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review1 - #HUTP-93/A003 1/93 Effective Field Theory Howard...

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#HUTP-93/A003 1/93 Effective Field Theory *†‡ Howard Georgi Lyman Laboratory of Physics Harvard University Cambridge, MA 02138 * Research supported in part by the National Science Foundation under Grant #PHY-8714654. Research supported in part by the Texas National Research Laboratory Commission, under Grant #RGFY9206. To appear in Annual Review of Nuclear and Particle Science, vol. 43 .
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Contents Prologue 3 1 Effective Field Theory 3 1.1 The principles of effective field theory . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Wilson versus continuum EFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Why continuum effective field theory? . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Roots 10 2.1 Chiral Lagrangians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Gauge model building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Renormalization logs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 Mass independent schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.5 Back to Appelquist-Carazone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.6 Witten, Gilman-Wise, and heavy quarks . . . . . . . . . . . . . . . . . . . . . . . . 19 3 “Integrating Out” versus “Matching” 19 3.1 Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2 The operator product expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4 Applications 28 4.1 Symmetries at low energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.2 Composite Higgs bosons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.3 Above the Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.4 Resumming large radiative corrections . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.5 Nonperturbative matching corrections . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Acknowledgements 43 References 43
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Prologue When I agreed to write this review article (in a moment of weakness) in 1991, I didn’t really realize how poorly suited I am to this kind of activity. As I gathered ideas and materials for the article over the next year, it dawned on me that I hadn’t even read a review article in 25 years. I’m not quite sure what they are good for. Obviously, I cannot summarize all the work that has gone on in the field in any detail. I could try to give a guide to the literature, but it is easy to summarize the proper approach to the old literature on this (or almost any) subject. Two words suffice. Ignore it! With rare exceptions, old papers are difficult to read because the issues have changed over the years. The model that I will use instead is my “textbook” on Weak Interactions, [1] which was originally intended as a thinly disguised monograph on effective field theory. There will be more words than formulas. I will concentrate on what I think are the critical ideas from which all the applications flow, illustrating the technical issues in just a few important and rather new examples. I will refer to many of the old papers on the subject in section 2, but usually in the hope that people will not actually go back and read them. I introduce the effective field theory idea in 1. Section 2 contains a brief review of some of the history of effective field theory. In section 3 I discuss the process of matching from on effective field theory to the next in some detail. Finally in section 4 I discuss a few applications of the effective field theory idea. These are illustrative, but not at all exhaustive. For example, I do not mention the beautiful example of heavy quark effective theory [2] at all because it is reviewed elsewhere in this volume. I end this section with a frankly speculative discussion of nonperturbative matching corrections.
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