Surveys in Theoretical High Energy Physics - 2: Lecture Notes from SERC Schools PDF
Preview Surveys in Theoretical High Energy Physics - 2: Lecture Notes from SERC Schools
Texts and Readings in Physical Sciences 15 Raghavan Rangarajan M. Sivakumar Editors Surveys in Theoretical High Energy Physics - 2 Lecture Notes from SERC Schools Texts and Readings in Physical Sciences Volume 15 Managing Editors H.S. Mani, Chennai Mathematical Institute, Chennai Ram Ramaswamy, Vice Chancellor, University of Hyderabad, Hyderabad Editors Kedar Damle, TIFR, Mumbai Debashis Ghoshal, JNU, New Delhi Rajaram Nityananda, NCRA, Pune Gautam Menon, IMSc, Chennai Tarun Souradeep, IUCAA, Pune The Texts and Readings in Physical Sciences series publishes high-quality textbooks, research-level monographs, lecture notes and contributed volumes. Undergraduateandgraduatestudentsofphysicalsciencesandappliedmathematics, researchscholars,andteacherswouldfindthisbookseriesuseful.Thevolumesare carefullywrittenasteachingaidsandhighlightcharacteristicfeaturesofthetheory. Thebooksinthisseriesareco-publishedwithHindustanBookAgency,NewDelhi, India. More information about this series at http://www.springer.com/series/15139 Raghavan Rangarajan M. Sivakumar (cid:129) Editors Surveys in Theoretical High Energy Physics - 2 Lecture Notes from SERC Schools 123 Editors Raghavan Rangarajan M.Sivakumar Theoretical Physics Division Schoolof Physics Physical Research Laboratory University of Hyderabad Ahmedabad, Gujarat Hyderabad, Andhra Pradesh India India Thisworkisaco-publicationwithHindustanBookAgency,NewDelhi,licensedforsalein all countries in electronic form,in print form only outside of India.Soldanddistributed in printinIndiabyHindustanBookAgency,P-19GreenParkExtension,NewDelhi110016, India.ISBN: 978-93-80250-67-0 ©Hindustan BookAgency 2014. ISSN 2366-8849 ISSN 2366-8857 (electronic) TextsandReadings inPhysical Sciences ISBN978-981-10-2590-7 ISBN978-981-10-2591-4 (eBook) DOI 10.1007/978-981-10-2591-4 LibraryofCongressControlNumber:2016951671 ©SpringerScience+BusinessMediaSingapore2016andHindustanBookAgency2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublishers,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. Thepublishers,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthis book are believed to be true and accurate at the date of publication. Neither the publishers nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerNatureSingaporePteLtd. Theregisteredcompanyaddressis:152BeachRoad,#22-06/08GatewayEast,Singapore189721,Singapore In memory of Abhee K. Dutt-Mazumder scientist and dear colleague Contents Preface ix Acknowledgements xi List of Contributors xiii About theEditors xv 1 Quark-Gluon Plasma: An Overview 1 Ajit Mohan Srivastava 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Running Coupling Constant in QCD . . . . . . . . . . . . 18 1.4 Field Theory at Finite Temperature . . . . . . . . . . . . . 33 1.5 Quark Confinement. . . . . . . . . . . . . . . . . . . . . . . 38 1.6 Relativistic Heavy-Ion Collisions . . . . . . . . . . . . . . . 45 1.7 Bjorken’s Picture of Relativistic Heavy-Ion Collisions . . . 47 1.8 QGP Signals . . . . . . . . . . . . . . . . . . . . . . . . . . 52 1.9 Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . 54 2 An Introduction to Thermal Field Theory 63 Abhee K. Dutt-Mazumder 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.2 Green’s Function . . . . . . . . . . . . . . . . . . . . . . . . 64 2.3 Thermodynamic Potential and Pressure . . . . . . . . . . . 68 2.4 φ4 Theory at Finite Temperature . . . . . . . . . . . . . . . 72 2.5 Pressure in φ4 Theory . . . . . . . . . . . . . . . . . . . . . 74 2.6 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3 Perturbative Quantum Chromodynamics 83 V. Ravindran 3.1 Structure of Hadrons . . . . . . . . . . . . . . . . . . . . . . 83 3.2 Operator Product Expansion and Parton Model. . . . . . . 88 3.3 Gauge Symmetry . . . . . . . . . . . . . . . . . . . . . . . . 94 3.4 Gauge Fixing . . . . . . . . . . . . . . . . . . . . . . . . . . 102 viii Contents 3.5 Regularisation and Renormalisation of YM Theory with n f Fermions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 3.6 Asymptotic Freedom . . . . . . . . . . . . . . . . . . . . . . 115 3.7 Wilson Coefficients . . . . . . . . . . . . . . . . . . . . . . . 119 3.8 Infrared Safe Observables . . . . . . . . . . . . . . . . . . . 124 3.9 QCD Predictions Beyond Leading Order . . . . . . . . . . . 131 4 Introduction to Anomalies 141 Dileep P. Jatkar 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4.2 Two Dimensional Gauge Theory . . . . . . . . . . . . . . . 143 4.3 The Point-Splitting Regularization Method . . . . . . . . . 150 4.4 The Pauli-Villars Regularization Method . . . . . . . . . . . 152 4.5 n-vacua and θ-vacua . . . . . . . . . . . . . . . . . . . . . . 155 4.6 Four Dimensional Gauge Theory . . . . . . . . . . . . . . . 162 4.7 Path Integral Method . . . . . . . . . . . . . . . . . . . . . 168 4.8 Path Integral Formalism for Anomalies . . . . . . . . . . . . 175 5 Cosmology for Particle Physicists 187 Urjit Yajnik 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 5.2 Friedmann-Robertson-Walker Metrics . . . . . . . . . . . . 192 5.3 The Three Laws of Cosmology . . . . . . . . . . . . . . . . 196 5.4 The Big Bang Universe . . . . . . . . . . . . . . . . . . . . 200 5.5 PhaseTransitionswithQuantumFieldsintheEarlyUniverse 206 5.6 First Order Phase Transition . . . . . . . . . . . . . . . . . 216 5.7 Inflationary Universe . . . . . . . . . . . . . . . . . . . . . . 222 5.8 Density Perturbations and Galaxy Formation . . . . . . . . 235 5.9 Relics of the Big Bang . . . . . . . . . . . . . . . . . . . . . 244 5.10 Baryogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . 252 5.11 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 6 A Collection of Problems on Cosmology 263 L. Sriramkumar Volumes published sofar 291 Index 293 Preface Results from LHC, the Large Hadron Collider at CERN, relativistic heavy–ion collision experiments as well as various cosmological observations are expected to shed much light on several aspects of particle physics in the years to come. Study of the formation of the Quark Gluon Plasma in high temperature and high density environments can, for example, lead to a better understanding of stronginteractions.Inturn,QCDeffectshavetobeunderstoodwelltocorrectly interpret collider results at the electroweak scale. Higher energy processes can be studied in the laboratory of the Universe and particle cosmology can teach us much about issues such as the number of light neutrinos and the effective Lagrangian on GUT scales. This volume includes reviews that cover various topics in strong interac- tion physics, anomalies and particle cosmology and are based on lectures that were delivered at the XXI and XXII SERC Main School in Theoretical High EnergyPhysicsheldatthePhysicalResearchLaboratory,Ahmedabadandthe University of Hyderabad from February 11 - March 3, 2006 and January 18 - February 7, 2007 respectively. We believe that these reviews will be of value to any student of particle physics who is keen on understanding issues in these important areas. The SERC Schools in Theoretical High Energy Physics have been held regularly since 1985 and provide Ph.D. students with an introduction to im- portanttopicsinHighEnergyPhysics.TheAhmedabadSchoolcoveredcourses onCosmologyforParticlePhysicists,QuarkGluonPlasma,BlackHolePhysics and Flavour Physics. Each course consisted of nine lectures, and nine tutorial sessions in which certain concepts and problems were discussed. The lectur- ers and the tutors for the courses were Urjit A. Yajnik (Indian Institute of Technology Bombay, Mumbai) and L. Sriramkumar (then at Harish-Chandra ResearchInstitute(HRI), Allahabad),Ajit M. Srivastava(Instituteof Physics, Bhubaneswar)and(late)AbheeK.Dutt-Mazumder(SahaInstituteofNuclear Physics (SINP), Kolkata), Soumitra Sengupta (Indian Association for the Cul- tivation of Science, Kolkata) and Sumati Surya (Raman Research Institute, Bangalore), and Sreerup Raychaudhuri (then at Indian Institute of Technol- x Preface ogy Kanpur) and Anirban Kundu (Calcutta University, Kolkata). This volume contains the lectures on Cosmology for Particle Physicists and Quark Gluon Plasma. TheHyderabadSchoolhadfourcourseswiththefollowingtopicsandlec- turersandtutors:WilsonianRGandEffectiveFieldtheorybyShirazMinwalla and S. Lahiri (Tata Institute of Fundamental Research, Mumbai), Perturba- tive QCD by V. Ravindran (then at HRI, Allahabad) and P. Mathews (SINP, Kolkata), An Introduction to Anomalies by Dileep Jatkar and Sumathi Rao (HRI, Allahabad) and Electro-Weaksymmetry BreakingScenariosby Gautam Bhattacharyya and Probir Roy (SINP, Kolkata). This volume contains the lec- tures on Perturbative QCD and Anomalies. We thank all the lecturers, tutors and students for their dedication and enthusiasm which contributed greatly to the success of the Schools, and also to the preparation of this volume. While this book was being prepared, Abhee Dutt-Mazumder passed away. His lectures on thermal field theory at Ahmed- abad were greatly appreciated and we dedicate this book to his memory. Raghavan Rangarajan M. Sivakumar Physical Research Laboratory University of Hyderabad Ahmedabad Hyderabad
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