Ian J.R. Aitchison is Emeritus Professor of Physics at the University of Oxford. He has previously held research positions at Brookhaven National Laboratory, Saclay, and the University of Cambridge. He was a visiting professor at the University of Rochester and the University of Washington, and a scientific associate at CERN and SLAC. Dr. Aitchison has published over 90 scientific papers mainly on hadronic physics and quantum field theory. He is the author of two books and joint editor of further two.Anthony J.G. Hey is now Honorary Senior Data Scientist at the UK’s National Laboratory at Harwell. He began his career with a doctorate in particle physics from the University of Oxford. After a career in particle physics that included a professorship at the University of Southampton and research positions at Caltech, MIT and CERN, he moved to Computer Science and founded a parallel computing research group. The group were one of the pioneers of distributed memory message-passing computers and helped establish the ‘MPI’ message passing standard. After leaving Southampton in 2001 he was director of the UK’s ‘eScience’ initiative before becoming a Vice-President in Microsoft Research. He returned to the UK in 2015 as Chief Data Scientist at the U.K.’s Rutherford Appleton Laboratory. He then founded a new ‘Scientific Machine Learning’ group to apply AI technologies to the ‘Big Scientific Data’ generated by the Diamond Synchrotron, the ISIS neutron source, and the Central Laser Facility that are located on the Harwell campus. He is the author of over 100 scientific papers on physics and computing and editor of ‘The Feynman Lectures on Computation’.

Praise for the 5th edition"Aitchison and Hey was the ‘bible’ for me as a young post-doc in the 1980s … The book has been revised regularly as the field progressed and I am delighted to see a new edition which brings it up to date to the discovery of a Higgs-like boson at the LHC in July 2012. … Its strength has always been the combination of the theory with discussion of experimental results. The new edition continues this tradition by including … discussion of the related important observations of the last ten years—CP violation and oscillations in the B sector and the now rich phenomenology of neutrino oscillations. This will become a new classic."—Amanda Cooper-Sarkar, Oxford University, UK"This is an indispensable textbook for all particle physicists, experimentalists and theorists alike, providing an accessible exposé of the Standard Model, covering the mathematics used to describe it and some of the most important experimental results which vindicate it. … Volume 2 has been updated with extended discussions on quark and neutrino mixing and inclusion of results on CP violation and neutrino oscillations … these textbooks will remain on the top of a high energy physicist’s reading list for years to come."—Matthew Wing, University College London, UK"The editions of the book have developed as the experimental evidence has developed. The 5th edition adds 10 years of progress to the 4th edition.This means that, as well as some updates on neutrino oscillation results and CP violation an extra chapter has been added on Further Developments. This means the progress at the LHC, because in 10 years we have not just seen a Higgs boson we have checked out the relative rates of its production modes and decay channels to an accuracy which establishes the Standard Model Higgs very securely. The book covers the Higgs to third generation quark and lepton couplings and the Higgs to muon coupling limit and explains why the Higgs triple coupling should be measured in the high luminosity phase of the LHC. Evidence for physics beyond the Standard Model is most obviously sought in the Higgs and top sectors and the section on the top is expanded to cover this. The recent expansion of theoretical calculations to NNLO in QCD is covered, such that one can begin to see convergence of the theory in most processes.Most valuably it is explained why the non-observation of beyond Standard Model (BSM) physics at the few TeV scale presents us with a problem of naturalness, or fine-tuning of parameters. Two of the most promising avenues for exploration of BSM physics, supersymmetry and technicolour are explained and because of the multiplicity of choices within these theories the more general framework of Standard Model Effective Theory (SMEFT) is presented. Just as Fermi theory of the weak interaction was a low energy approximation to the full electroweak theory, so the Standard Model can be a low energy approximation to the full theory and thus we can add suitable operators to our Lagrangian to describe this. The net effect would be to modify couplings and to introduce new vertices. Even here there is much choice, but the advantage is that it provides a common picture for understanding many different phenomena. This is an area where much progress is being made at the moment. In current data there is no evidence for non-zero additional operators, but useful limits are being set and we can gauge the significance of anomalous results. This chapter thus brings the book up to date which the current state of the art."- Amanda Cooper-Sarkar, Emeritus Professor of Particle Physics, University of Oxford, November 2024"This has long been known as the best book for students, be they experimentalists or budding theorists, to get to grips as fast as possible with the gauge theories that describe our world. Now, with the final piece in the Standard Model jigsaw - the Higgs boson - in place, this new updated fifth edition is a timely one, with a detailed discussion of what we have learnt about the physics of both the Higgs boson and the top quark, as well as a view as to what might lie beyond. The book is rounded off with a welcome introduction to the modern view of gauge field theories as effective field theories, which will leave readers well set for the future of particle physics, whatever it may hold."- Ben Gripaios, Professor of Theoretical Physics, University of Cambridge, November 2024"What you get for your money with Aitchison and Hey is the detailed and complete pedagogy of the physics of the Standard Model of sub-nuclear physics explained incomparably well by two expert researchers. Neither of them tolerates anything less than completely clear exposition as they see, understand and explain their physics with the involvement of the committed reader very much in mind. In my experience, based on the evolution of now five editions of Aitchison and Hey throughout my own working life (and with the advantage of 'Oxonian aficionadism' a very long time ago!), what they continue to be are two stand-alone volumes offering the scriptures as well as the mathematics that always has and always will explain my puzzles as I continue to pursue experiments concerned with the sub-nuclear unknown. For I cannot contemplate further pursuit of my passion in life without my two volumes of an up to date Aitchison and Hey, and with my copies of the 40th anniversary edition I am very pleased to be able to say that I won’t have to!"- John Dainton, Formerly Sir James Chadwick Chair of Physics, University of Liverpool, June 2025

• Chapter 1: The particles and forces of the Standard Model. Chapter 2: Electromagnetism as a Gauge Theory. Chapter 3: Relativistic Quantum Mechanics. Chapter 4: Lorentz Transformations and Discrete Symmetries. Chapter 5: Quantum Field Theory I: the Free Scalar Field. Chapter 6: Quantum Field Theory II: Interacting Scalar Fields. Chapter 7: Quantum Field Theory III. Chapter 8: Elementary processes. Chapter 9: Deep inelastic electron-nucleon scattering. Chapter 10: Loops and Renormalization I: the ABC Theory. Chapter 11: Loops and Renormalization II: QED. Appendix A: Non-relativistic Quantum Mechanics. Appendix B: Natural Units. Appendix C: Maxwell's Equations: Choice of Units. Appendix D: Special Relativity: Invariance and Covariance. Appendix E: Dirac δ-Function. Appendix F: Contour Integration. Appendix G: Green Functions. Appendix H: Elements of Non-relativistic Scattering Theory. Appendix I: The particles and forces of the Standard Model Schrodinger and Heisenberg Pictures. Appendix J: Dirac Algebra and Trace Identities. Appendix K: Example of a Cross Section Calculation. Appendix L: Feynman Rules for Tree Graphs in QED. References.

Ian J.R. Aitchison is Emeritus Professor of Physics at the University of Oxford. He has previously held research positions at Brookhaven National Laboratory, Saclay, and the University of Cambridge. He was a visiting professor at the University of Rochester and the University of Washington, and a scientific associate at CERN and SLAC. Dr. Aitchison has published over 90 scientific papers mainly on hadronic physics and quantum field theory. He is the author of two books and joint editor of further two.Anthony J.G. Hey is now Honorary Senior Data Scientist at the UK’s National Laboratory at Harwell. He began his career with a doctorate in particle physics from the University of Oxford. After a career in particle physics that included a professorship at the University of Southampton and research positions at Caltech, MIT and CERN, he moved to Computer Science and founded a parallel computing research group. The group were one of the pioneers of distributed memory message-passing computers and helped establish the ‘MPI’ message passing standard. After leaving Southampton in 2001 he was director of the UK’s ‘eScience’ initiative before becoming a Vice-President in Microsoft Research. He returned to the UK in 2015 as Chief Data Scientist at the U.K.’s Rutherford Appleton Laboratory. He then founded a new ‘Scientific Machine Learning’ group to apply AI technologies to the ‘Big Scientific Data’ generated by the Diamond Synchrotron, the ISIS neutron source, and the Central Laser Facility that are located on the Harwell campus. He is the author of over 100 scientific papers on physics and computing and editor of ‘The Feynman Lectures on Computation’.

Praise for the 5th edition"Aitchison and Hey was the ‘bible’ for me as a young post-doc in the 1980s … The book has been revised regularly as the field progressed and I am delighted to see a new edition which brings it up to date to the discovery of a Higgs-like boson at the LHC in July 2012. … Its strength has always been the combination of the theory with discussion of experimental results. The new edition continues this tradition by including … discussion of the related important observations of the last ten years—CP violation and oscillations in the B sector and the now rich phenomenology of neutrino oscillations. This will become a new classic."—Amanda Cooper-Sarkar, Oxford University, UK"This is an indispensable textbook for all particle physicists, experimentalists and theorists alike, providing an accessible exposé of the Standard Model, covering the mathematics used to describe it and some of the most important experimental results which vindicate it. … Volume 2 has been updated with extended discussions on quark and neutrino mixing and inclusion of results on CP violation and neutrino oscillations … these textbooks will remain on the top of a high energy physicist’s reading list for years to come."—Matthew Wing, University College London, UK"The editions of the book have developed as the experimental evidence has developed. The 5th edition adds 10 years of progress to the 4th edition.This means that, as well as some updates on neutrino oscillation results and CP violation an extra chapter has been added on Further Developments. This means the progress at the LHC, because in 10 years we have not just seen a Higgs boson we have checked out the relative rates of its production modes and decay channels to an accuracy which establishes the Standard Model Higgs very securely. The book covers the Higgs to third generation quark and lepton couplings and the Higgs to muon coupling limit and explains why the Higgs triple coupling should be measured in the high luminosity phase of the LHC. Evidence for physics beyond the Standard Model is most obviously sought in the Higgs and top sectors and the section on the top is expanded to cover this. The recent expansion of theoretical calculations to NNLO in QCD is covered, such that one can begin to see convergence of the theory in most processes.Most valuably it is explained why the non-observation of beyond Standard Model (BSM) physics at the few TeV scale presents us with a problem of naturalness, or fine-tuning of parameters. Two of the most promising avenues for exploration of BSM physics, supersymmetry and technicolour are explained and because of the multiplicity of choices within these theories the more general framework of Standard Model Effective Theory (SMEFT) is presented. Just as Fermi theory of the weak interaction was a low energy approximation to the full electroweak theory, so the Standard Model can be a low energy approximation to the full theory and thus we can add suitable operators to our Lagrangian to describe this. The net effect would be to modify couplings and to introduce new vertices. Even here there is much choice, but the advantage is that it provides a common picture for understanding many different phenomena. This is an area where much progress is being made at the moment. In current data there is no evidence for non-zero additional operators, but useful limits are being set and we can gauge the significance of anomalous results. This chapter thus brings the book up to date which the current state of the art."- Amanda Cooper-Sarkar, Emeritus Professor of Particle Physics, University of Oxford, November 2024"This has long been known as the best book for students, be they experimentalists or budding theorists, to get to grips as fast as possible with the gauge theories that describe our world. Now, with the final piece in the Standard Model jigsaw - the Higgs boson - in place, this new updated fifth edition is a timely one, with a detailed discussion of what we have learnt about the physics of both the Higgs boson and the top quark, as well as a view as to what might lie beyond. The book is rounded off with a welcome introduction to the modern view of gauge field theories as effective field theories, which will leave readers well set for the future of particle physics, whatever it may hold."- Ben Gripaios, Professor of Theoretical Physics, University of Cambridge, November 2024"What you get for your money with Aitchison and Hey is the detailed and complete pedagogy of the physics of the Standard Model of sub-nuclear physics explained incomparably well by two expert researchers. Neither of them tolerates anything less than completely clear exposition as they see, understand and explain their physics with the involvement of the committed reader very much in mind. In my experience, based on the evolution of now five editions of Aitchison and Hey throughout my own working life (and with the advantage of 'Oxonian aficionadism' a very long time ago!), what they continue to be are two stand-alone volumes offering the scriptures as well as the mathematics that always has and always will explain my puzzles as I continue to pursue experiments concerned with the sub-nuclear unknown. For I cannot contemplate further pursuit of my passion in life without my two volumes of an up to date Aitchison and Hey, and with my copies of the 40th anniversary edition I am very pleased to be able to say that I won’t have to!"- John Dainton, Formerly Sir James Chadwick Chair of Physics, University of Liverpool, June 2025

• Chapter 1: The particles and forces of the Standard Model. Chapter 2: Electromagnetism as a Gauge Theory. Chapter 3: Relativistic Quantum Mechanics. Chapter 4: Lorentz Transformations and Discrete Symmetries. Chapter 5: Quantum Field Theory I: the Free Scalar Field. Chapter 6: Quantum Field Theory II: Interacting Scalar Fields. Chapter 7: Quantum Field Theory III. Chapter 8: Elementary processes. Chapter 9: Deep inelastic electron-nucleon scattering. Chapter 10: Loops and Renormalization I: the ABC Theory. Chapter 11: Loops and Renormalization II: QED. Appendix A: Non-relativistic Quantum Mechanics. Appendix B: Natural Units. Appendix C: Maxwell's Equations: Choice of Units. Appendix D: Special Relativity: Invariance and Covariance. Appendix E: Dirac δ-Function. Appendix F: Contour Integration. Appendix G: Green Functions. Appendix H: Elements of Non-relativistic Scattering Theory. Appendix I: The particles and forces of the Standard Model Schrodinger and Heisenberg Pictures. Appendix J: Dirac Algebra and Trace Identities. Appendix K: Example of a Cross Section Calculation. Appendix L: Feynman Rules for Tree Graphs in QED. References.

Ian J.R. Aitchison is Emeritus Professor of Physics at the University of Oxford. He has previously held research positions at Brookhaven National Laboratory, Saclay, and the University of Cambridge. He was a visiting professor at the University of Rochester and the University of Washington, and a scientific associate at CERN and SLAC. Dr. Aitchison has published over 90 scientific papers mainly on hadronic physics and quantum field theory. He is the author of two books and joint editor of further two.Anthony J.G. Hey is now Honorary Senior Data Scientist at the UK’s National Laboratory at Harwell. He began his career with a doctorate in particle physics from the University of Oxford. After a career in particle physics that included a professorship at the University of Southampton and research positions at Caltech, MIT and CERN, he moved to Computer Science and founded a parallel computing research group. The group were one of the pioneers of distributed memory message-passing computers and helped establish the ‘MPI’ message passing standard. After leaving Southampton in 2001 he was director of the UK’s ‘eScience’ initiative before becoming a Vice-President in Microsoft Research. He returned to the UK in 2015 as Chief Data Scientist at the U.K.’s Rutherford Appleton Laboratory. He then founded a new ‘Scientific Machine Learning’ group to apply AI technologies to the ‘Big Scientific Data’ generated by the Diamond Synchrotron, the ISIS neutron source, and the Central Laser Facility that are located on the Harwell campus. He is the author of over 100 scientific papers on physics and computing and editor of ‘The Feynman Lectures on Computation’.

Praise for the 5th edition"Aitchison and Hey was the ‘bible’ for me as a young post-doc in the 1980s … The book has been revised regularly as the field progressed and I am delighted to see a new edition which brings it up to date to the discovery of a Higgs-like boson at the LHC in July 2012. … Its strength has always been the combination of the theory with discussion of experimental results. The new edition continues this tradition by including … discussion of the related important observations of the last ten years—CP violation and oscillations in the B sector and the now rich phenomenology of neutrino oscillations. This will become a new classic."—Amanda Cooper-Sarkar, Oxford University, UK"This is an indispensable textbook for all particle physicists, experimentalists and theorists alike, providing an accessible exposé of the Standard Model, covering the mathematics used to describe it and some of the most important experimental results which vindicate it. … Volume 2 has been updated with extended discussions on quark and neutrino mixing and inclusion of results on CP violation and neutrino oscillations … these textbooks will remain on the top of a high energy physicist’s reading list for years to come."—Matthew Wing, University College London, UK"The editions of the book have developed as the experimental evidence has developed. The 5th edition adds 10 years of progress to the 4th edition.This means that, as well as some updates on neutrino oscillation results and CP violation an extra chapter has been added on Further Developments. This means the progress at the LHC, because in 10 years we have not just seen a Higgs boson we have checked out the relative rates of its production modes and decay channels to an accuracy which establishes the Standard Model Higgs very securely. The book covers the Higgs to third generation quark and lepton couplings and the Higgs to muon coupling limit and explains why the Higgs triple coupling should be measured in the high luminosity phase of the LHC. Evidence for physics beyond the Standard Model is most obviously sought in the Higgs and top sectors and the section on the top is expanded to cover this. The recent expansion of theoretical calculations to NNLO in QCD is covered, such that one can begin to see convergence of the theory in most processes.Most valuably it is explained why the non-observation of beyond Standard Model (BSM) physics at the few TeV scale presents us with a problem of naturalness, or fine-tuning of parameters. Two of the most promising avenues for exploration of BSM physics, supersymmetry and technicolour are explained and because of the multiplicity of choices within these theories the more general framework of Standard Model Effective Theory (SMEFT) is presented. Just as Fermi theory of the weak interaction was a low energy approximation to the full electroweak theory, so the Standard Model can be a low energy approximation to the full theory and thus we can add suitable operators to our Lagrangian to describe this. The net effect would be to modify couplings and to introduce new vertices. Even here there is much choice, but the advantage is that it provides a common picture for understanding many different phenomena. This is an area where much progress is being made at the moment. In current data there is no evidence for non-zero additional operators, but useful limits are being set and we can gauge the significance of anomalous results. This chapter thus brings the book up to date which the current state of the art."- Amanda Cooper-Sarkar, Emeritus Professor of Particle Physics, University of Oxford, November 2024"This has long been known as the best book for students, be they experimentalists or budding theorists, to get to grips as fast as possible with the gauge theories that describe our world. Now, with the final piece in the Standard Model jigsaw - the Higgs boson - in place, this new updated fifth edition is a timely one, with a detailed discussion of what we have learnt about the physics of both the Higgs boson and the top quark, as well as a view as to what might lie beyond. The book is rounded off with a welcome introduction to the modern view of gauge field theories as effective field theories, which will leave readers well set for the future of particle physics, whatever it may hold."- Ben Gripaios, Professor of Theoretical Physics, University of Cambridge, November 2024"What you get for your money with Aitchison and Hey is the detailed and complete pedagogy of the physics of the Standard Model of sub-nuclear physics explained incomparably well by two expert researchers. Neither of them tolerates anything less than completely clear exposition as they see, understand and explain their physics with the involvement of the committed reader very much in mind. In my experience, based on the evolution of now five editions of Aitchison and Hey throughout my own working life (and with the advantage of 'Oxonian aficionadism' a very long time ago!), what they continue to be are two stand-alone volumes offering the scriptures as well as the mathematics that always has and always will explain my puzzles as I continue to pursue experiments concerned with the sub-nuclear unknown. For I cannot contemplate further pursuit of my passion in life without my two volumes of an up to date Aitchison and Hey, and with my copies of the 40th anniversary edition I am very pleased to be able to say that I won’t have to!"- John Dainton, Formerly Sir James Chadwick Chair of Physics, University of Liverpool, June 2025

• Chapter 1: The particles and forces of the Standard Model. Chapter 2: Electromagnetism as a Gauge Theory. Chapter 3: Relativistic Quantum Mechanics. Chapter 4: Lorentz Transformations and Discrete Symmetries. Chapter 5: Quantum Field Theory I: the Free Scalar Field. Chapter 6: Quantum Field Theory II: Interacting Scalar Fields. Chapter 7: Quantum Field Theory III. Chapter 8: Elementary processes. Chapter 9: Deep inelastic electron-nucleon scattering. Chapter 10: Loops and Renormalization I: the ABC Theory. Chapter 11: Loops and Renormalization II: QED. Appendix A: Non-relativistic Quantum Mechanics. Appendix B: Natural Units. Appendix C: Maxwell's Equations: Choice of Units. Appendix D: Special Relativity: Invariance and Covariance. Appendix E: Dirac δ-Function. Appendix F: Contour Integration. Appendix G: Green Functions. Appendix H: Elements of Non-relativistic Scattering Theory. Appendix I: The particles and forces of the Standard Model Schrodinger and Heisenberg Pictures. Appendix J: Dirac Algebra and Trace Identities. Appendix K: Example of a Cross Section Calculation. Appendix L: Feynman Rules for Tree Graphs in QED. References.