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9. Quantum Chromodynamics 1 9
9. Quantum chromodynamics 1 9. Quantum Chromodynamics Revised September 2017 by S. Bethke (Max-Planck-Institute of Physics, Munich), G. Dissertori (ETH Zurich), and G.P. Salam (CERN).1 This update retains the 2016 summary of αs values, as few new results were available at the deadline for this Review. Those and further new results will be included in the next update. 9.1. Basics Quantum Chromodynamics (QCD), the gauge field theory that describes the strong interactions of colored quarks and gluons, is the SU(3) component of the SU(3) SU(2) U(1) Standard Model of Particle Physics. × × The Lagrangian of QCD is given by 1 = ψ¯ (iγµ∂ δ g γµtC C m δ )ψ F A F A µν , (9.1) q,a µ ab s ab µ q ab q,b 4 µν L q − A − − X µ where repeated indices are summed over. The γ are the Dirac γ-matrices. The ψq,a are quark-field spinors for a quark of flavor q and mass mq, with a color-index a that runs from a =1 to Nc = 3, i.e. quarks come in three “colors.” Quarks are said to be in the fundamental representation of the SU(3) color group. C 2 The µ correspond to the gluon fields, with C running from 1 to Nc 1 = 8, i.e. there areA eight kinds of gluon. Gluons transform under the adjoint representation− of the C SU(3) color group. The tab correspond to eight 3 3 matrices and are the generators of the SU(3) group (cf. -
From Superpotential to Model Files for Feynarts and Calchep/Comphep
Preprint typeset in JHEP style. - HYPER VERSION From Superpotential to Model Files for FeynArts and CalcHep/CompHep Florian Staub Institut f¨ur Theoretische Physik und Astrophysik, Universit¨at W¨urzburg, D-97074 W¨urzburg, GERMANY Email: [email protected] Abstract: SARAH is a Mathematica package for building and studying supersym- metric models. It calculates for a given superpotential and gauge sector the full Lagrangian of a model. With the new version of SARAH it is possible to calculate automatically all interactions for the different eigenstates and write model files for FeynArts and CompHep/CalcHep. In addition, the tadpole equations are calculated, gauge fixing terms can be given and ghost interactions are added, particles can be integrated out and non supersymmetric limits of the theory can be chosen. CP and flavor violation can easily be switched on or off. arXiv:0909.2863v1 [hep-ph] 15 Sep 2009 1. Introduction Supersymmetry is one of the most popular extensions of the standard model (SM) of particle physics [1, 2, 3, 4, 5, 6, 7]. The minimal supersymmetric standard model (MSSM) is well studied and there are several tools to explore the model: For every event generator or diagram calculator exists a model file, thus the MSSM can be handled out of the box. But what happens, if you want to change the model, extend the particle content, add a new gauge group or drop some assumptions about the parameters? Before you are able to do really physics and phenomenology you have to do a lot of work before: Check if your new model is free from gauge anomalies, get the Lagrangian out of the superpotential and extract all interactions, calculate the mass matrices and diagonalize them to get your mass spectrum, derive the tadpole equations to find the minimum conditions for your potential and so on. -
Quantum Field Theory and the Electroweak Standard Model
Published by CERN in the Proceedings of the 2013 European School of High-Energy Physics, Parádfürdo,˝ Hungary, 5 – 18 June 2013, edited by M. Mulders and G. Perez, CERN–2015–004 (CERN, Geneva, 2015) Quantum Field Theory and the Electroweak Standard Model E. Boos M. V. Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics (SINP MSU), Moscow 119991, Russia Abstract The Standard Model is one of the main intellectual achievements for about the last 50 years, a result of many theoretical and experimental studies. In this lecture a brief introduction to the electroweak part of the Standard Model is given. Since the Standard Model is a quantum field theory, some aspects for understanding of quantization of abelian and non-abelian gauge theories are also briefly discussed. It is demonstrated how well the electroweak Standard Model works in describing a large variety of precise experimental measure- ments at lepton and hadron colliders. 1 Introduction The Standard Model (SM) of strong and electroweak (EW) interactions is the basis for understanding of nature at extremely small distances. In high-energy physics usually the relativistic system of units is used in which the Planck constant ~ and the speed of light c are equal to unity, ~ = c = 1. Taking into account well-known values for ~ = 1.055 1027 erg s, c = 3 1010 cm/s and the positron electric · · charge e = 1.6 10 19 C and using the relation between the electronvolt and erg (1 eV = e 1 V = 1 V · − · 1.6 10 19 C = 1.6 10 12 erg), one easily gets the following very useful relation between length and · · − · − energy units: 1/GeV = 2 10 14 cm. -
Comphep- a Package for Evaluation of Feynman Diagrams and Integration Over Multi-Particle Phase Space
CompHEP- a package for evaluation of Feynman diagrams and integration over multi-particle phase space A.Pukhov∗ E.Boos M.Dubinin V.Edneral V.Ilyin D.Kovalenko A.Kryukov V.Savrin Skobeltsyn Institute of Nuclear Physics, Moscow State University S.Shichanin Institute for High Energy Physics, Protvino, Russia A.Semenov Joint Institute for Nuclear Research, Dubna, Russia User's manual for version 33 Preprint INP-MSU 98-41/542 ∗contact persons: Alexander Pukhov: [email protected] and Viacheslav Ilyin: [email protected] 1 Contents 1 Preface 6 1.1 Introduction . 6 1.2 History and contributions . 8 1.3 Acknowledgments . 10 2 Installation procedure 12 2.1 CompHEP Web page . 12 2.2 License . 12 2.3 How to get the codes . 13 2.4 Compilation procedure . 13 2.5 User installation and start of the CompHEP session . 16 2.6 Installation under MS Windows9x/NT . 17 3 User guide 18 3.1 Elements of the user interface . 18 3.1.1 Graphical interface . 18 3.1.2 Interface for a text-screen mode . 22 3.2 Menu system for symbolic calculation . 23 3.2.1 Choice of the model and work with it . 23 3.2.2 Input of the process . 26 3.2.3 Squaring of diagrams and symbolic calculation . 27 3.2.4 Output of results and launching of the numerical cal- culation . 31 3.2.5 Non-interactive session . 32 3.3 Numerical calculation by CompHEP . 33 3.3.1 Sketch of the menu system . 34 3.3.2 Numeration of Monte Carlo sessions . -
A Duality As a Theory for the Electroweak Interactions Xavier
A Duality as a Theory for the Electroweak Interactions Dissertation der Fakultat¨ fur¨ Physik der Ludwig-Maximilians-Universitat¨ Munchen¨ vorgelegt von Xavier Calmet aus Marignane Januar 2002 1. Gutachter: Prof. Dr. H. Fritzsch 2. Gutachter: Prof. Dr. J. Wess Prufungstag:¨ 8.05.2002 2 Deutsche Zusammenfassung Im Rahmen dieser Doktorarbeit wurde ein Modell fur¨ die elektroschwache Wechselwirkung entwickelt. Das Modell basiert auf der Tatsache, daß die sog. “Confinement”-Phase und Higgs-Phase der Theorie mit einem Higgs-Boson in der fundamentalen Darstellung der Eich- gruppe ¢¡¤£¦¥¨§ identisch sind. In der Higgs-Phase wird die Eichsymmetrie durch den Hig- gsmechanismus gebrochen. Dies fuhrt¨ zu Massentermen fur¨ die Eichbosonen, und uber¨ die Yukawa-Kopplungen zu Massentermen fur¨ die Fermionen. In der “Confinement”-Phase ist die Eichsymmetrie ungebrochen. Nur ¢¡¤£¦¥©§ -Singuletts kann eine Masse zugeordnet wer- den, d.h., physikalische Teilchen mussen¨ ¢¡¤£¦¥©§ -Singuletts sein. Man nimmt an, daß die rechtshandigen¨ Quarks und Leptonen elementare Objekte sind, wahrend¨ die linkshandigen¨ Dupletts Bindungszustande¨ darstellen. Es stellt sich heraus, daß das Modell in der “Confinement”-Phase dual zum Standard- Modell ist. Diese Dualitat¨ ermoglicht¨ eine Berechnung des elektroschwachen Mischungswin- kels und der Masse des Higgs-Bosons. Solange die Dualitat¨ gilt, erwartet man keine neue Physik. Es ist aber vorstellbar, daß die Dualitat¨ bei einer kritischen Energie zusammenbricht. Diese Energieskala konnte¨ sogar relativ niedrig sein. Insbesondere ist es moglich,¨ daß das Standard-Modell im Yukawa-Sektor zusammenbricht. Falls die Natur durch die “Confinement”- Phase beschrieben wird, koennte man davon ausgehen, daß die leichten Fermionmassen erzeugt werden, ohne daß das Higgs-Boson an die Fermionen gekoppelt wird. Dann wurde¨ aber das Higgs-Boson anders als im Standard Modell zerfallen. -
Arxiv:0805.0555V1 [Hep-Ph] 5 May 2008 Ls Hc Losoet Tr Acltoso Rcse Ntenwph As New Or the Format Format
LAPTH–1249/08 LanHEP— a package for the automatic generation of Feynman rules in field theory Version 3.0 A. V. Semenov Laboratory of Particle Physics, Joint Institute for Nuclear Research, 141 980 Dubna, Moscow Region, Russian Federation and Laboratoire de Physique Th´eorique LAPTH, Universit´ede Savoie, Chemin de Bellevue, B.P. 110, F-74941 Annecy-le-Vieux, Cedex, France. Abstract. The LanHEP program version 3.0 for Feynman rules generation from the La- grangian is described. It reads the Lagrangian written in a compact form, close to the one used arXiv:0805.0555v1 [hep-ph] 5 May 2008 in publications. It means that Lagrangian terms can be written with summation over indices of broken symmetries and using special symbols for complicated expressions, such as covariant derivative and strength tensor for gauge fields. Supersymmetric theories can be described using the superpotential formalism and the 2-component fermion notation. The output is Feynman rules in terms of physical fields and independent parameters in the form of CompHEP model files, which allows one to start calculations of processes in the new physical model. Alter- natively, Feynman rules can be generated in FeynArts format or as LaTeX table. One-loop counterterms can be generated in FeynArts format. E-mail: [email protected] WWW page: http://theory.sinp.msu.ru/~semenov/lanhep.html 2008 Introduction LanHEP has been designed as part of the CompHEP package [1], a software for automatic calculations in high energy physics. CompHEP allows symbolic computation of the matrix element squared of any process with up to 6 incoming and outgoing particles for a given physical model (i.e. -
Comphep- a Package for Evaluation of Feynman Diagrams And
CompHEP- a package for evaluation of Feynman diagrams and integration over multi-particle phase space A.Pukhov∗ E.Boos M.Dubinin V.Edneral V.Ilyin D.Kovalenko A.Kryukov V.Savrin Skobeltsyn Institute of Nuclear Physics, Moscow State University S.Shichanin Institute for High Energy Physics, Protvino, Russia A.Semenov Joint Institute for Nuclear Research, Dubna, Russia User’s manual for version 33 Preprint INP-MSU 98-41/542 arXiv:hep-ph/9908288v2 11 Feb 2000 ∗contact persons: Alexander Pukhov: [email protected] and Viacheslav Ilyin: [email protected] 1 Contents 1 Preface 6 1.1 Introduction............................ 6 1.2 Historyandcontributions . 8 1.3 Acknowledgments ........................ 10 2 Installation procedure 12 2.1 CompHEP Webpage ...................... 12 2.2 License............................... 12 2.3 Howtogetthecodes ....................... 13 2.4 Compilationprocedure . 13 2.5 User installation and start of the CompHEP session . 16 2.6 Installation under MS Windows9x/NT . 17 3 User guide 18 3.1 Elementsoftheuserinterface . 18 3.1.1 Graphicalinterface . 18 3.1.2 Interfaceforatext-screenmode . 22 3.2 Menu system for symbolic calculation . 23 3.2.1 Choiceofthemodelandworkwithit . 23 3.2.2 Inputoftheprocess. 26 3.2.3 Squaring of diagrams and symbolic calculation . 27 3.2.4 Output of results and launching of the numerical cal- culation .......................... 31 3.2.5 Non-interactivesession . 32 3.3 Numerical calculation by CompHEP . 33 3.3.1 Sketchofthemenusystem . 34 3.3.2 Numeration of Monte Carlo sessions . 35 3.3.3 QCDscale......................... 35 3.3.4 Breit-Wignerpropagator . 36 3.3.5 Phasespacefunctions . 37 3.3.6 Cuts ............................ 38 3.3.7 Kinematics ....................... -
Applications of Effective Field Theories Within and Beyond the Standard Model Oleg Antipin Iowa State University
Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 2008 Applications of effective field theories within and beyond the Standard Model Oleg Antipin Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Other Physics Commons Recommended Citation Antipin, Oleg, "Applications of effective field theories within and beyond the Standard Model" (2008). Retrospective Theses and Dissertations. 15801. https://lib.dr.iastate.edu/rtd/15801 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Applications of effective field theories within and beyond the Standard Model by Oleg Antipin A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: High Energy Physics Program of Study Committee: German Valencia, Major Professor Soeren Prell Kerry Whisnant James Vary Domenico D’Alessandro Iowa State University Ames, Iowa 2008 Copyright °c Oleg Antipin, 2008. All rights reserved. 3310801 3310801 2008 ii TABLE OF CONTENTS LIST OF TABLES . iv LIST OF FIGURES . v ACKNOWLEDGMENT . ix CHAPTER 1. Introduction . 1 1.1 Standard Model . 1 1.2 Effective field theories . 3 1.2.1 Examples of effective field theories . 4 CHAPTER 2. Theoretical tools . 7 2.1 Chiral perturbation theory . 7 2.2 Heavy quark effective theory . 9 2.2.1 Heavy Quark Symmetries . -
Introduction to QCD∗
Introduction to QCD∗ P. Z. Skandsy Theoretical Physics, CERN, 1211 Geneva 23, Switzerland School of Physics & Astronomy, Monash University, Clayton VIC 3800, Australia Updated: July, 2017 Abstract These lectures were originally given at TASI 2012 and are directed at a level suitable for graduate students in High Energy Physics. They are intended to give an introduction to the theory and phenomenology of quantum chromodynamics (QCD), focusing on collider physics applications. The aim is to bring the reader to a level where informed decisions can be made concerning different approaches and their uncertainties. The material is divided into five main areas: 1) fundamentals, 2) fixed-order perturbative QCD, 3) Monte Carlo event generators and parton showers, 4) Matching at Leading and Next-to-Leading Order, and 5) Hadronization and soft hadron-hadron physics. Useful Complementary References Basic Quantum Field Theory: [1] • Textbooks on QCD: [2–4] • Jets and Jet Algorithms: [5] • General-Purpose Event Generators: [6] • The String Model: [7, 8] • Underlying Event and Multiple Parton Interactions: [9, 10] • Step-by-step PYTHIA tutorial: see “worksheet” available on the PYTHIA homepage. arXiv:1207.2389v5 [hep-ph] 7 Jul 2017 • Monte Carlo methods and Random Numbers: [11, 12] • The veto algorithm, trial showers, the Sudakov algorithm [13–15] • ∗Lectures presented at TASI 2012: Theoretical Advanced Study Institute in Elementary Particle Physics — Searching for New Physics at Small and Large Scales. University of Colorado, Boulder, CO, June 4 – 29, 2012. Based on lectures first given at ESHEP 2010 (Raseborg, Finland); updated for AEPSHEP 2014 (Puri, India), pre- SUSY 2016 (Melbourne, Australia), and for MCNET 2017 (Lund, Sweden). -
Arxiv:Hep-Ph/9508235V1 4 Aug 1995
LAPP-EXP-95.06 Towards a Complete Feynman Diagrams Automatic Computation System D. PERRET-GALLIX L.A.P.P., IN2P3, CNRS e-mail: [email protected] B.P. 110 74941 Annecy-Le-Vieux France, Abstract: Complete Feynman diagram automatic computation systems are now coming of age after many years of development. They are made available to the high energy physics community through user-friendly interfaces. Theorists and experimen- talists can benefit from these powerful packages for speeding up time consuming calculations and for preparing event gen- erators. The general architecture of these packages is pre- sented and the current development of the one-loop diagrams extension is discussed. A rapid description of the prominent packages and tools is then proposed. Finally, the necessity for defining a standardization scheme is heavily stressed for arXiv:hep-ph/9508235v1 4 Aug 1995 the benefit of developers and users. Invited talk at the Fourth International Workshop on Software Engineering and Artificial Intelligence for High Energy and Nuclear Physics. AIHENP-95 Pisa April 3-8 1995 2 Towards a Complete Feynman Diagrams Automatic Computation System D. PERRET-GALLIX L.A.P.P., IN2P3, CNRS e-mail: [email protected] B.P. 110 74941 Annecy-Le-Vieux France, Complete Feynman diagram automatic computation systems are now coming of age after many years of development. They are made available to the high energy physics com- munity through user-friendly interfaces. Theorists and experimentalists can benefit from these powerful packages for speeding up time consuming calculations and for preparing event generators. The general architecture of these packages is presented and the cur- rent development of the one-loop diagrams extension is discussed. -
Comphep: Developments and Applications Dirk Zerwas - Single Production of Charged Gauge
Journal of Physics: Conference Series PAPER • OPEN ACCESS Related content - Search for Higgs and Supersymmetry CompHEP: developments and applications Dirk Zerwas - Single Production of Charged Gauge To cite this article: E.E. Boos et al 2017 J. Phys.: Conf. Ser. 920 012007 Boson WH from Left-Right Twin Higgs Model in Association with Top Quark at LHC Liu Yao-Bei, Wang Xue-Lei, Han Hong- Mei et al. View the article online for updates and enhancements. - Effective SUSY modified after LHC run Jihn E Kim This content was downloaded from IP address 131.169.5.251 on 17/11/2017 at 20:50 4th Computational Particle Physics Workshop IOP Publishing IOP Conf. Series: Journal of Physics: Conf. Series 1234567890920 (2017) 012007 doi :10.1088/1742-6596/920/1/012007 CompHEP: developments and applications E.E. Boos, V.E. Bunichev, M.N. Dubinin, V.A. Ilyin and V.I. Savrin (on behalf of CompHEP Collaboration) Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Leninskiye Gory, 119991 Moscow, Russian Federation E-mail: [email protected] Abstract. New developments of the CompHEP package and its applications to the top quark and the Higgs boson physics at the LHC collider are reviewed. These developments were motivated mainly by the needs of experimental searches of DO (Tevatron) and CMS (LHC) collaborations where identification of the top quark and the Higgs boson in the framework of the Standard Model (SM) or possible extensions of the SM played an important role. New useful features of the CompHEP Graphics User Interface (GUI) are described. 1.