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COMPOSITE K>DELS of QUARKS and LEPTONS 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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