Covariant diagrams for one-loop matching

  • Zhengkang ZhangEmail author
Open Access
Regular Article - Theoretical Physics


We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed “covariant diagrams.” The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.


Effective Field Theories Gauge Symmetry Beyond Standard Model 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Michigan Center for Theoretical Physics (MCTP)University of MichiganAnn ArborU.S.A.
  2. 2.Deutsches Elektronen-Synchrotron (DESY)HamburgGermany

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