRSM by adapting the scalar sector and computing the mass of the ± charged right-handed gauge bosons WR for this particular scalar sector. I carried out a study of the theory and implemented it into FeynRules, in order to simulate LHC events using ± MadGraph. This allowed computation of the cross-section for the decay WR ! tb as a function of the mass of W ±, which was compared with CMS data for the same decay, with R p proton-proton collisions at a centre of mass energy of s = 13 TeV. The final result was a ± constraint on the mass of WR , with a lower bound of MWR ≥ 3 TeV. 1 Popul¨arvetenskaplig Sammanfattning Inom partikelfysik kallas den mest v¨alk¨andaoch accepterade teorin f¨orpartikelfysikens stan- dardmodell (SM). Aven¨ om teorin har testats noggrant och i de flesta fall st¨ammer¨overens med experimentella resultat finns det vissa fenomen som den inte kan f¨orklara. P˚agrund av SMs tillkortakommanden finns en gren av fysiken som kallas bortom standardmodellen (BSM). D¨ar utvecklas teorier f¨oratt f¨orb¨attraSM och f¨orklarade fenomen som SM inte kan. Dessa teorier kallas s˚af¨or att de, snarare ¨anatt b¨orjafr˚anb¨orjanoch utveckla en helt ny modell, bygger vidare p˚aSMs framg˚angargenom att l¨aggatill nya delar. I det h¨arprojektet har jag studerat den v¨anster-h¨ogersymmetriska modellen (LRSM) som kandidatteori f¨orpartikelfysik BSM. Den vanligaste varianten av teorin, kallad minimal LRSM, har testats noggrant under flera decennier. D¨arf¨orhar jag modifierat denna minimala LRSM genom att anpassa den skal¨arasektorn och ber¨aknamassan hos de laddade h¨ogerh¨anta gauge- bosonerna WR i denna specifika skal¨arasektor. Jag genomf¨ordeen studie av teorin och imple- menterade den i FeynRules f¨oratt simulera LHC-h¨andelsermed hj¨alpav MadGraph. Detta gjorde det m¨ojligt att ber¨aknatv¨arsnittet f¨ors¨onderfallet WR ! tb som funktion av massan hos WR, vilket j¨amf¨ordesmed data f¨ordetta s¨onderfallfr˚anCMS-detektorn i proton-proton- kollisioner vid masscentrumenergi sqrts = 13 TeV. Slutresulatet ¨aren l¨agregr¨ansf¨ormassan hos WR, MWR = 3 TeV. 2 Contents 1 Introduction 5 1.1 Success and Limitations of the Standard Model . .5 1.2 Looking Beyond the Standard Model . .5 1.3 Why Study the Left-Right Symmetric Model? . .6 1.4 Outline of the Project . .7 2 Overview of the Standard Model 8 2.1 Group Structure . .8 2.1.1 SU(3) . .8 2.1.2 SU(2) . .8 2.1.3 U(1) . .9 2.2 Chirality . .9 2.3 Matter Particle Content . .9 2.4 Gauge Transformations . 10 2.5 The Higgs Mechanism . 11 3 Left-Right Symmetric Model 14 3.1 Gauge Group and Multiplet Structure . 14 3.2 Scalar Sector . 16 3.3 The Left-Right Symmetric Lagrangian . 16 3.3.1 Gauge Field Lagrangian . 16 3.3.2 Fermionic Gauge Lagrangian . 17 3.3.3 Scalar Lagrangian . 17 3.3.4 Yukawa Lagrangian . 17 3.3.5 Higgs Potential Lagrangian . 18 3.4 Left-Right Symmetry as Parity . 19 3.5 Spontaneous Symmetry Breaking . 20 3.5.1 Symmetry Breaking: Step 1 . 21 3.5.2 Symmetry Breaking: Step 2 . 22 3.5.3 Symmetry Breaking: Step 3 . 23 3.6 Physical Consequences of Symmetry Breaking . 25 3.6.1 Neutral Gauge Boson Masses . 25 3.6.2 Charged Gauge Boson Masses . 29 4 Running Simulations of the LRSM 31 4.1 FeynRules . 31 4.1.1 Gauge Groups . 31 4.1.2 Indices . 32 4.1.3 Fields . 32 4.1.4 Parameters . 33 3 4.1.5 Lagrangian . 33 4.2 MadGraph . 34 5 Comparison of Simulations with CMS Data 35 5.1 Production and Decay of W boson . 35 5.2 Cross-section and the Narrow Width Approximation . 36 5.3 CMS Search for W Boson . 36 5.4 Putting Mass Limits on W Boson . 36 6 Conclusion 38 6.1 Future possibilities in this project . 38 6.2 Future work beyond this thesis . 38 7 References 40 4 1 Introduction 1.1 Success and Limitations of the Standard Model In the study of particle physics, the most well known and accepted theory to date is the stan- dard model (SM) of particle physics. The SM is a combination of the Glashow-Weinberg-Salam theory of electroweak interactions and the theory of quantum chromodynamics (QCD). The theory associates each known particle with a quantum field and predicts which interactions oc- cur and the probabilities of such interactions. All of the particles occurring in the SM have been experimentally observed, with the final observation being the Higgs boson in 2012 by ATLAS and CMS [1], [2]. The SM has predictive power and is in strong agreement with experimental data. Despite the success of the SM, the theory has its shortcomings. There are a number of phenom- ena which can't be explained by the SM [3]. According to the SM, the neutrinos are massless, however experiments have shown that the neutrinos do have masses and mixing occurs between them. Additionally, there is no particle in the SM which can explain the existence of cold dark matter. The asymmetry of matter over anti-matter is yet another feature of the observable universe which can't be explained by the SM. There is another reason why physicists are not satisfied with the SM. There are 19 free pa- rameters which describe the theory and determine, for example, the particle masses. These parameters can only be determined by experiment and there is no explanation as to why they have the values they do. There exists a hierarchy in the masses of the three generations of particles which is not explained. It is therefore natural to question the completeness of the SM and look for explanations of how these parameters arise. 1.2 Looking Beyond the Standard Model Due to the shortcomings of the SM, there is a branch of physics called beyond the standard model (BSM), where theories are developed to improve the SM and explain the phenomena which the SM can't. These theories are so called, because rather than starting from the very beginning and developing an entirely new model, they build on the success of the SM by adding extensions to the theory. One benefit to this approach is that the SM describes processes which occur at energies which are reachable by current accelerators. Therefore, it is entirely possible that BSM theories can also be probed in particle accelerators. The field of high energy physics is therefore important for both theorists and experimentalists. From the theoretical point of view, a theory can be studied in detail and computer programs can be used to predict observa- tions at accelerators. These predictions can then be compared to data which is collected and processed by the experimentalists. 5 A natural way to extend the SM is to analyse the group structure. The SM is based on the gauge group: GSM = SU(3)C × SU(2)L × U(1)Y It is a direct product of the electroweak group SU(2)L × U(1)Y with the QCD group SU(3)C . The electroweak group is broken down via a process called spontaneous symmetry breaking to give the group describing the electromagnetic interactions observed in nature: SU(2)L × U(1)Y ! U(1)EM This process is caused by having a scalar field with a non-zero vacuum expectation value in- cluded in the theory. It is also the process responsible for the matter particles and gauge bosons acquiring their masses. The energy scale of this electroweak symmetry breaking is de- fined roughly by the vacuum expectation value of the Higgs field, νH ' 246 GeV [4]. It is predicted that the SM is an effective theory of a more complete theory which has the Planck scale of ∼ 1019GeV as its energy scale. This is known as a Grand Unified Theory (GUT). There then exists a gauge group to describe the GUT at this higher energy, which contains the SM at lower energies: GGUT ⊃ SU(3)C × SU(2)L × U(1)Y A number of symmetry breaking steps are then responsible for breaking down the GUT gauge group to the SM gauge group. It is not yet known which group corresponds to GGUT , and searches for a suitable candidate are ongoing [5]. There are two main approaches in this search. The first is a so-called "top-down" approach, where the GGUT is hypothesised, then broken down in a number of steps to GSM . The alternative method is a "bottom-up" approach, beginning with GSM and gradually extending the group. The latter is the approach taken in the left-right symmetric model (LRSM). 1.3 Why Study the Left-Right Symmetric Model? The left-right symmetric model is formed by modifying the electroweak gauge group. A right- handed SU(2)R group is added and the charge on U(1) is modified to a new charge denoted by Y~ : GLR = SU(2)L × SU(2)R × U(1)Y~ This model was first suggested by physicists Jogesh Pati and Abdus Salam, in an attempt to introduce left-right symmetry.
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