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M305; the Standard Model of Fundamental Particles and Their MISN-0-305 THE STANDARD MODEL OF FUNDAMENTAL PARTICLES AND THEIR INTERACTIONS by THE STANDARD MODEL Mesgun Sebhatu OF FUNDAMENTAL PARTICLES AND THEIR INTERACTIONS 1. Overview . 1 2. Historical Introduction a. Gravity . 2 b. Electromagnetism . 2 RUN 7339 EVENT 1279 c. The Weak \Nuclear" Force . 3 e+ e- d. The Strong \Nuclear" Force . 4 ET = 50 GeV ET = 11 GeV 3. The Standard Model a. Symmetry . 5 b. Constituents and Mediators of the Standard Model . 6 c. Weak Isospin and W Bosons . 7 d. Electroweak Theory . 7 e. Spontaneously Broken Symmetry|Phase Transition . 8 + 27 3.0 f. Higgs Bosons . 8 0.0 + g. Relations Between Electroweak Theory Parameters . 9 f h h. Experimental Detection of the W Boson . 9 - i. The Uni¯cation of QCD and Electroweak Theory . 10 90 .0 -3.0 Acknowledgments . 13 Project PHYSNET·Physics Bldg.·Michigan State University·East Lansing, MI 1 2 ID Sheet: MISN-0-305 THIS IS A DEVELOPMENTAL-STAGE PUBLICATION Title: The Standard Model of Fundamental Particles and Their OF PROJECT PHYSNET Interactions The goal of our project is to assist a network of educators and scientists in Author: Mesgun Sebhatu, Department of Physics, Winthrop College, transferring physics from one person to another. We support manuscript Rock Hill, SC 29733 processing and distribution, along with communication and information Version: 11/14/2001 Evaluation: Stage 0 systems. We also work with employers to identify basic scienti¯c skills as well as physics topics that are needed in science and technology. A Length: 2 hr; 20 pages number of our publications are aimed at assisting users in acquiring such Input Skills: skills. 1. Using the quark model with four flavors and three colors, construct Our publications are designed: (i) to be updated quickly in response to hadron multiplets. (MISN-0-283). ¯eld tests and new scienti¯c developments; (ii) to be used in both class- room and professional settings; (iii) to show the prerequisite dependen- Output Skills (Knowledge): cies existing among the various chunks of physics knowledge and skill, K1. State the major objective of physics and mention key events as as a guide both to mental organization and to use of the materials; and well as physicists in history that contributed towards this goal. (iv) to be adapted quickly to speci¯c user needs ranging from single-skill K2. Describe the four fundamental forces and compare their strength, instruction to complete custom textbooks. range, and the masses of their gauge bosons. New authors, reviewers and ¯eld testers are welcome. K3. Describe QED, QCD, and GSW theories and explain how they are uni¯ed by the standard model. PROJECT STAFF K4. List fundamental fermions and gauge bosons of the standard model and give their generation number, mass, charge, and spin. Andrew Schnepp Webmaster K5. Describe how the W and Z gauge bosons are rendered massive. Eugene Kales Graphics K6. Describe an experiment that supports the GSW theory. Peter Signell Project Director K7. List two major phenomena that the SSC may help uncover. Output Skills (Rule Application): ADVISORY COMMITTEE R1. Given any two of exchanged gauge boson mass, life time, and range D. Alan Bromley Yale University for an interaction, estimate the third. E. Leonard Jossem The Ohio State University R2. Given any two of W boson mass, Z boson mass, and Weinberg A. A. Strassenburg S. U. N. Y., Stony Brook angle, calculate the third. R3. For any N, calculate the number of expected gauge bosons in an Views expressed in a module are those of the module author(s) and are SU(N). not necessarily those of other project participants. R4. Given any two of the neutral (g0) and charged (g) electroweak c 2001, Peter Signell for Project PHYSNET, Physics-Astronomy Bldg., coupling constants as well as the Weinberg mixing angle (θW), ° calculate the third. Mich. State Univ., E. Lansing, MI 48824; (517) 355-3784. For our liberal use policies see: http://www.physnet.org/home/modules/license.html. 3 4 MISN-0-305 1 MISN-0-305 2 THE STANDARD MODEL OF FUNDAMENTAL PARTICLES AND THEIR INTERACTIONS graviton by ÖG ÖG Mesgun Sebhatu 1. Overview m1 m2 In the last three decades, signi¯cant progress has been made in the Figure 1. Second order Feynman diagram for gravitational identi¯cation of fundamental particles and the uni¯cation of their inter- interaction of two massive objects via graviton exchange. actions. This remarkable result is summarized by what is now con¯dently called the Standard Model. This module presents a descriptive account of 2a. Gravity. The ¯rst fundamental force (interaction) to be de¯ned the Standard Model and its possible extensions. According to the Stan- accurately was gravity. This was accomplished by Isaac Newton in the dard Model, all matter in the universe is made up of a dozen fermions|six seventeenth century when he stated his law of universal gravitation (F = quarks and six leptons. The quarks and leptons interact by exchanging 2 Gm1m2=r ) in his Principa. Using his law, Newton was able to show a dozen gauge bosons|eight gluons and four electroweak bosons. The that the force of gravity was responsible for motions of planets around model provides a framework for the uni¯cation of the electroweak and the sun as well as for projectile motion on the earth's surface. This was strong \nuclear" forces. A major de¯ciency of the model is its lack of a revolutionary achievement since celestial and terrestrial motions were incorporation of gravity. believed to be caused by di®erent forces. His gravitational law was re¯ned by Albert Einstein in 1916, almost three centuries later. According to 2. Historical Introduction Einstein's general theory of relativity, gravity results from the curvature of space{time due to the presence of mass (or energy). There is now a Our job in physics is to see things simply, to understand a concerted e®ort to develop the quantum theory of gravity. In the quantum great many complicated phenomena in a uni¯ed way, in terms theory formalism, the gravitational interaction is a consequence of the 1 of a few simple principles.|Steven Weinberg exchange of gravitons, which are massless particles with spin 2. Figure 1 represents a Feynman diagram that shows gravitational interaction as a The development of the Standard Model of particle physics may be consequence of graviton exchange. This is analogous to the case of weak 2 the best example for the major goal of physics|simpli¯cation and uni- interaction mediated by a W or Z boson. The measure of strength in ¯cation of seemingly diverse and complicated natural phenomena. The the gravitation case is Newton's gravitational constant (G) and in the Standard Model can account for all atomic, nuclear, and subnuclear phe- case of the weak interaction Fermi's coupling constant (GF ). At each nomena in terms of a dozen fermions and a dozen bosons. To appreciate vertex of the diagrams the strengths are characterized by pG and pGF the Standard Model, we need to start with a brief historical background for gravitational and weak interaction respectively. of the four (three after 1967) fundamental forces|Gravity, Electromag- 2b. Electromagnetism. Prior to the eighteenth century, magnetic netism, the Weak Nuclear force and the Strong Nuclear force. and electrical forces were regarded as unrelated entities. After Oersted, 1S. Weinberg, Rev. of Mod. Phys,\Conceptual Foundations of the Uni¯ed Theory in 1819, discovered by accident that a current carrying wire deflected a of Weak and Electromagnetic Interactions" 52, 515 (1980); Science 210, 1212 (1980). magnetic compass needle, a series of experiments in the 1820's by Faraday I have quoted the ¯rst sentence of his Nobel lecture. and Henry showed that a change in a magnetic ¯eld creates an electric 2See\The Weak Interaction" (MISN-0-281). 5 6 MISN-0-305 3 MISN-0-305 4 ¯eld. In addition, Amp`ere was able to conclude that electric current is, up to about 100 GeV. loops of atomic size were the basis for all magnetism. The intimate rela- 2d. The Strong \Nuclear" Force. The strong force is responsi- tionship between electric and magnetic forces culminated in the develop- ble for binding nuclei. A direct means of studying the force is to study ment of the electromagnetic theory by Clerk Maxwell in 1879. Maxwell's the interaction between two nucleons. The neutron was discovered in electromagnetic theory provided a complete uni¯cation of electricity and 1932. This meant that the nucleus is made up of protons and neutrons, magnetism|electromagnetism. This is the ¯rst example of a uni¯cation together nucleons. Using the then-known forces, primarily the electro- of forces. magnetic force, it was impossible to account for the stability of nuclei. At any point in space a change in electric ¯eld (force per unit charge) The electromagnetic force would, in fact, push protons violently apart. is accompanied by a compensating change in the magnetic ¯eld at that This paved the way for Yukawa (1935) to suggest a short-range strong point. This is characteristic of vector ¯elds called gauge ¯elds where local nuclear force. symmetry is preserved via compensating changes in various ¯eld com- A short-range force requires the exchange of a massive particle. ponents. A relativistic quantum version of electromagnetic theory was Yukawa, therefore, predicted the mediator of the strong nuclear force, developed in the 1940's mainly by Feynman, Schwinger, and Tomonaga. the pion, with a mass of approximately 140 MeV. It follows from the un- It is called quantum electrodynamics or QED for short.3 It is a theory un- certainty principle (¢t¢E ¹h) that the range of the strong nuclear force precedented in its precise determination of observable quantities.
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