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

Abstract

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.

Authors:
 [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:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Japan Society for the Promotion of Science (JSPS); Ministry of Education, Culture, Sports, Science and Technology (MEXT) (Japan)
OSTI Identifier:
1435097
Grant/Contract Number:  
AC02-05CH11231; FG02-92ER40704; SC0009999; PHY-1316783; 26400241; 15H05887
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Volume: 2018; Journal Issue: 1; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; effective field theories; gauge symmetry; renormalization group

Citation Formats

Henning, Brian, Lu, Xiaochuan, and Murayama, Hitoshi. One-loop matching and running with covariant derivative expansion. United States: N. p., 2018. Web. doi:10.1007/JHEP01(2018)123.
Henning, Brian, Lu, Xiaochuan, & Murayama, Hitoshi. One-loop matching and running with covariant derivative expansion. United States. https://doi.org/10.1007/JHEP01(2018)123
Henning, Brian, Lu, Xiaochuan, and Murayama, Hitoshi. 2018. "One-loop matching and running with covariant derivative expansion". United States. https://doi.org/10.1007/JHEP01(2018)123. https://www.osti.gov/servlets/purl/1435097.
@article{osti_1435097,
title = {One-loop matching and running with covariant derivative expansion},
author = {Henning, Brian and Lu, Xiaochuan and Murayama, Hitoshi},
abstractNote = {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.},
doi = {10.1007/JHEP01(2018)123},
url = {https://www.osti.gov/biblio/1435097}, journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 1,
volume = 2018,
place = {United States},
year = {Wed Jan 24 00:00:00 EST 2018},
month = {Wed Jan 24 00:00:00 EST 2018}
}

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Works referenced in this record:

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preprint, January 2015


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The Universal One-Loop Effective Action
text, January 2015


One-loop effective lagrangians after matching
text, January 2016


Low energy behaviour of standard model extensions
preprint, January 2016


Mixed Heavy-Light Matching in the Universal One-Loop Effective Action
text, January 2016


Integrating out heavy particles with functional methods: a simplified framework
text, January 2016


Extending the Universal One-Loop Effective Action: Heavy-Light Coefficients
text, January 2017


Works referencing / citing this record:

Field redefinitions in effective theories at higher orders
journal, March 2019


HEPfit: a Code for the Combination of Indirect and Direct Constraints on High Energy Physics Models
text, January 2020


HEPfit: a code for the combination of indirect and direct constraints on high energy physics models
journal, May 2020


Completing the scalar and fermionic universal one-loop effective action
text, January 2020


Complete One-Loop Matching for a Singlet Scalar in the Standard Model EFT
text, January 2018


Field redefinitions in effective theories at higher orders
text, January 2018