Weak Interactions Outline
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Quantum Field Theory*
Quantum Field Theory y Frank Wilczek Institute for Advanced Study, School of Natural Science, Olden Lane, Princeton, NJ 08540 I discuss the general principles underlying quantum eld theory, and attempt to identify its most profound consequences. The deep est of these consequences result from the in nite number of degrees of freedom invoked to implement lo cality.Imention a few of its most striking successes, b oth achieved and prosp ective. Possible limitation s of quantum eld theory are viewed in the light of its history. I. SURVEY Quantum eld theory is the framework in which the regnant theories of the electroweak and strong interactions, which together form the Standard Mo del, are formulated. Quantum electro dynamics (QED), b esides providing a com- plete foundation for atomic physics and chemistry, has supp orted calculations of physical quantities with unparalleled precision. The exp erimentally measured value of the magnetic dip ole moment of the muon, 11 (g 2) = 233 184 600 (1680) 10 ; (1) exp: for example, should b e compared with the theoretical prediction 11 (g 2) = 233 183 478 (308) 10 : (2) theor: In quantum chromo dynamics (QCD) we cannot, for the forseeable future, aspire to to comparable accuracy.Yet QCD provides di erent, and at least equally impressive, evidence for the validity of the basic principles of quantum eld theory. Indeed, b ecause in QCD the interactions are stronger, QCD manifests a wider variety of phenomena characteristic of quantum eld theory. These include esp ecially running of the e ective coupling with distance or energy scale and the phenomenon of con nement. -
Frstfo O Ztif
FRStfo o ztif * CONNISSARIAT A L'ENERGIE ATOMIQUE CENTRE D'ETUDES NUCLEAIRES DE SACLAY CEA-CONF -- 8070 Service de Documentation F9119! GIF SUR YVETTE CEDEX L2 \ PARTICLE PHYSICS AND GAUGE THEORIES MOREL, A. CEA CEN Socloy, IRF, SPh-T Communication présentée à : Court* on poxticlo phytic* Cargos* (Franc*) 15-28 Jul 1985 PARTICLE PHYSICS AND GAUGE THEORIES A. MOREL Service de Physique Théorique CEN SACLA Y 91191 Gif-sur-Yvette Cedex, France These notes are intended to help readers not familiar with parti cle physics in entering the domain of gauge field theory applied to the so-called standard model of strong and electroweak interactions. They are mainly based on previous notes written in common with A. Billoire. With re3pect to the latter ones, the introduction is considerably enlar ged in order to give non specialists a general overview of present days "elementary" particle physics. The Glashow-Salam-Weinberg model is then treated,with the details which its unquestioned successes deserve, most probably for a long time. Finally SU(5) is presented as a prototype of these developments of particle physics which aim at a unification of all forces. Although its intrinsic theoretical difficulties and the. non- observation of a sizable proton decay rate do not qualify this model as a realistic one, it has many of the properties expected from a "good" unified theory. In particular, it allows one to study interesting con nections between particle physics and cosmology. It is a pleasure to thank the organizing committee of the Cargèse school "Particules et Cosmologie", and especially J. Audouze, for the invitation to lecture on these subjects, and M.F. -
Weak Interaction Processes: Which Quantum Information Is Revealed?
Weak Interaction Processes: Which Quantum Information is revealed? B. C. Hiesmayr1 1University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Vienna, Austria We analyze the achievable limits of the quantum information processing of the weak interaction revealed by hyperons with spin. We find that the weak decay process corresponds to an interferometric device with a fixed visibility and fixed phase difference for each hyperon. Nature chooses rather low visibilities expressing a preference to parity conserving or violating processes (except for the decay Σ+ pπ0). The decay process can be considered as an open quantum channel that carries the information of the−→ hyperon spin to the angular distribution of the momentum of the daughter particles. We find a simple geometrical information theoretic 1 α interpretation of this process: two quantization axes are chosen spontaneously with probabilities ±2 where α is proportional to the visibility times the real part of the phase shift. Differently stated the weak interaction process corresponds to spin measurements with an imperfect Stern-Gerlach apparatus. Equipped with this information theoretic insight we show how entanglement can be measured in these systems and why Bell’s nonlocality (in contradiction to common misconception in literature) cannot be revealed in hyperon decays. We study also under which circumstances contextuality can be revealed. PACS numbers: 03.67.-a, 14.20.Jn, 03.65.Ud Weak interactions are one out of the four fundamental in- systems. teractions that we think that rules our universe. The weak in- Information theoretic content of an interfering and de- teraction is the only interaction that breaks the parity symme- caying system: Let us start by assuming that the initial state try and the combined charge-conjugation–parity( P) symme- of a decaying hyperon is in a separable state between momen- C try. -
1 Drawing Feynman Diagrams
1 Drawing Feynman Diagrams 1. A fermion (quark, lepton, neutrino) is drawn by a straight line with an arrow pointing to the left: f f 2. An antifermion is drawn by a straight line with an arrow pointing to the right: f f 3. A photon or W ±, Z0 boson is drawn by a wavy line: γ W ±;Z0 4. A gluon is drawn by a curled line: g 5. The emission of a photon from a lepton or a quark doesn’t change the fermion: γ l; q l; q But a photon cannot be emitted from a neutrino: γ ν ν 6. The emission of a W ± from a fermion changes the flavour of the fermion in the following way: − − − 2 Q = −1 e µ τ u c t Q = + 3 1 Q = 0 νe νµ ντ d s b Q = − 3 But for quarks, we have an additional mixing between families: u c t d s b This means that when emitting a W ±, an u quark for example will mostly change into a d quark, but it has a small chance to change into a s quark instead, and an even smaller chance to change into a b quark. Similarly, a c will mostly change into a s quark, but has small chances of changing into an u or b. Note that there is no horizontal mixing, i.e. an u never changes into a c quark! In practice, we will limit ourselves to the light quarks (u; d; s): 1 DRAWING FEYNMAN DIAGRAMS 2 u d s Some examples for diagrams emitting a W ±: W − W + e− νe u d And using quark mixing: W + u s To know the sign of the W -boson, we use charge conservation: the sum of the charges at the left hand side must equal the sum of the charges at the right hand side. -
Introduction to Supersymmetry
Introduction to Supersymmetry Pre-SUSY Summer School Corpus Christi, Texas May 15-18, 2019 Stephen P. Martin Northern Illinois University [email protected] 1 Topics: Why: Motivation for supersymmetry (SUSY) • What: SUSY Lagrangians, SUSY breaking and the Minimal • Supersymmetric Standard Model, superpartner decays Who: Sorry, not covered. • For some more details and a slightly better attempt at proper referencing: A supersymmetry primer, hep-ph/9709356, version 7, January 2016 • TASI 2011 lectures notes: two-component fermion notation and • supersymmetry, arXiv:1205.4076. If you find corrections, please do let me know! 2 Lecture 1: Motivation and Introduction to Supersymmetry Motivation: The Hierarchy Problem • Supermultiplets • Particle content of the Minimal Supersymmetric Standard Model • (MSSM) Need for “soft” breaking of supersymmetry • The Wess-Zumino Model • 3 People have cited many reasons why extensions of the Standard Model might involve supersymmetry (SUSY). Some of them are: A possible cold dark matter particle • A light Higgs boson, M = 125 GeV • h Unification of gauge couplings • Mathematical elegance, beauty • ⋆ “What does that even mean? No such thing!” – Some modern pundits ⋆ “We beg to differ.” – Einstein, Dirac, . However, for me, the single compelling reason is: The Hierarchy Problem • 4 An analogy: Coulomb self-energy correction to the electron’s mass A point-like electron would have an infinite classical electrostatic energy. Instead, suppose the electron is a solid sphere of uniform charge density and radius R. An undergraduate problem gives: 3e2 ∆ECoulomb = 20πǫ0R 2 Interpreting this as a correction ∆me = ∆ECoulomb/c to the electron mass: 15 0.86 10− meters m = m + (1 MeV/c2) × . -
Fundamental Physical Constants: Looking from Different Angles
1 Fundamental Physical Constants: Looking from Different Angles Savely G. Karshenboim Abstract: We consider fundamental physical constants which are among a few of the most important pieces of information we have learned about Nature after its intensive centuries- long studies. We discuss their multifunctional role in modern physics including problems related to the art of measurement, natural and practical units, origin of the constants, their possible calculability and variability etc. PACS Nos.: 06.02.Jr, 06.02.Fn Resum´ e´ : Nous ... French version of abstract (supplied by CJP) arXiv:physics/0506173v2 [physics.atom-ph] 28 Jul 2005 [Traduit par la r´edaction] Received 2004. Accepted 2005. Savely G. Karshenboim. D. I. Mendeleev Institute for Metrology, St. Petersburg, 189620, Russia and Max- Planck-Institut f¨ur Quantenoptik, Garching, 85748, Germany; e-mail: [email protected] unknown 99: 1–46 (2005) 2005 NRC Canada 2 unknown Vol. 99, 2005 Contents 1 Introduction 3 2 Physical Constants, Units and Art of Measurement 4 3 Physical Constants and Precision Measurements 7 4 The International System of Units SI: Vacuum constant ǫ0, candela, kelvin, mole and other questions 10 4.1 ‘Unnecessary’units. .... .... ... .... .... .... ... ... ...... 10 4.2 ‘Human-related’units. ....... 11 4.3 Vacuum constant ǫ0 andGaussianunits ......................... 13 4.4 ‘Unnecessary’units,II . ....... 14 5 Physical Phenomena Governed by Fundamental Constants 15 5.1 Freeparticles ................................... .... 16 5.2 Simpleatomsandmolecules . ..... -
Threshold Corrections in Grand Unified Theories
Threshold Corrections in Grand Unified Theories Zur Erlangung des akademischen Grades eines DOKTORS DER NATURWISSENSCHAFTEN von der Fakult¨at f¨ur Physik des Karlsruher Instituts f¨ur Technologie genehmigte DISSERTATION von Dipl.-Phys. Waldemar Martens aus Nowosibirsk Tag der m¨undlichen Pr¨ufung: 8. Juli 2011 Referent: Prof. Dr. M. Steinhauser Korreferent: Prof. Dr. U. Nierste Contents 1. Introduction 1 2. Supersymmetric Grand Unified Theories 5 2.1. The Standard Model and its Limitations . ....... 5 2.2. The Georgi-Glashow SU(5) Model . .... 6 2.3. Supersymmetry (SUSY) .............................. 9 2.4. SupersymmetricGrandUnification . ...... 10 2.4.1. MinimalSupersymmetricSU(5). 11 2.4.2. MissingDoubletModel . 12 2.5. RunningandDecoupling. 12 2.5.1. Renormalization Group Equations . 13 2.5.2. Decoupling of Heavy Particles . 14 2.5.3. One-Loop Decoupling Coefficients for Various GUT Models . 17 2.5.4. One-Loop Decoupling Coefficients for the Matching of the MSSM to the SM ...................................... 18 2.6. ProtonDecay .................................... 21 2.7. Schur’sLemma ................................... 22 3. Supersymmetric GUTs and Gauge Coupling Unification at Three Loops 25 3.1. RunningandDecoupling. 25 3.2. Predictions for MHc from Gauge Coupling Unification . 32 3.2.1. Dependence on the Decoupling Scales µSUSY and µGUT ........ 33 3.2.2. Dependence on the SUSY Spectrum ................... 36 3.2.3. Dependence on the Uncertainty on the Input Parameters ....... 36 3.2.4. Top-Down Approach and the Missing Doublet Model . ...... 39 3.2.5. Comparison with Proton Decay Constraints . ...... 43 3.3. Summary ...................................... 44 4. Field-Theoretical Framework for the Two-Loop Matching Calculation 45 4.1. TheLagrangian.................................. 45 4.1.1. -
Arxiv:0901.3958V2 [Hep-Ph] 29 Jan 2009 Eul Rkn SU(2) Broken, Neously Information
Gedanken Worlds without Higgs: QCD-Induced Electroweak Symmetry Breaking Chris Quigg1, 2 and Robert Shrock3 1Theoretical Physics Department Fermi National Accelerator Laboratory, Batavia, Illinois 60510 USA 2Institut f¨ur Theoretische Teilchenphysik Universit¨at Karlsruhe, D-76128 Karlsruhe, Germany 3C. N. Yang Institute for Theoretical Physics Stony Brook University, Stony Brook, New York 11794 USA To illuminate how electroweak symmetry breaking shapes the physical world, we investigate toy models in which no Higgs fields or other constructs are introduced to induce spontaneous symme- ⊗ ⊗ try breaking. Two models incorporate the standard SU(3)c SU(2)L U(1)Y gauge symmetry and fermion content similar to that of the standard model. The first class—like the standard elec- troweak theory—contains no bare mass terms, so the spontaneous breaking of chiral symmetry within quantum chromodynamics is the only source of electroweak symmetry breaking. The second class adds bare fermion masses sufficiently small that QCD remains the dominant source of elec- troweak symmetry breaking and the model can serve as a well-behaved low-energy effective field theory to energies somewhat above the hadronic scale. A third class of models is based on the left- ⊗ ⊗ ⊗ right–symmetric SU(3)c SU(2)L SU(2)R U(1)B−L gauge group. In a fourth class of models, built on SU(4)PS ⊗ SU(2)L ⊗ SU(2)R gauge symmetry, lepton number is treated as a fourth color. Many interesting characteristics of the models stem from the fact that the effective strength of the weak interactions is much closer to that of the residual strong interactions than in the real world. -
Atomic Parity Violation, Polarized Electron Scattering and Neutrino-Nucleus Coherent Scattering
Available online at www.sciencedirect.com ScienceDirect Nuclear Physics B 959 (2020) 115158 www.elsevier.com/locate/nuclphysb New physics probes: Atomic parity violation, polarized electron scattering and neutrino-nucleus coherent scattering Giorgio Arcadi a,b, Manfred Lindner c, Jessica Martins d, Farinaldo S. Queiroz e,∗ a Dipartimento di Matematica e Fisica, Università di Roma 3, Via della Vasca Navale 84, 00146, Roma, Italy b INFN Sezione Roma 3, Italy c Max-Planck-Institut für Kernphysik (MPIK), Saupfercheckweg 1, 69117 Heidelberg, Germany d Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil e International Institute of Physics, Universidade Federal do Rio Grande do Norte, Campus Universitário, Lagoa Nova, Natal-RN 59078-970, Brazil Received 7 April 2020; received in revised form 22 July 2020; accepted 20 August 2020 Available online 27 August 2020 Editor: Hong-Jian He Abstract Atomic Parity Violation (APV) is usually quantified in terms of the weak nuclear charge QW of a nucleus, which depends on the coupling strength between the atomic electrons and quarks. In this work, we review the importance of APV to probing new physics using effective field theory. Furthermore, we correlate our findings with the results from neutrino-nucleus coherent scattering. We revisit signs of parity violation in polarized electron scattering and show how precise measurements on the Weinberg’s angle give rise to competitive bounds on light mediators over a wide range of masses and interactions strengths. Our bounds are firstly derived in the context of simplified setups and then applied to several concrete models, namely Dark Z, Two Higgs Doublet Model-U(1)X and 3-3-1, considering both light and heavy mediator regimes. -
Supersymmetry Min Raj Lamsal Department of Physics, Prithvi Narayan Campus, Pokhara Min [email protected]
Supersymmetry Min Raj Lamsal Department of Physics, Prithvi Narayan Campus, Pokhara [email protected] Abstract : This article deals with the introduction of supersymmetry as the latest and most emerging burning issue for the explanation of nature including elementary particles as well as the universe. Supersymmetry is a conjectured symmetry of space and time. It has been a very popular idea among theoretical physicists. It is nearly an article of faith among elementary-particle physicists that the four fundamental physical forces in nature ultimately derive from a single force. For years scientists have tried to construct a Grand Unified Theory showing this basic unity. Physicists have already unified the electron-magnetic and weak forces in an 'electroweak' theory, and recent work has focused on trying to include the strong force. Gravity is much harder to handle, but work continues on that, as well. In the world of everyday experience, the strengths of the forces are very different, leading physicists to conclude that their convergence could occur only at very high energies, such as those existing in the earliest moments of the universe, just after the Big Bang. Keywords: standard model, grand unified theories, theory of everything, superpartner, higgs boson, neutrino oscillation. 1. INTRODUCTION unifies the weak and electromagnetic forces. The What is the world made of? What are the most basic idea is that the mass difference between photons fundamental constituents of matter? We still do not having zero mass and the weak bosons makes the have anything that could be a final answer, but we electromagnetic and weak interactions behave quite have come a long way. -
Spontaneous Symmetry Breaking in the Higgs Mechanism
Spontaneous symmetry breaking in the Higgs mechanism August 2012 Abstract The Higgs mechanism is very powerful: it furnishes a description of the elec- troweak theory in the Standard Model which has a convincing experimental ver- ification. But although the Higgs mechanism had been applied successfully, the conceptual background is not clear. The Higgs mechanism is often presented as spontaneous breaking of a local gauge symmetry. But a local gauge symmetry is rooted in redundancy of description: gauge transformations connect states that cannot be physically distinguished. A gauge symmetry is therefore not a sym- metry of nature, but of our description of nature. The spontaneous breaking of such a symmetry cannot be expected to have physical e↵ects since asymmetries are not reflected in the physics. If spontaneous gauge symmetry breaking cannot have physical e↵ects, this causes conceptual problems for the Higgs mechanism, if taken to be described as spontaneous gauge symmetry breaking. In a gauge invariant theory, gauge fixing is necessary to retrieve the physics from the theory. This means that also in a theory with spontaneous gauge sym- metry breaking, a gauge should be fixed. But gauge fixing itself breaks the gauge symmetry, and thereby obscures the spontaneous breaking of the symmetry. It suggests that spontaneous gauge symmetry breaking is not part of the physics, but an unphysical artifact of the redundancy in description. However, the Higgs mechanism can be formulated in a gauge independent way, without spontaneous symmetry breaking. The same outcome as in the account with spontaneous symmetry breaking is obtained. It is concluded that even though spontaneous gauge symmetry breaking cannot have physical consequences, the Higgs mechanism is not in conceptual danger. -
Standard Model (SM)
International School on Theory & Analysis in Particle Physics The Standard Model (SM) Main textbook: Modern Elementary Particle Physics, Kane Additional reading: SM: An Introduction, Novaes, arXiv:hep-ph/0001283 Symmetries of SM, Willenbrock, arXiv:hep-ph/0410370 Other advanced undergraduate / beginning graduate level textbooks: Quantum Field Theory, Ryder Introduction to Elementary Particles, Griffiths Quarks & Leptons, Halzen & Martin An Introduction to the SM of P.P., Cottingham & Greenwood Gauge Theories in Particle Physics, Aitchison & Hey Nefer Şenoğuz / Doğuş University Outline Lecture 1 Review: groups, spinors, gauge invariance The Standard Model: introduction and particle content Lecture 2 QCD: Quarks, confinement, mesons and baryons Electroweak Theory: Neutral and charged currents Lecture 3 Spontaneous symmetry breaking and Higgs mechanism Cross sections and decay widths: W and Z Lecture 4 Higgs Boson Quark mixing and CP violation Open questions, grand unification 2 What is the Standard Model (SM) of Particle Physics? • SM is the theory describing electromagnetic, weak & strong interactions • ~40 years old, spectacularly confirmed (except Higgs) • beyond the SM: neutrino masses, theoretical puzzles • whatever LHC finds, SM is valid as an effective theory for E < TeV • SM is a gauge theory based on review: groups, gauge invariance • matter content: quarks and leptons review: Dirac spinors 3 review: groups Rotation group O(n): [Orthogonal], n(n-1)/2 parameters SO(n): [Special] determinant = 1 Generators of rotation: SO(3): 3 parameter