Effective Field Theories

The following sections are included:

• Dedication
• Preface
• Contents

The following sections are included:

• Wherefore EFT?
• EFT vs MFT
• An example from Newton
• A theorem of Weinberg
• Organization of the book

The following sections are included:

• Introduction
• Noether's Theorem
• Examples of Noether currents
• Gauged symmetries and Noether's procedure
• Broken symmetries and Goldstone's Theorem
  • Nonrelativistic NG-bosons
• The BEHGHK Mechanism of Anderson
  • A little history
  • An example
  • An interlude: superconductivity
• CCWZ construction of EFT
• Explicit breaking; spurion analysis
• Anomalous symmetries
  • Anomalies in the path integral
  • The chiral anomaly and its consequences
  • 't Hooft anomaly matching
• Notes for further reading
• Problems for Chapter 2

Now that we have reviewed the important topics from field theory related to symmetry management, we would like to start working out some Effective Field Theories. The best way to see how the subject works is to consider several examples, and point out the methods that can be used to solve problems. But before we dive into the field, we want to present a collection of results that apply for nearly all EFTs. In this chapter we will discuss these general, all-purpose results, most notably the concept of the Renormalization Group, the ideas that lead up to it, and its many consequences. It is primarily because of this result that “effective field theory” works at all…

The following sections are included:

• Introduction
• Real physics: Euler-Heisenberg Lagrangian
• Fermi Theory of Weak Interactions as an effective theory
• Fermi theory to one loop: ΔS = 2 processes in EFT
  • Setting up the EFT approach
  • A more detailed calculation
• QCD corrections in EFTs
  • Matching at one loop in QCD
  • Renormalization group improvement and EFTs
  • Complete basis. Penguin operators
• Chiral perturbation theory
  • Goldstone bosons and their properties
  • Sources in chiral perturbation theory
  • Applications: Gell-Mann-Okubo relation
  • Power counting. Chiral loops and higher orders in _χPT
  • Naive dimensional analysis
  • Baryons and chiral perturbation theory
• Notes for further reading
• Problems for Chapter 4

The following sections are included:

• Introduction
• Heavy quark effective theory
  • Quantum mechanics of heavy particles
  • From quantum mechanics to field theory: HQET. Field redefinitions
  • Spin symmetry and its consequences
  • More symmetry: reparameterization invariance
  • HQET Green's functions. Radiative corrections.
  • External currents and external states
• Different degrees of freedom: heavy mesons
  • Heavy meson states. Tensor formalism
  • Leading-order Lagrangian
  • Subleading Lagrangians
  • Calculations with HH_χPT
• Light baryons in heavy particle formalism
  • Leading-order Lagrangian
• Notes for further reading
• Problems for Chapter 5

The following sections are included:

• Introduction. Non-relativistic QED and QCD
• NRQCD Lagrangian at the scale m_Q
• Going down: non-perturbative scales m_Qv and m_Qv²
  • Electromagnetic decays of the η_c
  • Inclusive decays of the η_c into light hadrons
  • Inclusive decays of the χ_cJ into light hadrons
• Going down: perturbative scales m_Qv and m_Qv². pNRQCD
  • Example: heavy quarkonium potential
• Different degrees of freedom: hadronic molecules
• Notes for further reading
• Problems for Chapter 6

The following sections are included:

• Infrared divergences
• Soft-Collinear Effective Theory
  • Quantum mechanics of fast particles
  • SCET power counting
  • SCET action
• Symmetries of SCET
  • Gauge invariance
  • Reparametrization invariance
• Examples
  • B → X_sγ
  • B → Dπ
  • Deep Inelastic Scattering
  • Jet production
• Notes for further reading
• Problems for Chapter 7

The following sections are included:

• Introduction
• Standard model as the leading term in the EFT expansion
  • Dimension-5 operators: fermion number violation
  • Dimension-6 operators: parameterizing new physics
  • Experimental tests and observables
• BSM particles in EFT
  • Dark matter at colliders: effective operators
  • Mono-Higgs signatures of dark matter at LHC
• Notes for further reading
• Problems for Chapter 8

The following sections are included:

• Introduction
• Review of general relativity
  • Geodesics and affine connection
  • General relativity and the weak field limit
  • Gravity sources: energy-momentum tensor
• Building an effective field theory
  • Quantization. Feynman rules
  • Quantum EFT for gravity
  • Newtonian potential
  • Postscript
• Classical EFT: NRGR
  • Setting up the problem
  • Gravition modes
  • Feynman rules
  • Gravitational radiation
  • Renormalization
• Notes for further reading
• Problems for Chapter 9

In this book, we have delved deeply into the practical applications of effective field theory, studying problems varying from pion physics and superconductors to gravitational radiation. And yet, when we think of all the ways EFT can be used to solve real-world problems, it seems like we have hardly scratched the surface. The methods we have discussed in these pages are so far reaching that they can find application in almost any context. The true beauty of EFT is its ability to approach a problem in a model-independent way, properly identifying the relevant operators, and cordoning off any additional assumptions into coefficients that can be measured, calculated or in some way quantified. Intuitively, it is the most sensible way to approach a problem in physics; logically, it is the most robust…

The following sections are included:

• Appendix A: Review of Group Theory
• Appendix B: Short Review of QED and QCD
• Appendix C: Useful Features of Dimensional Regularization

The following sections are included:

• Bibliography
• Index