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Searching for New Vector Particles at the Lhc UNIVERSIDAD TÉCNICA FEDERICO SANTA MARÍA DEPARTAMENTO DE FÍSICA SEARCHING FOR NEW VECTOR PARTICLES AT THE LHC Tesis de Grado presentada por Sr. Bastián Díaz Sáez como requisito parcial para optar al grado de Magíster en Ciencias, Mención Física Profesor Guía Dr. Alfonso R. Zerwekh Valparaíso - Chile 2013 Valparaíso, Chile. 2013 TÍTULO DE LA TESIS: SEARCHING FOR NEW VECTOR PARTICLES AT THE LHC AUTOR: BASTIÁN JAIME DÍAZ SÁEZ TRABAJO DE TESIS, presentado en cumplimiento parcial de los requisitos para el Grado de Magister en Ciencias Mención Física de la Universidad Técnica Federico Santa María. Dr. Alfonso Zerwekh Universidad Técnica Federico Santa María Dr. Gorazd Cvetic Universidad Técnica Federico Santa María Dr. Alfredo Vega Universidad de Valparaíso Valparaíso, Chile. 2013 2 ...dedicada a mis padres Gloria y Jaime. 3 Agradecimientos Mis más sinceros agradecimientos a mi familia, sobretodo a mi madre, Gloria, por haberme acompañado siempre hasta el día de hoy, y a mi padre Jaime por haberme apoyado incondicionalmente, sobretodo en los primeros años de universidad. Quisiera agradecer también a mi profesor de tesis Alfonso Zerwekh, que gracias a su buena dis- posición y entrega pudo ser posible este trabajo. Sin duda, quiero agradecer a mi polola Camila por todo el amor, paciencia, apoyo y cariño que me ha brindado. Agradezco a Conicyt por el apoyo económico durante el año 2012 y a la UTFSM por el apoyo financiero. 4 Resumen En el Modelo Estandar de Física de Partículas (SM), eventos de dos-jets (dijet) son producidos en colisiones proton-(anti)proton predominantemente de las interacciones de dos partones de la cromodinámica cuántica (QCD). La fragmentación y la hadronización de los partones finales producen jets hadrónicos. El espectro de masa invariante del dijet predicha por QCD cae suave y rápidamente con el incremento de la masa de éste. Muchas extensiones del SM predicen la existencia de nuevas partículas masivas que decaen en dos partones energéticos (quarks, q, or gluons, g), que potencialmente pueden ser observadas como una resonancia en el espectro de masa invariante del dijet. En modelos quirales de color, el grupo de gauge de color de QCD, SU(3)c, resulta del rompimiento espontáneo del grupo de gauge de color quiral SU(3) × SU(3). Cualquier modelo quiral de color predice la existencia de un axigluon, un gluón masivo que se acopla a los quarks de manera axial, que decae a un par qq¯. En este trabajo mostramos algunos modelos quirales, y veremos como algunos de estos modelos se acoplan a las observaciones hechas en CDF, CMS y ATLAS. El corazón de esta tesis se centra en simulaciones en CalcHEP del proceso p+p ! A ! jet + jet, donde A corresponde a un axigluón universal, con energías centro momentum a 7, 8 y 14 TeV. Estas simulaciones tienen distintos fines. Una es que a través de las comparaciones entre las secciones eficaces dadas por nuestros resultados con los límites superiores al 95% C.L. en la sección eficaz para una resonancia de modelo-independiente dados por el experimento ATLAS a 7 y 8 TeV, excluimos posibles masas del axigluón e imponemos límites en la constante de acoplamiento gA entre los quarks y el axigluón. También, es mostrado como la sección eficaz del axigluón es afectada cuando se considera adicionalmente el efecto del “smearing” de un detector real y cuando consideramos un axigluón ancho (Γ=M & 0:2), el cual éste último podría potencialmente dar cuenta de la FB anomalía Att¯ observada años atras en el Tevatron. Finalmente, tomando en cuenta que el LHC en un futuro cercano colisionará protones a energías sobre los 14 TeV, hacemos predicciones para la sección eficaz de resonancias a este rango de energías. Todas las simulaciones obtenidas de CalcHEP son analizadas con PAW. 5 Abstract Within the Standard Model (SM) of Particle Physics, two-jet (dijet) events are produced in proton−(anti)proton collisions predominantly from hard quantum chromodynamics (QCD) interactions of two partons. The fragmentation and hadronization of the outgoing partons produce hadronic jets. The dijet mass spectrum predicted by QCD falls smoothly and steeply with increasing dijet mass. Many extensions of the SM predict the existence of new massive particles that decay into two energetic partons (quarks, q, or gluons, g), which can potentially be observed as a resonance in the dijet mass spectrum. In chiral color models, the SU(3) color gauge group of QCD results from the spontaneous breaking of the SU(3) × SU(3) chiral color gauge group. Any model of chiral color predicts the presence of an axigluon, a massive vector gluon which couple to quarks in a pseudo-vector form, that decays to a pair qq¯. In this work we show some chiral models, and we will se how they coupled to the recent seaches performed by CDF, CMS and ATLAS. The hearth of this thesis is focused on simulations in CalcHEP of the process p + p ! A ! jet + jet, where A correspond to an universal-axigluon, at 7, 8 and 14 TeV center momentum energies. These simulations have different purposes. One of them is, through the comparation among our axigluon cross section simulations to the cross section upper limits 95% C.L. for a resonance model-independent given by ATLAS experiment at 7 and 8 TeV, we exlude posibles axigluon masses and set limits on the coupling constant gA between quarks and axigluon. Also, it is show how the axigluon cross section is affected when is considered both the smearing effect of a real detector in the analisis of the data FB and a broad axigluon (Γ=M & 0:2), which this latter is viable explanation for the Att¯ anomaly observed at the Tevatron. Finally, taking into account that LHC in the near future will operate at energies above 14 TeV, we make predictions on the cross section for resonances at this range of energies. All the simulation obtained from CalcHEP are analized in the frame of PAW. 6 Contents 1. Introduction 9 1.1. Elementary particle physics ......................... 9 1.2. New Particles ................................. 11 1.3. Natural Units . 12 2. Theoretical fundamentals 13 2.1. Elements of QCD . 13 2.1.1. The quantum chromodynamics Lagrangian . 13 2.1.2. Confinament and asymptotic freedom . 14 2.1.3. Jets . 15 2.2. Resonances . 16 2.2.1. What are they? . 16 2.2.2. Breit-Wigner resonance . 18 2.2.3. Narrow with approximation . 20 2.3. Non-lineal sigma model . 21 3. Motivation for New Physics in the Strong Sector 25 3.1. Enlarging the strong sector symmetry group . 25 3.2. The Forward-Backward Asymmetry . 25 4. Axigluons models 30 4.1. Flavor-universal models . 30 4.1.1. Minimal axigluon model . 30 4.1.2. Non-minimal model: Four gauge fields . 32 4.2. Flavor-nonuniversal models . 34 4.2.1. Frampton Model . 34 4.2.2. A simplified three-site model . 36 4.2.3. A Two-Site Model with a New Vector-like Quark . 38 5. Searching resonances in the dijet spectrum 41 5.1. Introduction . 41 5.2. Parton-parton scattering . 41 5.3. CDF II at TEVATRON . 42 5.4. ATLAS at LHC . 45 5.4.1. The ATLAS experiment . 45 5.4.2. Collider Kinematics . 47 5.4.3. Trigger . 48 7 5.4.4. Kinematical cuts for pp collision at 7 TeV and 8 TeV . 48 5.4.5. Model-independent limits on dijet resonance production . 49 6. Simulation and Analysis of data 51 6.1. Introduction . 51 6.2. The Simulation . 52 6.3. Analisis with Paw . 56 6.4. Results at 7 and 8 TeV . 60 6.5. Simulation at 8 TeV with smearing . 64 6.6. Broad Axigluon . 65 6.7. Calculus at 14 TeV . 66 7. Conclusions 68 A. Data obtained from simulation 70 B. Electron-proton scattering 74 B.1. Introduction . 74 B.2. Elastic scattering e− + µ− ! e− + µ− .................... 74 B.3. Elastic scattering e− + p ! e− + p ...................... 78 B.4. Electron-proton inelastic scattering . 80 B.5. Bjorken scaling . 82 C. σ-lineal model 86 C.1. Symmetries of the model . 86 C.2. Spontaneous symmetry breaking . 87 D. Anomalies 90 E. Parity 94 8 1. Introduction 1.1. Elementary particle physics What is matter made of? This is one of the fundamental question of physics. Physicist through the years have been studying the composition of the matter by different tech- niques. Now, accompanied by the technology, we can “look” inside of the matter to a very small lenght scales where the dynamics and the rules of the nature are very different to our experience. We call this tiny world, the subatomic world. In this subatomic world we have found a lot of families of particles, and at this moment, we have found the basic bricks of matter and how they interact. The best known elementary particle is the elec- tron, which, for example, are passing through the wires of your computer, cellphone, etc. This is what we call current. These particles, also, have the role of make fundamental structures of the matter which surround us: the atom. Atoms are structures constitued of three basic particles: electrons, neutrons and protons. The regularities in Mendeleev’s table were a stepping-stone to nuclei and to particles called protons and neutrons (colllec- tively labeled nucleons), which are “glued” together by a strong or nuclear force to form the nuclei. These subsequently bind with electrons through the electromagnetic force to produce the atoms of the chemical elements. There are a lot of different atoms compiled in the famous Periodic Table, which now contains well over 100 chemical elements. Also, in the last century, experiments have shown that the atomic nucleous is composed by another kind of entities: quarks.
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