“Gauge Theories of the Strong, Weak, and Electromagnetic Interactions is an indispensable reference for both advanced graduate students and experts in collider physics phenomenology. Quigg’s broad experience is seen in the clear and thorough exposition of the principles underlying the interactions of gauge fields and elementary particles. The book’s numerous examples will aid students in understanding technical details.”–Sally Dawson, Brookhaven National Laboratory

“This textbook represents the author’s state-of-the-art knowledge of particle physics and the history of its modern formulation. Providing a clear picture of physical laws and new perspectives, the book is elegantly written and wonderfully engaging.”–Christopher Tully, Princeton University

“This nearly perfect textbook will be valuable for advanced graduate students and researchers working in theoretical and experimental particle physics, and related fields such as cosmology and nuclear theory. With elegance and clarity, it sets a good example for other texts to follow. I salute the author for such a great piece of work.”–Tao Han, University of Pittsburgh

Gauge Theories of the Strong, Weak, and Electromagnetic Interactions

By Chris Quigg

PRINCETON UNIVERSITY PRESS

Copyright © 2013 Princeton University Press
All rights reserved.
ISBN: 978-0-691-13548-9

Contents

Preface…………………………………………………………..xiOne Introduction…………………………………………………..1Two Lagrangian Formalism and Conservation Laws………………………..25Three The Idea of Gauge Invariance…………………………………..38Four Non-Abelian Gauge Theories……………………………………..57Five Hidden Symmetries……………………………………………..71Six Electroweak Interactions of Leptons………………………………95Seven Electroweak Interactions of Quarks……………………………..187Eight Strong Interactions among Quarks……………………………….269Nine Unified Theories………………………………………………387Epilogue………………………………………………………….430Appendix A Notations and Conventions…………………………………433Appendix B Observables and Feynman Rules……………………………..447Appendix C Physical Constants……………………………………….457For Further Reading………………………………………………..457Author Index………………………………………………………459Subject Index……………………………………………………..475
<h2>CHAPTER 1</h2><p><b>Introduction</b></p><br><p>Over the past three decades, an animated conversation between experimentand theory has brought us to a new and radically simple conception of matter.Fundamental particles called quarks and leptons make up the everyday world,and new laws of nature—in the form of theories of the strong, weak, andelectromagnetic forces—govern their interactions. Quantum chromodynamics, thetheory of the strong interaction among quarks, and the electroweak theory haveboth been abstracted from experiment, refined within the framework of local gaugesymmetries, and validated to an extraordinary degree through confrontation withexperiment. What we have learned suggests paths to a more complete picture ofnature—perhaps a unified theory of the fundamental particles and interactions.</p><p>But the triumph of this new picture is incomplete. We are still searching for amissing piece, the agent of electroweak symmetry breaking. We also need to discoverwhat accounts for the masses of the electron and the other leptons and quarks,without which there would be no atoms, no chemistry, no liquids or solids—nostable structures. In the standard electroweak theory, both tasks are the work of theHiggs mechanism. Moreover, we have reason to believe that the electroweak theoryis imperfect and that new symmetries or new dynamical principles are required tomake it fully robust.</p><p>To extend our understanding, particle physicists from around the world havelaunched remarkable experiments using the Large Hadron Collider in Geneva,Switzerland, a superconducting synchrotron 27km in circumference, in whichcounterrotating proton beams collide at c.m. energies planned to reach 14 TeV. Wedo not know what the new wave of exploration will find, but the discoveries wemake and the new puzzles we encounter are certain to change the face of particlephysics and echo through neighboring sciences. Decisive results on the agent ofelectroweak symmetry breaking appear imminent.</p><p>This book is devoted to an exposition of the logic, structure, and phenomenologyof our “standard model” of particle physics, from the experimental systematicsand theoretical constructs that underlie it to the highly successful form that joinsquantum chromodynamics to the electroweak theory. We shall see how the idea ofgauge theories—interactions derived from symmetries observed in nature—makesit possible to capture the regularities embodied in earlier theoretical descriptionsin an economical and richly predictive framework that gives new understandingand suggests new consequences. The standard model displays in full measure theattributes of an exemplary theory expressed in Heinrich Hertz’s celebration ofclassical electrodynamics:</p><p>One cannot study Maxwell’s marvelous electromagnetic theory of light without sometimeshaving the feeling that these mathematical formulae have an independent existence and anintelligence of their own, that they are wiser than we are, wiser even than their inventor,that they give back to us more than was originally put into them.</p><br><p>The utility of the quark model as a classification tool that provides a systematicbasis for hadron spectroscopy has long been appreciated. The quark languagealso provides an apt description of the dynamics of hadronic interactions. Thequark-parton model, refined by quantum chromodynamics, underlies a quantitativephenomenology of deeply inelastic lepton–hadron scattering, electron–positronannihilation into hadrons, hard scattering of hadrons, and decays of hadrons,especially those containing heavy quarks.</p><p>An elementary particle, in the time-honored sense of the term, is structurelessand indivisible. Although history cautions that the physicist’s list of elementaryparticles is dependent upon experimental resolution—and thus subject to revisionwith the passage of time—it has also rewarded the hope that interactions among theelementary particles of the moment would be simpler and more fundamental thanthose among composite systems. Neither quarks nor leptons exhibit any structureon a scale of about 10-16 cm, the currently attained resolution. We thus haveno experimental reason but tradition to suspect that they are not the ultimateelementary particles. Accordingly, we idealize the quarks and leptons as pointlikeparticles, remembering that elementarity is subject to experimental test.</p><p>Analyses of collision phenomena suggest that quarks behave as free particleswithin hadrons, and yet the nonobservation of isolated free quarks encourages theidealization that quarks must be permanently confined within the hadrons. Thisapparently paradoxical state of affairs requires that the strong interaction amongquarks be off a rather particular sort. No rigorous theoretical demonstration oftthe confinement hypothesis has yet been given, but it is widely held tttthat quantumchromodynamics (QCD) contains the necessary elements. In common with othernon-Abelian gauge theories, QCD exhibits an effective interaction strength thatdecreases at short distances and grows at large distances. This property—asymptotic(ultraviolet) freedom vs. infrared slavery—suggests a resolution of the parton-modelconundrum. Monte Carlo simulations of the gauge-theory vacuum provide strongnumerical evidence for quark confinement.</p><p>The appeal of a unified theory of the weak and electromagnetic interactionsis at once aesthetic and practical. The effective weak-interaction Lagrangian thatevolved from Fermi’s description of nuclear ß-decay and provided a serviceablelow-energy phenomenology is now seen to be the limiting form of a renormalizablefield theory. At the same time, neutral-current interactions predicted by the newelectroweak theory have been found to occur at approximately the strength ofthe long-studied charged-current interactions. The observed neutral currents areneutral not only with respect to electric charge, but with respect to all other additivequantum numbers as well. To accommodate this property in the theory requiresthe introduction of a new quark species, bearing a new additive quantum numberknown as charm. This, too, has subsequently been observed in experiments. Theprice for this neat picture includes the prediction of several hypothetical particles:the intermediate vector bosons, W⁺, W^-, and Z⁰, that carry the weak interactions.Definite predictions for the masses and properties of the intermediate bosons havebeen confirmed by experiment.</p><p>Electromagnetism is a force of infinite range, whereas the influence of thecharged-current weak interaction responsible for radioactive beta decay spans onlydistances shorter than about 10^-15 cm, less than 1% of the proton radius. If thesetwo interactions, so different in their range and apparent strength, originate in acommon gauge symmetry, that symmetry must be spontaneously broken. That isto say, the vacuum state of the universe must not respect the full symmetry. Howthe electroweak gauge symmetry is spontaneously broken is one of the most urgentand challenging questions before particle physics. The standard-model answer is anelementary scalar field whose self-interactions select a vacuum state in which thefull electroweak symmetry is hidden. Experiments in 2012 have discovered a newparticle that—at first look—fits the profile of the Higgs boson, as the elementaryscalar is known. We do not yet know whether this observation means that afundamental Higgs field exists or a different agent breaks electroweak symmetry.General arguments imply that the Higgs boson or other new physics is requiredon the TeV energy scale. Indirect constraints from global analyses of electroweakmeasurements suggest that the mass of the standard-model Higgs boson is lessthan 200 GeV. Once its mass is assumed, the properties of the Higgs boson followfrom the electroweak theory. Finding the Higgs boson or its replacement is one ofthe great campaigns now under way in both experimental and theoretical particlephysics. The answer—expected soon—will steer the future development of theelectroweak theory.</p><p>One measure of the electroweak theory’s sweep is that its predictions hold overa prodigious range of distances, from about 10^-18 m to more than 10⁸ m. Theorigins of the theory lie in the discovery of Coulomb’s law in tabletop experimentsby Cavendish and Coulomb. It was stretched to longer and shorter distances bythe progress of experiment. In the long-distance limit, the classical electrodynamicsof a massless photon suffices. At shorter distances than the human scale, classicalelectrodynamics was superseded by quantum electrodynamics (QED), which is nowsubsumed in the electroweak theory, tested at energies up to a few hundred GeV.</p><p>Because the charged-current weak interactions are purely left-handed, it isnot possible to construct a self-consistent theory of the weak and electromagneticinteractions based solely on leptons or solely on quarks. They must come in matchedsets. This fact suggests a deep connection between the quarks (which experiencethe strong interactions) and the leptons (which do not). That observation, inturn, motivates a description that gathers both quarks and leptons into extendedfamilies—a unified theory of the strong, weak, and electromagnetic interactions.Such a theory can give an understanding of the low-energy strengths of the individualinteractions. Another consequence of the unification of forces is the implication ofnew forces that can transform quarks into leptons.</p><p>For all its triumphs, the standard model is not entirely satisfying. The electroweaktheory does not make specific predictions for the masses of the quarks andleptons or for the mixing among different flavors. It leaves unexplained how anelementary Higgs-boson mass could remain below 1 TeV in the face of quantumcorrections that tend to lift it toward the Planck scale or a unification scale. TheHiggs field thought to pervade all of space to hide the electroweak symmetrycontributes a vacuum energy density far in excess of what is observed. And thestandard model, even when extended to a unified theory of the strong, weak, andelectromagnetic interactions, responds inadequately to challenges raised by astronomicalobservations, including the dark-matter problem and the predominance ofmatter over antimatter in the universe. These shortcomings argue for physics beyondthe standard model.</p><p>The remainder of this chapter is a concise review of some of the primitiveconcepts of particle phenomenology that serve as a basis for our development ofthe standard model. In succeeding chapters, we shall assemble a detailed descriptionof the electroweak theory and quantum chromodynamics, the two pillars of thestandard model, with close attention to the experimental foundations. Our goal isnot only to exhibit the successes of the two theories and to establish their utilityfor reliable calculations, but also to highlight unfinished business and point to theneed for future developments. We shall also see how QCD and the electroweaktheory might be joined into a unified theory of the strong, weak, and electromagneticinteractions. The text closes by posing essential questions for theory and experiment.</p><br><p><b>1.1 ELEMENTS OF THE STANDARD MODEL OF PARTICLE PHYSICS</b></p><p>Our picture of matter is based on the identification of a set of pointlike spin-1/2constituents: the (up, down, charm, strange, top, and bottom) quarks,</p><p>[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1.1.1)</p><br><p>and the leptons (electron, muon, and tau, plus three neutrinos),</p><p>[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1.1.2)</p><br><p>where the subscript L denotes the left-handed components, plus a few fundamentalforces derived from gauge symmetries. The quarks are influenced by the stronginteraction and so carry <i>color</i>, the strong-interaction charge, whereas the leptonsdo not feel the strong interaction and are colorless. Each of the six quark flavorscomes in three distinct colors: red, green, and blue. The right-handed fermionsare weak-interaction singlets. By pointlike, we understand that the quarks andleptons show no evidence of internal structure at the current limit of our resolution,(<i>r</i> [?? 10^-18 m).</p><p>The notion that the quarks and leptons are elementary—structureless andindivisible—is necessarily provisional. <i>Elementarity</i> is one of the aspects of ourpicture of matter that we test ever more stringently as we improve the resolutionwith which we can examine the quarks and leptons. For the moment, the world’smost powerful microscope is the Large Hadron Collider at CERN, where the ATLASand CMS Collaborations have studied <i>pp</i> collisions at c.m. energy √<i>s</i> = 8 TeV. Forthe production of hadron jets at transverse energy E?, we may roughly estimate theresolution as <i>r</i> ≈ ([??]<i>c</i>)/<i>E]<i>perpendicular to] ≈ 2 × 10^-19 TeV m/<i>E]<i>perpendicular to].</p><p>The left-handed and right-handed fermions behave very differently under theinfluence of the charged-current weak interactions. In 1956, Wu and collaboratorsstudied the ß-decay ⁶⁰Co -> ⁶⁰Ni <i>e</i>^- [bar.ν]_<i>e</i> and observed a correlation betweenthe direction [??]_<i>e</i> of the outgoing electron and the spin vector [??] of the polarized⁶⁰Co nucleus. Spatial reflection, or parity, leaves the (axial vector) spin unchanged,P : [??] -> [??], but reverses the electron direction, P : [??}_<i>e</i> -> -[??]_<i>e</i>. Accordingly, thecorrelation [??] · [??]_<i>e</i> is manifestly <i>parity violating</i>. Experiments in the late 1950s (cf.§6.3) established that (charged-current) weak interactions are left-handed, andmotivated the construction of a manifestly parity-violating theory of the weakinteractions with only a left-handed neutrino ν_L.</p><p>Perhaps our familiarity with parity violation in the weak interactions has dulledour senses a bit. It seems to me that nature’s broken mirror—the distinction betweenleft-handed and right-handed fermions—qualifies as one of the great mysteries. Evenif we will not get to the bottom of this mystery next week or next year, it should beprominent in our consciousness—and among the goals we present to others as theaspirations of our science.</p><p>The family relationships among the quarks and the leptons are depictedin figure 1.1. To excellent approximation, the observed charged-current weakinteractions connect up quarks with down, charm with strange, and top withbottom. At the current limits of experimental sensitivity, the charged-currentinteractions conserve electron number, muon number, and tau number. Althoughthe right-handed quarks and charged leptons do not participate in charged-currentweak interactions, their existence is implied by charged-fermion masses and thecharacteristics of the strong and electromagnetic interactions. We take the weak-isospindoublets as evidence for SU(2)_L gauge symmetry and infer SU(3)_c gaugesymmetry from the three quark colors, interpreted as a continuous symmetry.As we shall see, the successful electroweak theory incorporates a U(1)_Y weak-hyperchargephase symmetry, along with SU(2)_L. We have already commented thatthe electroweak gauge symmetry must be hidden, SU(2)_L [cross [product] U(1)_Y -> U(1)_EM, withthe phase symmetry of electromagnetism the residual symmetry.</p><p>The discovery of neutrino oscillations (cf. §6.7), which implies that neutrinoshave mass, motivates the inclusion of the right-handed neutrinos, <i>N_i</i>, in figure 1.1.The right-handed neutrinos would be sterile—inert with respect to the knownSU(3)_c [cross [product] SU(2)_L [cross product] U(1)_Y interactions.</p><p>The representation of the quarks and leptons in figure 1.1 invites not onlyspeculations about the symmetries that lead to the strong, weak, and electromagneticinteractions, but also questions about possible relations between quarks and leptonsor between the left-handed and right-handed particles.</p><p>Let us now look in slightly greater detail at each of the ingredients of thestandard model of particle physics.
(Continues…)Excerpted from Gauge Theories of the Strong, Weak, and Electromagnetic Interactions by Chris Quigg. Copyright © 2013 Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.