{"@context":{"@language":"en","Affiliation":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","AggregatedSourceRepository":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","Campus":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","Creator":"http:\/\/purl.org\/dc\/terms\/creator","DateAvailable":"http:\/\/purl.org\/dc\/terms\/issued","DateIssued":"http:\/\/purl.org\/dc\/terms\/issued","Degree":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","DegreeGrantor":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","Description":"http:\/\/purl.org\/dc\/terms\/description","DigitalResourceOriginalRecord":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","Extent":"http:\/\/purl.org\/dc\/terms\/extent","FileFormat":"http:\/\/purl.org\/dc\/elements\/1.1\/format","FullText":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","Genre":"http:\/\/www.europeana.eu\/schemas\/edm\/hasType","GraduationDate":"http:\/\/vivoweb.org\/ontology\/core#dateIssued","IsShownAt":"http:\/\/www.europeana.eu\/schemas\/edm\/isShownAt","Language":"http:\/\/purl.org\/dc\/terms\/language","Program":"https:\/\/open.library.ubc.ca\/terms#degreeDiscipline","Provider":"http:\/\/www.europeana.eu\/schemas\/edm\/provider","Publisher":"http:\/\/purl.org\/dc\/terms\/publisher","Rights":"http:\/\/purl.org\/dc\/terms\/rights","ScholarlyLevel":"https:\/\/open.library.ubc.ca\/terms#scholarLevel","Title":"http:\/\/purl.org\/dc\/terms\/title","Type":"http:\/\/purl.org\/dc\/terms\/type","URI":"https:\/\/open.library.ubc.ca\/terms#identifierURI","SortDate":"http:\/\/purl.org\/dc\/terms\/date"},"Affiliation":[{"@value":"Science, Faculty of","@language":"en"},{"@value":"Physics and Astronomy, Department of","@language":"en"}],"AggregatedSourceRepository":[{"@value":"DSpace","@language":"en"}],"Campus":[{"@value":"UBCV","@language":"en"}],"Creator":[{"@value":"Fugleberg, Todd Darwin","@language":"en"}],"DateAvailable":[{"@value":"2009-07-23T17:37:16Z","@language":"en"}],"DateIssued":[{"@value":"2000","@language":"en"}],"Degree":[{"@value":"Doctor of Philosophy - PhD","@language":"en"}],"DegreeGrantor":[{"@value":"University of British Columbia","@language":"en"}],"Description":[{"@value":"The vacuum structure of QCD is studied using an anomalous effective Lagrangian approach.\r\nThis approach makes it possible to determine how physical observables depend\r\non the strong CP violation parameter, \u03b8. The \u03b8 -dependence of QCD and the phenomenology\r\nof the light pseudoscalar mesons in this theory are illustrated. The vacuum structure\r\nof QCD is shown to be quite complex with the prediction of a number of different types\r\nof nontrivial vacuum states. Two specific examples of nontrivial vacuum states are analysed\r\nin more detail. The decay rate of a metastable vacuum state for the \u03b8 = 0 case\r\nis nonperturbatively calculated in both the zero and high temperature limits. The formation\r\nof a nontrivial vacuum state in heavy ion collisions is predicted in a simplified\r\nnumerical model. These results have implications for the study of the evolution of the\r\nearly universe near the QCD phase transition and may be tested experimentally very\r\nsoon in heavy ion collision experiments.","@language":"en"}],"DigitalResourceOriginalRecord":[{"@value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/11141?expand=metadata","@language":"en"}],"Extent":[{"@value":"4490681 bytes","@language":"en"}],"FileFormat":[{"@value":"application\/pdf","@language":"en"}],"FullText":[{"@value":"V A C U U M S T R U C T U R E O F Q C D I N A N E F F E C T I V E L A G R A N G I A N A P P R O A C H By Todd Darwin Fugleberg B. Sc., The University of Saskatchewan, 1993 M. Sc., The University of British Columbia, 1996 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S D E P A R T M E N T O F P H Y S I C S We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A August 2000 \u00a9 Todd Darwin Fugleberg, 2000 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Br i t i sh Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics The University of Br i t i sh Columbia 6224 Agricul tural Road Vancouver, B . C . , Canada V 6 T 1Z1 Date: Abstract The vacuum structure of QCD is studied using an anomalous effective Lagrangian ap-proach. This approach makes it possible to determine how physical observables depend on the strong CP violation parameter, 6. The ^ -dependence of QCD and the phenomenol-ogy of the light pseudoscalar mesons in this theory are illustrated. The vacuum structure of QCD is shown to be quite complex with the prediction of a number of different types of nontrivial vacuum states. Two specific examples of nontrivial vacuum states are anal-ysed in more detail. The decay rate of a metastable vacuum state for the 6 = 0 case is nonperturbatively calculated in both the zero and high temperature limits. The for-mation of a nontrivial vacuum state in heavy ion collisions is predicted in a simplified numerical model. These results have implications for the study of the evolution of the early universe near the QCD phase transition and may be tested experimentally very soon in heavy ion collision experiments. ii Table of Contents Abs t rac t i i Table of Contents i i i L is t of Figures v Acknowledgement v i 1 In t roduct ion 1 1.1 Review of Quantum Chromodynamics and the ^-parameter 2 1.2 Motivation 9 1.3 Overview 12 2 The Anomalous Effective Lagrangian and Implications 15 2.1 The Anomalous Effective Lagrangian 15 2.2 Theta Dependence 20 2.3 Vacuum Structure 21 2.3.1 q=l 23 2.3.2 q ^ l 25 2.4 Phenomenology of the Pseudoscalar Mesons for Non-Zero 9 25 3 False V a c u u m Decay 35 3.1 The Domain Wall Solution 38 3.2 Semiclassical Theory 40 iii 3.3 Quantum Corrections at Zero Temperature 42 3.3.1 Positive Eigenvalues 43 3.3.2 Zero and Negative Eigenvalues 53 3.3.3 Decay Rate for Zero Temperature 54 3.4 Quantum Corrections for High Temperature 55 3.4.1 Positive Eigenvalues 55 3.4.2 Zero and Negative Eigenvalues 58 3.4.3 Decay Rate for High Temperature 59 3.5 Summary 59 4 P roduc t ion of N o n t r i v i a l The ta Vacua 61 4.1 DCC 62 4.2 Nontrivial #-vacua 64 4.3 Numerical Evolution 67 5 Conclusions 74 5.1 Results 74 5.2 Future Research 76 Bibl iography 79 Appendices 84 A Der iva t ion of the Effective Poten t ia l for Q C D 84 A . l Anomalous Effective Lagrangian for QCD 84 A.2 Determining the values of p and q 91 B Hyperspher ica l Harmonics i n Four Dimensions 94 iv Lis t of Figures 2.1 Branches of the effective potential before the infinite volume limit is taken. 19 2.2 Piecewise smooth effective potential after the infinite volume limit is taken. 20 2.3 Two flavour effective potential 24 2.4 Vacuum energy as a function of vacuum angle 9 24 2.5 Effective potential for q=2 and Nf = 2 26 2.6 7T\u00b0 mass as a function of 9 31 2.7 TJ mass as a function of 9 31 2.8 Tj' mass as a function of 9 31 2.9 The Euler 9 angle as a function of 9 33 2.10 The Euler
u = 0 M\/(<\/>) if 0 < 0 \/ 27T \\ cos JnJNf QNf \u2014 cos (3.57) The effective potential (3.57) has a global minimum at 4>+ = (TTfn)\/'(2q^Nf) and a local minimum at = ~(Trfv)\/(2q,jN~f), with a cusp singularity between them (see Figure 3.12). The minima are interpreted as two vacua separated by a high potential barrier (~ G2) which is fairly wide, while the energy splitting, AE, between the states is fairly small in comparison: 2TT ' AE = mqNf (tyty) cos qNf\/ + 0 K ) (3.58) Therefore we can use the thin wall approximation [39] in our calculations. The domain wall solution in this approximation corresponding to the effective potential (3.57) is: Pfir d.w.(R - r) for r \u00ab R , (3.65)