## Effective Field TheoriesThis book is a broad-based text intended to help the growing student body interested in constructing and applying methods of effective field theory to solve problems in their research. It begins with a review of using symmetries to identify the relevant degrees of freedom in a problem, and then presents a variety of methods that can be used to construct various effective theories. A detailed discussion of canonical applications of effective field theory techniques with increasing complexity is given, including Fermi's weak interaction, heavy-quark effective theory, and soft-collinear effective theory. Applications of these techniques to study physics beyond the standard model, dark matter, and quantum and classical gravity are explored. Although most examples come from questions in high-energy physics, many of the methods can also be applied in condensed-matter settings. Appendices include various factoids from group theory and other topics that are used throughout the text, in an attempt to make the book self-contained. |

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### Contents

1 Introduction | 1 |

2 Symmetries | 9 |

3 Elementary Techniques | 41 |

4 Effective Field Theories of Type I | 65 |

5 Effective Field Theories of Type II Part A | 107 |

6 Effective Field Theories of TypeII Part B | 145 |

7 Effective Field Theories of TypeIII Fast Particles in Effective Theories | 171 |

8 Standard Model as an Effective Field Theory | 203 |

9 Effective Field Theories of Gravity | 219 |

10 Outlook | 249 |

Appendix A Review of Group Theory | 253 |

Appendix B Short Review of QED and QCD | 269 |

Appendix C Useful Features of Dimensional Regularization | 279 |

291 | |

301 | |

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### Common terms and phrases

action amplitude anomalous dimension baryon bosons calculations chapter chiral perturbation theory collinear compute contributions correlation functions covariant derivative decay defined degrees of freedom described diagrams dimensional regularization discussed effective field theory effective Lagrangian effective theory example expansion factor fermion Feynman diagrams Feynman rules finite flavor full theory gluon graviton gravity Green’s functions hadronic heavy meson heavy quark Higgs HQET integral interactions Lagrangian Lagrangian of Eq leading order logarithms loop low energy massless matrix elements meson momenta momentum Noether current NRQCD operators parameter perturbation theory Peskin and Schroeder photon physics pion potential graviton power counting problem propagator quantum field theory quark mass quarkonium relevant renormalization representation result scalar field scale SCET Schroeder 1995 simply spin standard model tensor theorem transformation ultrasoft UV divergences vector vertex Wilson coefficients