Abstract
Recently, a general result for evaluating the path integral at one loop was obtained in the form of the Universal One-Loop Effective Action. It may be used to derive effective field theory operators of dimensions up to six, by evaluating the traces of matrices in this expression, with the mass-dependence encapsulated in the universal coefficients. Here we show that it can account for loops of mixed heavy-light particles in the matching procedure. Our prescription for computing these mixed contributions to the Wilson coefficients is conceptually simple. Moreover it has the advantage of maintaining the universal structure of the effective action, which we illustrate using the example of integrating out a heavy electroweak triplet scalar coupling to a light Higgs doublet. Finally we also identify new structures that were previously neglected in the universal results.
Highlights
Matching from an ultraviolet (UV) theory to a low-energy effective field theory (EFT) can be performed using either Feynman diagrams or functional methods
This Universal One-Loop Effective Action (UOLEA) is a general expression that may be applied in any context where a one-loop path integral needs to be computed, as for example in matching new physics models to the Standard Model (SM) EFT.1
We have demonstrated a conceptually simple and transparent method for including mixed heavy–light contributions to integrating out heavy particles using the Universal One-Loop Effective Action (UOLEA)
Summary
Matching from an ultraviolet (UV) theory to a low-energy effective field theory (EFT) can be performed using either Feynman diagrams or functional methods. Compared to previous functional methods [18,19,20], our prescription for treating mixed heavy–light contributions is relatively simple and transparent: in addition to the usual expansion of the heavy fields around their classical solution, we separate the light fields into classical and quantum parts, and extend the quadratic term to include quantum fluctuations of the light fields This essentially amounts to computing the 1PI effective action for the full theory, from which the Wilsonian effective Lagrangian, namely the low-energy EFT, can be extracted. Ellis et al / Physics Letters B 762 (2016) 166–176 after evaluating the matrix traces In this extended case, the universal coefficients contain parts that are in the full 1PI effective action but not in the EFT, diagrammatically corresponding to tree-generated operator insertions in EFT loops.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
