Notes on the Soft-Collinear Effective Theory
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چکیده
Contents 1 Introduction to SCET 4 1. 1 Introduction to SCET These notes provide reading material on the Soft-Collinear Effective Theory (SCET) for Chrisitian's SCET Lectures in TASI 2013. They also served as lecture notes for Iain's 2013 EFT course taught at MIT. The notes assume some familiarity with various basic effective field theory (EFT) concepts, including power counting with operator dimensions, the use of field redefinitions, and top-down effective theories. Also the use of dimensional regularization for scale separation, the equivalences and differences with Wilso-nian effective field theory, and the steps required to carry out matching computations for Wilson coefficients. A basic familiarity with heavy quark effective theory (HQET), the theory of static sources, will likely be helpful. If on reading these notes you feel that your knowledge on any of these topics seems lacking you can consult the lecture notes for the first part of the MIT EFT course or the following EFT reviews: A basic familiarity with QCD as a gauge theory will also be assumed. Given that SCET is a top-down EFT, we can derive it directly from expanding QCD and integrating out offshell degrees of freedom. This includes concepts like the fact that energetic quarks and gluons form jets, renormalization and renormal-ization group evolution for nonabelian gauge theory, and color algebra. Also some basic familiarity with the role of infrared divergences is assumed, namely how they cancel between virtual and real emission diagrams, and how they otherwise signal the presence of nonperturbative physics as they do for parton distribution functions. It should be remarked that later parts of the notes are still a work in progress, and this file will be updated as more parts become available. Please let us know if you spot typos. Finally, let us give a list of references that we used in preparing these notes: Note that this is NOT a complete list of SCET references by any means. We will include a complete bibliography later. (1) hep-ph/0005275 Degrees of Freedom (2) hep-ph/0011336 Degrees of Freedom, Lagrangian, collinear Wilson lines (3) hep-ph/0107001 hard-collinear factorization (4) hep-ph/0109045 gauge invariance, soft-collinear (5) hep-ph/0205289 power counting (6) hep-ph/0204229 Reparametrization invariance (7) hep-ph/0303156 Gauge invariance, subleading Lagrangians (8) hep-ph/0202088 Hard scattering (9) hep-ph/0107002 B → Dπ (10) hep-ph/0605001 0-bin (11) hep-ph/0211069 Matching from SCET I to SCET II The Soft-Collinear Effective Theory is an effective theory describing the interactions of soft and collinear degrees …
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