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Title: One-loop matching and running with covariant derivative expansion

We develop tools for performing effective field theory (EFT) calculations in a manifestly gauge-covariant fashion. We clarify how functional methods account for one-loop diagrams resulting from the exchange of both heavy and light fields, as some confusion has recently arisen in the literature. To efficiently evaluate functional traces containing these “mixed” one-loop terms, we develop a new covariant derivative expansion (CDE) technique that is capable of evaluating a much wider class of traces than previous methods. The technique is detailed in an appendix, so that it can be read independently from the rest of this work. We review the well-known matching procedure to one-loop order with functional methods. What we add to this story is showing how to isolate one-loop terms coming from diagrams involving only heavy propagators from diagrams with mixed heavy and light propagators. This is done using a non-local effective action, which physically connects to the notion of “integrating out” heavy fields. Lastly, we show how to use a CDE to do running analyses in EFTs, i.e. to obtain the anomalous dimension matrix. We demonstrate the methodologies by several explicit example calculations.
 [1] ; ORCiD logo [2] ;  [3]
  1. Yale Univ., New Haven, CT (United States). Dept. of Physics
  2. Univ. of California, Davis, CA (United States). Dept. of Physics
  3. Univ. of California, Berkeley, CA (United States). Dept. of Physics. Center for Japanese Studies; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Theoretical Physics Group; Univ. of Tokyo, Kashiwa (Japan). Kavli Inst. for the Physics and Mathematics of the Universe (WPI). Todai Inst. for Advanced Study
Publication Date:
Grant/Contract Number:
AC02-05CH11231; FG02-92ER40704; SC0009999; PHY-1316783; 26400241; 15H05887
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 1; Journal ID: ISSN 1029-8479
Springer Berlin
Research Org:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Yale Univ., New Haven, CT (United States); Univ. of California, Davis, CA (United States); Univ. of Tokyo, Kashiwa (Japan)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); National Science Foundation (NSF); Japan Society for the Promotion of Science (JSPS); Ministry of Education, Culture, Sports, Science and Technology (MEXT) (Japan)
Country of Publication:
United States
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; effective field theories; gauge symmetry; renormalization group
OSTI Identifier: