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Electroweak Baryogenesis (Second Edition) An introduction Electroweak Baryogenesis (Second Edition) An introduction Graham White University of Tokyo, Tokyo, Japan IOP Publishing, Bristol, UK ªIOPPublishingLtd2022 Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording orotherwise,withoutthepriorpermissionofthepublisher,orasexpresslypermittedbylawor undertermsagreedwiththeappropriaterightsorganization.Multiplecopyingispermittedin accordancewiththetermsoflicencesissuedbytheCopyrightLicensingAgency,theCopyright ClearanceCentreandotherreproductionrightsorganizations. PermissiontomakeuseofIOPPublishingcontentotherthanassetoutabovemaybesought [email protected]. GrahamWhitehasassertedhisrighttobeidentifiedastheauthorofthisworkinaccordancewith sections77and78oftheCopyright,DesignsandPatentsAct1988. ISBN 978-0-7503-3571-3(ebook) ISBN 978-0-7503-3569-0(print) ISBN 978-0-7503-3572-0(myPrint) ISBN 978-0-7503-3570-6(mobi) DOI 10.1088/978-0-7503-3571-3 Version:20220401 IOPebooks BritishLibraryCataloguing-in-PublicationData:Acataloguerecordforthisbookisavailable fromtheBritishLibrary. PublishedbyIOPPublishing,whollyownedbyTheInstituteofPhysics,London IOPPublishing,TempleCircus,TempleWay,Bristol,BS16HG,UK USOffice:IOPPublishing,Inc.,190NorthIndependenceMallWest,Suite601,Philadelphia, PA19106,USA Contents Preface viii Acknowledgements ix Author biography x 1 Introduction 1-1 References 1-4 2 The Sakharov conditions 2-1 References 2-2 3 Baryon number violation in the Standard Model 3-1 3.1 The axial anomaly 3-1 3.1.1 Dimensional regularization 3-2 3.1.2 The Fujikawa method 3-4 3.1.3 Baryon and lepton number violation 3-7 3.2 The Chern–Simons form, baryon number violation, 3-8 and the winding number 3.3 Winding number and non-abelian gauge groups 3-10 3.4 Solitons and instantons 3-12 3.5 The sphaleron 3-15 References 3-21 4 Phase transitions 4-1 4.1 Closed time path formalism 4-3 4.2 A brief review of the effective potential at zero temperature 4-8 4.3 The effective potential at finite temperature 4-11 4.3.1 The Standard Model example 4-14 4.3.2 Issues of gauge invariance 4-16 4.3.3 The sphaleron rate at high temperature 4-18 4.4 The bounce solution 4-21 4.5 Analytic techniques for the single-field case 4-22 4.5.1 Single-field approximation 4-22 4.5.2 Developing ansatz solutions 4-23 4.6 Path deformation method 4-26 v ElectroweakBaryogenesis(SecondEdition) 4.7 Perturbative method 4-26 4.7.1 Observations on convergence 4-29 4.7.2 A numerical example 4-30 4.7.3 Wall width and variation in β 4-31 4.8 Baryon washout condition 4-33 References 4-35 5 Gravitational waves from a strongly first-order electroweak 5-1 phase transition References 5-10 6 CP violation 6-1 References 6-5 7 Particle dynamics during a phase transition, the vacuum 7-1 expectation value insertion approach 7.1 Particle current divergences and self-energy 7-1 7.2 Transport coefficients and sources 7-4 7.2.1 A biscalar with VEV insertions 7-5 7.2.2 Dirac fermions with VEV insertions 7-11 7.2.3 Chiral fermions with VEV insertions 7-14 7.2.4 Triscalar and Yukawa interactions 7-15 7.2.5 Four-body interactions 7-23 7.3 Local equilibrium approximations 7-23 7.4 Gauge and supergauge equilibrium 7-24 7.5 Fast rate approximations 7-25 References 7-26 8 Plasma and bubble dynamics 8-1 8.1 Imaginary time formalism 8-1 8.2 Diffusion coefficients 8-2 8.3 Thermal widths 8-6 8.4 Thermal masses 8-7 8.5 Bubble wall velocity 8-8 References 8-11 vi ElectroweakBaryogenesis(SecondEdition) 9 Perturbation theory and resummation at finite temperature 9-1 9.1 A brief introduction to dimensional reduction 9-8 References 9-15 10 Transport equations 10-1 10.1 The MSSM under supergauge equilibrium 10-1 10.2 Solution using fast rates, diffusion approximation, 10-3 and ultrathin wall approximations 10.3 Solution without fast rates 10-5 10.4 Deriving the analytic solution 10-5 10.5 Beyond ultrathin walls 10-9 References 10-10 11 The semi-classical force 11-1 References 11-5 12 The semi-classical force in fluid equations 12-1 References 12-4 13 The baryon asymmetry 13-1 References 13-2 14 A brief phenomenological summary 14-1 References 14-3 15 Other mechanisms for producing the baryon asymmetry 15-1 15.1 Leptogenesis 15-2 15.2 Affleck–Dine 15-4 15.3 Using inflation 15-5 References 15-6 16 Discussion and outlook 16-1 References 16-2 vii Preface The next generation of colliders, gravitational wave detectors and searches for electric dipole moments will all converge on answering the question of what happened during cosmological electroweak symmetry breaking. A compelling paradigm known as electroweak baryogenesis suggests the possibility the Universe boiled during electroweak symmetry breaking and as a result we were saved from complete annihilation. Speciﬁcally, strange interactions with bubbles in the early Universecreatedatinyimbalancebetweenparticlesandanti-particlesthat explains stars, planets and physicists. This wild environment of physics that is far from equilibriumisquiteachallengetounderstand.Therefore,thisbookaimstocovera pedagogical gap by giving a step-by-step explanation of the concepts involved at a graduate level. viii