Relativistic Quantum Field Theory, Volume 3: Applications of Quantum Field Theory

166 Pages·2019·16.876 MB·English

by  Michael Strickland

Relativistic Quantum Field Theory,
Volume 3
Applications of quantum field theory

Relativistic Quantum Field Theory,
Volume 3
Applications of quantum field theory
Michael Strickland
Kent State University, Kent, Ohio, USA
Morgan & Claypool Publishers
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ISBN 978-1-64327-762-2(ebook)
ISBN 978-1-64327-759-2(print)
ISBN 978-1-64327-760-8(mobi)
DOI 10.1088/2053-2571/ab3a99
Version:20191101
IOPConcisePhysics
ISSN2053-2571(online)
ISSN2054-7307(print)
AMorgan&ClaypoolpublicationaspartofIOPConcisePhysics
PublishedbyMorgan&ClaypoolPublishers,1210FifthAvenue,Suite250,SanRafael,CA,
94901,USA
IOPPublishing,TempleCircus,TempleWay,BristolBS16HG,UK
This book is dedicated to my wife, Dr Veronica Antocheviz Dexheimer Strickland,
and our amazing daughter Emily.

Contents
Preface xi
Acknowledgements xiv
Author biography xv
Units and conventions xvi
1 QCD phenomenology 1-1
1.1 Electron–muon scattering 1-1
1.2 Form factors 1-4
1.3 Elastic electron–proton scattering and the proton form factors 1-6
1.4 Inelastic electron–proton scattering 1-11
1.5 The parton model and Bjorken scaling 1-14
1.6 Valence partons and sea partons 1-17
1.7 Beyond the naive parton model 1-21
1.7.1 Gluon emission cross section 1-22
1.7.2 Small-angle approximation 1-23
1.7.3 Embedding γ∗-parton scattering in DIS 1-24
1.8 DGLAP evolution 1-26
1.9 Hadron production in e+e− collisions 1-32
1.10 Fragmentation functions 1-35
1.11 Solution of the DGLAP equations using Mellin moments 1-37
1.12 Drell–Yan scattering 1-39
References 1-41
2 Weak interactions 2-1
2.1 Early models of the weak interaction 2-2
2.2 Muon decay 2-3
2.3 Charged pion decay 2-7
2.4 Electron–neutrino and electron–antineutrino scattering 2-9
2.5 Neutrino–quark scattering 2-11
2.5.1 Charge raising current 2-11
2.5.2 Charge lowering current 2-11
2.5.3 Differential cross section 2-12
2.5.4 Embedding 2-12
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RelativisticQuantumFieldTheory,Volume3
2.6 Weak neutral currents 2-14
2.7 The Cabibbo angle and the CKM matrix 2-15
2.7.1 The Cabibbo–Kobayashi–Maskawa (CKM) matrix 2-16
References 2-17
3 Electroweak unification and the Higgs mechanism 3-1
3.1 Electroweak Feynman rules 3-5
3.2 Massive gauge fields with local gauge symmetry 3-6
3.2.1 Spontaneous symmetry breaking 3-7
3.2.2 Breaking of a continuous local symmetry 3-10
3.3 Gauge boson masses in SU(2) × U(1) 3-12
L Y
3.3.1 The resulting particle spectrum 3-12
3.3.2 Fermion masses 3-13
3.4 The discovery of the Higgs boson 3-14
3.4.1 The H → γγ decay channel 3-16
3.4.2 The H → ZZ → 4l decay channel 3-18
3.4.3 The H → τ+τ− decay channel 3-19
3.4.4 Other decay channels and the nature of the Higgs 3-19
References 3-20
4 Basics of finite temperature quantum field theory 4-1
4.1 Partition function for a quantum harmonic oscillator 4-1
4.1.1 The QHO canonical partition function in the energy basis 4-2
4.1.2 Computing the QHO partition function using the 4-3
path integral formalism
4.2 The partition function for a free scalar field theory 4-6
4.2.1 Fourier representation of the fields 4-7
4.2.2 Tricks for evaluating sum-integrals 4-9
4.3 Free scalar thermodynamics 4-11
4.3.1 Low temperature limit 4-15
4.3.2 High-temperature limit 4-15
4.4 The need for resummation 4-17
4.5 Perturbative expansion of thermodynamics for a scalar field theory 4-21
4.5.1 One loop 4-22
4.5.2 Two loops 4-22
4.5.3 Three loops 4-23
4.5.4 Pressure through g5 4-24
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RelativisticQuantumFieldTheory,Volume3
4.6 Screened perturbation theory 4-25
4.6.1 One-loop contribution 4-26
4.6.2 Two-loop contribution 4-27
4.6.3 Three-loop contribution 4-27
4.6.4 Pressure to three loops 4-28
4.6.5 Mass prescription 4-28
4.6.6 The tadpole mass prescription 4-29
4.6.7 Three-loop SPT Pressure 4-29
References 4-30
5 Hard-thermal-loops for QED and QCD 5-1
5.1 Photon polarization tensor 5-1
5.1.1 Generalization to d-dimensions 5-4
5.1.2 The HTL polarization tensor 5-5
5.1.3 Generalization to QCD 5-5
5.2 Fermionic self-energy 5-6
5.3 Collective modes 5-7
5.3.1 Gluon modes 5-8
5.3.2 Quark modes 5-9
5.3.3 Collective modes in an isotropic QGP 5-10
5.3.4 Gluon modes 5-10
5.3.5 Landau damping 5-12
5.3.6 Quark modes 5-13
5.4 Hard-thermal-loop effective action 5-15
5.4.1 Minkowski-space HTL gluon propagator 5-15
5.4.2 Minkowski-space HTL quark propagator 5-18
5.4.3 Three-gluon vertex 5-19
5.4.4 Four-gluon vertex 5-19
5.4.5 Quark-gluon three-vertex 5-20
5.4.6 Quark-gluon four-vertex 5-21
5.4.7 Hard thermal loop effective Lagrangian 5-21
5.4.8 Euclidean space HTL effective Lagrangian 5-22
and vertex functions
5.5 Hard-thermal-loop resummed thermodynamics 5-23
5.5.1 Contributions to the HTLpt thermodynamic 5-25
potential through NNLO
5.5.2 NNLO HTLpt thermodynamic potential 5-28
5.5.3 NNLO result for equal chemical potentials 5-28
ix