Abstract
The Universal One-Loop Effective Action (UOLEA) is a general expression for the effective action obtained by evaluating in a model-independent way the one-loop expansion of a functional path integral. It can be used to match UV theories to their low-energy EFTs more efficiently by avoiding redundant steps in the application of functional methods, simplifying the process of obtaining Wilson coefficients of operators up to dimension six. In addition to loops involving only heavy fields, matching may require the inclusion of loops containing both heavy and light particles. Here we use the recently-developed covariant diagram technique to extend the UOLEA to include heavy-light terms which retain the same universal structure as the previously-derived heavy-only terms. As an example of its application, we integrate out a heavy singlet scalar with a linear coupling to a light doublet Higgs. The extension presented here is a first step towards completing the UOLEA to incorporate all possible structures encountered in a covariant derivative expansion of the one-loop path integral.
Highlights
Heavy-only Universal One-Loop Effective Action (UOLEA)Consider a UV Lagrangian involving a multiplet of heavy fields Φ coupled to light fields φ, which for bosons may be arranged into the form
Techniques exist for doing so up to one-loop level [18,19,20,21,22,23,24,25,26,27,28,29].2 In practice, functional methods have typically been overlooked in favour of the more traditional Feynman diagram approach, where many tools have been developed to ease otherwise complicated calculations
Feynman diagram matching remains cumbersome for systematic derivations of a full set of Wilson coefficients, while recent developments in functional methods, which we summarise below, have led to a more straightforward way of dealing with the one-loop path integral
Summary
Consider a UV Lagrangian involving a multiplet of heavy fields Φ coupled to light fields φ, which for bosons may be arranged into the form. Regardless of the method used to evaluate the logarithm expansion, it can be done once-and-for-all, and the result is the same and universal in the sense that the final expression is independent of the details of the UV Lagrangian, which remain encapsulated in the UH matrix of light fields, covariant derivative Pμ, and mass matrix M. This heavy-only universal one-loop effective action (UOLEA) can be written as [24]. The result can be brought into a non-redundant EFT basis if desired
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