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COMPOSITE K>DELS OF QUARKS AND LEPTONS by Chaoq iang Geng Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Physics APPROVED: Robert E. Marshak, Chairman Luke W. MC( .,- .. -~.,I., August, 1987 Blacksburg, Virginia COMPOSITE fl>DELS OF QUARKS AND LEPTONS by Chaoqiang Geng Committee Chairman, R. E. Marshak Physics (ABSTRACT) We review the various constraints on composite models of quarks and leptons. Some dynamical mechanisms for chiral symmetry breaking in chiral preon models are discussed. We have constructed several "realistic candidate" chiral preon models satisfying complementarity between the Higgs and confining phases. The models predict three to four generations of ordinary quarks and leptons. ACKNOWLEDGEMENTS Foremost I would like to thank my thesis advisor Professor R. E. Marshak for his patient guidance and assistance during the research and the preparation of this thesis. His valuable insights and extensive knowledge of physics were truly inspirational to me. I would also like to thank Professor L. N. Chang for many valuable discussions and continuing encouragement. I am grateful to Professors S. P. Bowen, L. W. Mo, C. H. Tze, and R. K. P. Zia, for their advice and encouragement. I would also like to thank Professors , and and for many useful discussions and the secretaries and for their help and kindness. Finally, I would like to acknowledge the love, encouragement, and support of my wife without which this work would have been impossible. iii TABLE OF CONTENTS Title ........••...............•........................................ i Abstract •••••••••••••.•.•••••••••••••••••.•••••..••••.•••••••.•••••••• ii Acknowledgements ••••••••••••••••••••••••••••••••••••••••••••••••••••• iii· Chapter 1. Introduction ••••••••••••••••••••.•.••••••..••••••.••••..••• 1 Chapter 2. QCD Type Model for Hadrons 2.1 Preliminary ••.••••••••.•••••••••••.••••••••.••.•.••.•••••••.•• 9 2.2 't Hooft Anomaly Matching Condition •••••••••••••••••••••••••• 11 2.3 Mass Inequalities and the Large N Limit in Vector-like Theory •••••••••••••••••••••••••••••••••• 21 2. 4 Chiral Symmetry Breaking Induced by One-Gluon Exchange ••••••• 22 2.5 Chiral Symmetry Breaking Induced by Instantons ••••••••••••••• 26 2.6 Summa. ry • •••••••••••••.•••••••••••••••••••.••••.•••.•••••••••. 2 9 Chapter 3. Review of Composite Models of Quarks and Leptons 3.1 Preliminary ••••••••••••••.•..•.••••••••••••••••••.•••••••...• 31 3.2 Experimental Constraints on Preon Models ••••••••••••••••••••• 32 3.3 Dynamical Constraints on Freon Models •••••••••••••••••••••••• 38 3.4 Some Chiral Preon Models ••••••••••••••••••••••••••••••••••••• 41 Chapter 4. Dynamical Mechanisms for Chiral Symmetry Breaking in Chiral Freon Models 4.1 Preliminary.•••••••••••••••••••••••••••••••••••••••••••••••••50 4.2 Tumbling and Complementarity ••••••••••••••••••••••••••••••••• 51 4.3 Instanton Effects in Chiral Gauge Theory ••••••••••••••••••••• 59 Chapter 5. Realistic Candidate Preon Models with Complementarity 5.1 Preliminary ••••••.•••.•••••••••••••••••••••••••.••••••••••••• 63 5.2 High Composite Scale Preon Models •••••••••••••••••••••••••••• 63 iv 5.3 A Low Composite Scale Preon Model •••••••••••••••••••••••••••• 75 Chapter 6. Concluding Remarks ••••••••••••••••••••••••.•••••••••.••••• 81 References •••.••••.•.•••.•••••••.•••..••••••••.•.••••••••.•....••...•. 83 Vita ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• • 87 v LIST OF TABLES Table 1. Elementary Particles and Their Properties •••••••••••••••••••••••••• 2 2. Fermion and Scaler Quantum Numbers in the Standard Model ••••••••••• 3 3. Parameters Needed in the Standard Model •••••••••••••••••••••••••••• 6 4. The Quantum Numbers of Quarks in QCD •••••••••••••••••••••••••••••• 10 5. The Content of Quarks and Composites in Two-Flavor QCD Case ••••••• 16 6. The Content of Quarks and Composites inn-Flavor QCD Case ••••••••• 19 7. Particle Content of the Georgi Chiral Preon Model ••••••••••••••••• 43 8. Particle Content of the Bars-Yankielowicz Chiral Preon Model •••••• 45 9. Particle Content of the Okamoto-Marshak Chiral Preon Model •••••••• 48 10. Particle Content in Confining Phase of Case 1 ••••••••••••••••••••• 67 11. Higgs Phase of Case 2 ••••••••••••••••••••••••••••••••••••••••••••• 72 12. Confining Phase of Case 2 ••••••••••••••••••••••••••••••••••••••••• 74 13. Massless Fermions in Higgs Phase (low composite scale model) •••••• 78 14. Confining Phase (low composite scale model) ••••••••••••••••••••••• 80 vi LIST OF FIGURES Figure 1. Multiplet Structure in the Standard Model •••••••••••••••••••••••••• 7 2. Triangle Graph Connected to the Chiral Anomaly •••••••••••••••••••• 13 3. Direct Coupling of Goldstone Boson to Current of Spontaneously Broken Symmetry •••••••••••••••••••••••••• 15 4. Diagram Contributing to the Effective Potential r up 2 . to Order g •••••••••••••••••••••••••••••••••••••••••••••••••••••••25 S. Anomalous Magnetic Moments••••••••••••••••••••••••••••••••••••••••33 6. µ. + ey Decay ••••••••••••••••••••.••••••••••••.•••••••••••••••••••• 35 7. KL - Ks Mixing ••••••••••••••.•••..••••••••.••••••••••.•••••••••••• 37 8. The Phase Diagram for SU(N) Gauge Group ••••••••••••••••••••••••••• 55 vii Chapter 1 INTRODUCTION During the last thirty years, remarkable progress has been made in particle physics. A standard model of strong and electroweak interac- tions 1'2 based on a renomalizable quantum field theory and local SU(3)c x SU(2)L x U(l)y gauge invariance3 has been developed. It describes successfully all our experimental information aobut the structure of matter down to distances of lo-16 cm (corresponding to an energy of 100 GeV). Three generations of quarks and leptons exist as fundamental constituents and their interactions are mediated by gluons, w± and Z bosons, and the photon. We illustrate in Table 1 the presently known or anticipated elementary particles and some of their basic properties. The strong and electroweak interactions are mediated through the ex- change of gauge bosons G! (A = 1, ••• ,8), W~ (I = 1, ••• ,3) and Bµ which are contained in the gauge group SU(3)c x SU(2)L x U(l)y• The quantum numbers of the fermions and scalar under the gauge group SU(3)c x SU(2)L x U(l)y are shown in Table 2. Given the SU(3)c x SU(2)L x U(l)y quantum numbers of quark, lepton and Higgs field, their couplings to the gauge GA I bosons µ, Wµ and Bµ are entirely determined up to three universal gauge coupling constants g3, g2, and g1• On the contrary, the couplings between fermions and scalars are largely arbitrary. The most general gauge invariant Lagrangian of Yukawa couplings is given by (1. 1) and involves 3 unconstrained complex 3x3 matrices of Yukawa couplings. 1 2 Table 1. Elementary Particles and Their Properties particles symbol spin charge color Mass(GeV) 4 'V l/2 0 0 <2 x 10-8 Electron neutrino e Electron e l/2 -1 0 o. 511 x 10-3 Up quark u l/2 2/3 3 5 x 10-3 Down quark d lfi -1/3 3 9 x 1 0-3 5 Muon neutrino 'V lfi x 10-3 µ 0 0 <0.25 Muon µ 112 -1 0 0.106 Charm quark c l/2 2/3 3 1.25 Strange quark s l/2 -1/3 3 0.175 5 Tau neutrino 'V 't 112 0 0 <0.07 Ta.u 't l/2 -1 0 1. 78 Top quark t lfi 2/3 3 )23? Bottom quark b 1/2 -1/3 3 4.5 Photon y 1 0 0 0 W boson w± 1 ±1 0 81.8±1.5 Z boson z 1 0 0 92.6±1.7 Gluon g 1 0 8 0 Higgs scalar H 0 0 0 7,..., 10006, 7 3 Table 2. Fermion and Scalar Quantum Numbers in the Standard Model particles SU(3)c x SU(2)1 x U(l)y (3, 2, 1/3) (3, 1 , 4/3) (3, 1, -2/3) (1, 2, -1) (1, 1, -2) H (1, 2, 1) 4 In the standard model, the effective potential of the Higgs field8 H has a minimum which breaks the symmetry SU(2)1 x U(l)y to U(l)EM: <H> = ..!_ ( o) .. (1. 2) ./2 v This spontaneous symmetry breaking leads to masses for the w± and Z vector bosons: 2 2 GI l2 = g2 I BM--w (1. 3) v = 246 GeV • Furthermore, one obtains from equations (1.1) and (1. 2) mass matrices for u- and d-type quarks and for the charged leptons: v (u)i M(u): =- g . J ./2 J M(d)i =:::__g(d): (1. 4) j ./2 J M(e)i v (e)i = - g . j ./"'! J which yield the mass eignevalues ffiu, ••• mt and me ••• mi; (the masses of neutrinos are zero because of the absence of right-handed neutrinos) as well as the parameters 9 l, 9 2 , 9 3 and 6 of the Kobayashi-Maskawa ma- 5 trix9• In the strong color SU(3) C gauge interaction there is a free parameter 9QCD to describe strong violation of CP. In summary, there are 19 parameters needed to specify the model. These are given in Table 3. The multiplet structure of quarks and leptons in the standard model is illustrated in Fig. 1. 10 The structure of the matt-er sector of the standard model, as de- scribed above, gives rise to a number of important, theoretical ques- tions which cannot be answered within this framework. First, there are questions provoked by the poor understanding of the Higgs sector. In particular, one asks for a possible dynamical origin of the scale of spontaneously symmetry breaking (SSB) of the weak interactions (1. 5) and for a mechanism which could determine the Higgs mass as well as the finite and rapidly increasing massses of quarks and leptons as shown in Table 1. Second, the question of the origin of the intriguing family and generation patterns of the quarks and leptons has to be answered. In view of these questions, it is widely believed that there must be some new fundamental physics beyond the standard model. There are at least five approaches which have been proposed for describing the phys- ics beyond the standard model. These are Grand Unified Theories, 11 Technicolor Theories, 12 Supersymmetric Theories , 13 Superstring Theo- ries, 14 and Compositeness of Quarks and Leptons Theories. 15 The common feature of all of these approaches is the existence of a new fundamental underlying theory, valid at energies well above present energies, lead- 6 Table 3. Parameters Needed in the Standard Model No. of parameters Gauge coupling constants 3 1 Masses i = u,c,t,d,s,b 6 mti i = e, µ, • 3 MH ( = ( 2A ) 1/z v) 1 Mw ( = l!z g 2v) 1 Mixing angles 4 7 SU(2) x U(1) µ - : er sr - J:..sY.
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  • Discrete Family Symmetries and Tri-Bimaximal Leptonic Mixing

    Discrete Family Symmetries and Tri-Bimaximal Leptonic Mixing

    Discrete Family Symmetries and Tri-Bimaximal Leptonic Mixing Renato Miguel Sousa da Fonseca Dissertação para a obtenção de Grau de Mestre em Engenharia Física Tecnológica Júri Presidente: Gustavo Fonseca Castelo-Branco Orientador: Jorge Manuel Rodrigues Crispim Romão Co-orientador: Joaquim Inácio da Silva Marcos Vogais: David Emanuel da Costa Setembro 2008 ii Acknowledgements I am grateful to CFTP members and in particular to my supervisor, co-supervisor, and David Emmanuel Costa for the help given. The support of my colleagues and family was also of the utmost importance to me. iii iv Resumo Recentemente foi descoberto que os neutrinos oscilam pelo que têm massa. Contrariamente ao que se passa com os quarks, os ângulos de mistura dos leptões são grandes. De facto a mistura leptónica aproxima-se dum limite conhecido por tri-bimaximal mixing. O Modelo Padrão da física de partículas tem tido um enorme sucesso a descrever o comportamento da Natureza a um nível microscópico e pode facil- mente ser estendido de forma a ter em conta estes novos factos. No entanto, muitos dos seus parâmetros não se encontram constrangidos do ponto de vista teórico. Uma forma de introduzir relações em alguns dos seus parâmetros - massas e matrizes de mistura dos fermiões - consiste em postular a existência de simetrias discretas de sabor na teoria. Numa primeira parte deste trabalho, são revistas as bases da física teórica de partículas. Segue-se o estudo de uma classe de extensões do Modelo Padrão que contêm simetrias discretas de sabor, neutrinos com massa e um ou mais dubletos de Higgs. O objectivo é deduzir propriedade genéricas destes modelos e daí extrair conclusões acerca da possibilidade de se ter tri-bimaximal mixing leptónico.
  • Neutrinos, Symmetries and the Origin of Matter Engineering Physics

    Neutrinos, Symmetries and the Origin of Matter Engineering Physics

    Neutrinos, Symmetries and the Origin of Matter João Tiago Neves Penedo Thesis to obtain the Master of Science Degree in Engineering Physics Examination Committee Chairperson: Prof.a Doutora Maria Teresa Haderer de la Peña Stadler Supervisor: Prof. Doutor Filipe Rafael Joaquim Members of the Comittee: Prof. Doutor Gustavo da Fonseca Castelo Branco Prof. Doutor Ricardo Jorge Gonzalez Felipe November 2013 \Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected." { Richard P. Feynman (1918-1988) The Feynman Lectures on Physics, Vol. I i ii Acknowledgements This thesis is not a work of mine alone: behind the stage curtain, a larger cast hides. To them I thank for not only helping me construct a symmetric work, in the Vitruvian sense, but also for keeping me sane in the process (well, as sane as possible at least). I would like to start by thanking my supervisor, Professor Filipe Joaquim, for his guidance, patience, and incessant encouragement. Being one of the few great professors I had, he has been responsible for introducing me to the world of particle physics research, the do's and don'ts of the field, and for providing all the assistance needed in solving problems and answering questions, big or small, without exception.
  • Flavor Symmetries and Fermion Masses }

    Flavor Symmetries and Fermion Masses }

    LBL-35586; UCB-PTH-94/10 April 1994 Flavor symmetries and fermion masses } Andrija Rasin 2 Ph. D. Dissertation Department of Physics, University of California, k '•keley, CA 94720 and Theoretical Physics Group, Lawrence Berkeley Laboratory University of California, Berkeley, CA 9J, 720 Abstract We introduce several ways in which approximate flavo; ymmetries act on fermions and which are consistent with observed fermion masses and mixings. Flavor changing interactions mediated by new scalars appear as a consequence of approximate flavor symmetries. We discuss the experimental limits on masses of the new scalars, and show that the masses can easily be of the order of weak scale. Some implications for neutrino physics are also discussed. Such flavor changing interactions would easily erase any primordial baryon asymmetry. We show that this situation can be saved by simply adding a new charged particle with its own asymmetry. The neutral­ ity of the Universe, together with sphaleron processes, then ensures a survival of baryon asymmetry. Several topics on flavor structure of the supersymmetric grand uni­ fied theories are discussed. First, we show that the successful predic­ tions for the Kobayashi-Maskawa mixing matrix elements, V^/V^ = i , . Jm^/mc and Vtd/Vu = Jm,ilm„ are a consequence of a large class of models, rather than specific properties of a few models. Second, we discuss how the recent observation of the decay b —» 57 constrains the parameter space when the ratio of the vacuum expectation values of the two Higgs doublets, tan/?, is large. Finally, we discuss the flavor structure of proton decay. We observe a surprising enhancement of the branching ratio for the muon mode in SO(10) models compared to the same mode in the SU(5) model.